Sustainable Shell Structures: A Bibliometric and Critical Review of Buckling Behavior and Material-Efficient Design Strategies

Abstract

Sustainable shell structures are thin, curved systems such as domes, vaults, and cylindrical shells that achieve strength and stability primarily through membrane action, allowing significant material savings. Their sustainability lies in minimizing embodied energy and CO₂ emissions by using less material, integrating recycled or bio-based components, and applying optimization strategies to extend service life and enable reuse or recycling, all while maintaining structural performance and architectural quality. This review critically examines the state-of-the-art in sustainable shell structures, focusing on their buckling behavior and material-efficient design strategies. Integrating bibliometric analysis with thematic synthesis, the study identifies key research trends, theoretical advancements, and optimization tools that support structural efficiency. Emphasis is placed on recent developments in composite and bio-based materials, imperfection-sensitive buckling models, and performance-based design approaches. Advanced computational methods, including finite element analysis, machine learning, and digital twins, are highlighted as critical in enhancing predictive accuracy and sustainability outcomes. The findings underscore the dual challenge of achieving both structural stability and environmental responsibility, while outlining research gaps and future directions toward resilient, low-impact shell construction.

1. Introduction

Shell structures represent a remarkable combination of engineering efficiency and architectural elegance, recognized for their ability to achieve strength and stability with minimal material use. Their fundamental design principle, which involves distributing loads primarily through membrane forces across a curved surface, allows for the creation of expansive structures with a minimal expenditure of material. This inherent material efficiency positions shell structures as “optimal structures,” demonstrating exceptional structural performance alongside significant architectural beauty [1]. This characteristic is not merely an engineering advantage; it establishes a foundational premise for their role in sustainable construction. The ability to achieve robust structural integrity with less material directly translates into reduced resource consumption, thereby aligning closely with environmental responsibility goals.

The contemporary construction industry faces pressing global sustainability challenges, notably its substantial contribution to total CO₂ emissions and its reliance on finite natural resources [2]. A fundamental shift towards sustainable structural design practices is therefore imperative to reduce these environmental impacts. This shift necessitates a comprehensive consideration of environmental, economic, and social factors throughout the lifecycle of a structure [2]. Shell structures, by virtue of their material-efficient design, can be meticulously engineered to minimize their environmental footprint. This includes optimizing material usage, integrating renewable energy systems, and designing for extended longevity and recyclability, all of which collectively reduce the overall environmental impact of built environments [3]. Their form naturally lends itself to reduced resource consumption, making them a prime candidate for environmentally conscious building practices.

Despite their inherent material efficiency, shell structures present a critical engineering challenge: their susceptibility to buckling. This phenomenon, characterized by a sudden loss of stability under compressive loads, remains a fundamental consideration in the design of thin-walled shell structures [4,5,6,7]. The pursuit of lightweight and slender structural elements, increasingly favored in modern applications to enhance material efficiency and reduce overall dead weight, paradoxically amplifies this vulnerability. This creates a basic challenge: the same features that make shells efficient in material use also make them more likely to become unstable

The consequences of buckling failures can be catastrophic, particularly when they occur at critical connection points or under eccentric loading conditions [8,9]. Such failures underscore the necessity for rigorous structural stability assessments in design. This inherent paradox—where the drive for material efficiency directly increases the challenge of maintaining buckling stability—establishes a central theme for this review. It highlights the critical need to simultaneously achieve both material efficiency and high buckling performance, ensuring that sustainable designs do not compromise structural integrity.

The global challenges of finite natural resources and escalating CO₂ emissions from the built environment demand a transformative shift in structural engineering practices [2]. This imperative extends beyond merely adopting “green” materials; it requires a comprehensive approach to sustainability that encompasses environmental, economic, and social dimensions. Material efficiency emerges as a fundamental strategy within this broader sustainability framework, focusing on optimizing material use, minimizing energy consumption, and reducing the carbon footprint throughout a structure’s lifecycle [10]. This approach aims to reduce the overall environmental impact of construction.

A transformative concept gaining traction is the circular economy (CE), which advocates for a fundamental departure from the traditional linear “take-make-use-dispose” model [11]. The CE approach promotes reduced resource input, extensive reuse, and comprehensive recycling of materials and components, ensuring they retain their highest useful purpose for as long as possible [11]. This multi-faceted understanding of sustainability positions material efficiency not as an isolated goal, but as a critical component within a broader, integrated objective.

Engineering applications of sustainable shell structures are diverse, spanning civil, industrial, and architectural domains. In civil engineering, they are employed in long-span roofs for stadiums, exhibition halls, and transportation hubs, where their curved geometry minimizes material use while providing unobstructed interior spaces. In industrial settings, storage tanks, silos, and pressure vessels rely on shell forms for efficient containment of liquids, gases, or granular materials, with optimized thickness and material selection reducing environmental impact. In infrastructure, pipeline shells and bridge arches use thin-walled designs to balance structural strength and cost efficiency. In the energy sector, shells are applied in wind turbine towers, solar concentrator dishes, and water tanks, where lightweight and durable configurations improve performance and sustainability. Additionally, their adaptability to recycled and bio-based materials supports integration into circular economy frameworks.

This review integrates a bibliometric analysis with a critical evaluation of the existing literature to investigate how advancements in understanding shell buckling can significantly contribute to environmentally responsible construction practices. The primary objectives are to: (1) identify prevailing research trends, key contributors, and thematic clusters within the field of sustainable shell structures over the past decade; (2) review advances in analytical, experimental, and numerical approaches to shell stability, including the evolution of classical theories and the critical role of imperfections, particularly for composite materials; (3) detail material-efficient design strategies, encompassing optimization tools and advanced modeling techniques; (4) examine the integration and performance of recycled and bio-based materials in shell structures; and (5) outline critical research gaps and propose future directions, with a particular emphasis on performance-based design.

2. Bibliometric Analysis of Sustainable Shell Structures Research

In order to investigate the evolution of research at the intersection of structural stability and sustainable design, this study integrates bibliometric techniques with a targeted thematic review. The analysis centers on the scholarly output related to shell structures and buckling phenomena, particularly in the context of optimization and sustainability. By combining quantitative mapping with qualitative interpretation, we aim to reveal the dominant trajectories and emerging approaches within this scientific domain.

The methodological framework was structured in two main stages. Initially, a comprehensive dataset was built by querying the Web of Science Core Collection using the search string: (shell OR buckling) AND (optimization OR sustainability). This expression was formulated to capture studies addressing either geometric or material instabilities and their relevance to efficient or ecologically conscious design strategies. To ensure contemporary relevance, the temporal filter was applied to include only works published between 2016 and 2025 (up to 3 August 2025).

To maintain transparency and reproducibility, we applied the PRISMA approach for record selection, guiding the inclusion and exclusion process. Figure 1 illustrates this sequence, beginning with the identification of initial records and continuing through screening, eligibility checks, and final selection. The resulting dataset forms the empirical foundation for subsequent bibliometric mapping and thematic synthesis, designed to surface both well-established directions and novel insights shaping sustainable structural optimization.

The initial query returned a total of 5319 records, encompassing a broad range of studies intersecting shell structures or buckling behavior with themes of optimization or sustainability. To ensure relevance and temporal consistency, we limited the dataset to publications from 2016 to 2025, which reduced the pool to 3322 entries. Further refinement was applied by restricting the language to English, yielding 3308 articles.

All Web of Science Core Collection indices were queried, namely Science Citation Index Expanded (SCI-EXPANDED), Conference Proceedings Citation Index—Science (CPCI-S), Emerging Sources Citation Index (ESCI), Social Sciences Citation Index (SSCI), Book Citation Index—Science (BKCI-S), Conference Proceedings Citation Index—Social Science & Humanities (CPCI-SSH), Arts & Humanities Citation Index (A&HCI), and Index Chemicus (IC).

A total of 43 articles were excluded:

• 14 articles were excluded, as only English articles were considered;
• 6 of the articles were excluded: retracted publications (n = 2), letters (n = 2), and editorial materials (n = 2). Only the following document types were considered: article, proceeding paper, early access, book chapter, review article, and correction;
• 23 documents were manually excluded because neither the title nor the abstract contained the searched terms.

After this step, the resulting dataset comprised 3279 records. This curated corpus provides the empirical basis for the analyses that follow, aiming to uncover conceptual clusters, methodological patterns, and emerging research directions across this multifaceted field.

The bibliometric analysis was conducted using VOSviewer (version 1.6.20), a widely adopted tool for constructing and visualizing bibliographic networks. This software enabled the extraction of co-occurrence relationships, bibliographic coupling structures, and interconnected keyword clusters, offering a detailed view of the intellectual and thematic landscape of the field. These mappings allowed us to identify not only the dominant research trajectories and influential contributions but also the collaborative patterns and disciplinary intersections that shape this area of inquiry.

In parallel, a qualitative thematic review was carried out to enrich the quantitative insights with interpretative depth. This dual strategy helped pinpoint recurring lines of investigation, highlight emerging subfields, and identify gaps where further research could prove valuable. The visual outputs—ranging from thematic clusters to temporal overlays—illustrate the shifting contours of the field, from early conceptualizations of shell optimization to recent efforts integrating sustainability concerns into structural design.

Taken together, this combined approach yields a multifaceted understanding of how studies on shell structures and buckling, viewed through the lenses of optimization and sustainability, have matured and diversified over the past decade.

3. Buckling Behavior of Shell Structures

3.1. Classical Theories and Advancements for Composite Materials

The study of shell buckling has a rich history, with early investigations predominantly focusing on isotropic materials [4,12]. Classical theories, such as the Donnell-Mushtari-Vlasov (DMV) hypothesis, provided foundational insights into the stability of shells under various loading conditions [4,12]. These early theories were instrumental in establishing the basic principles of shell stability. However, with the advent of composite materials and the increasing demand for lightweight yet robust constructions, the limitations of classical theories, which presume homogeneous material properties, became apparent [4,13].

Composite materials, characterized by their anisotropy and heterogeneity, exhibit intricate buckling behavior that classical theories cannot accurately predict [4,14,15]. This necessity for more precise analytical tools led to significant advancements in shell theories. First-order shear deformation theories (FSDT) [16,17] were introduced to account for shear deformation across the thickness, incorporating a shear correction factor dependent on material properties, geometry, and loading [4]. Recognizing the deficiencies of FSDT, particularly in capturing nonlinear variations, higher-order shear deformation theories (HSDT) were subsequently formulated [18,19,20,21,22,23]. These theories integrate higher-order terms in the displacement field through Taylor series expansions, aiming to provide a more accurate representation of strain components across the laminate thickness [4]. While HSDT improved accuracy, they still faced challenges with interlaminar stress equilibrium. To address this, layer-wise (LW) theories were developed, defining separate variables for each layer to precisely model abrupt variations in shear strain [4,24,25,26,27,28]. Although LW theories enhanced precision, they were computationally demanding due to the increased number of unknowns. Further refinement led to higher-order zigzag theories (HOZT), which ensure interlaminar stress equilibrium throughout the laminate thickness [4,29,30,31,32]. Recent advancements in HOZT, such as those introduced by Alam et. all [33,34], explicitly incorporate the z/R term in strain-displacement relationships, which was often overlooked in previous formulations for computational simplicity. This continuous evolution of shell theories (see Figure 2) underscores the ongoing effort to accurately predict the complex buckling behavior of advanced composite and sandwich shells under diverse loading conditions, which is essential for ensuring their safety and reliability in applications ranging from automotive to aerospace industries.

3.2. Analytical, Experimental, and Numerical Approaches

The prediction of buckling loads in shell structures has historically faced significant discrepancies between theoretical calculations and experimental results, primarily due to the unavoidable presence of imperfections in real-world structures [35,36,37,38,39,40]. This gap has driven extensive research across analytical, experimental, and numerical domains to enhance the accuracy and reliability of buckling predictions.

Analytical approaches have evolved from early linear theories, such as Donnell’s “shallow shell theory,” which simplified the critical load problem to solvable partial differential equations [41,42,43]. Subsequent analytical efforts investigated the effects of pre-buckling deformations [44,45], in-plane boundary conditions, and geometrical imperfections [46,47]. The paper [48] develops a comprehensive nonlinear analytical shell theory for large displacement post-buckling analysis of thin-walled beams and shells subjected to in-plane and out-of-plane warping. For composite shells, analytical solutions for critical buckling pressures, incorporating initial imperfections, have been derived based on Sanders-type kinematic relations, showing good agreement with experimental and finite element (FE) results [49]. Semi-analytical models have also been developed to predict the elastic post-buckling response of cylinders with tailored non-uniform distributed stiffness, treating cylinder segments as individual panels and combining their responses [50]. These models can accurately predict the order of buckling events, though predicted buckling forces may be higher than experimental values [50].

Experimental investigations remain indispensable for validating theoretical models and numerical simulations, especially in complex fields like shell stability [51]. Early experimental studies on isotropic shells revealed critical load calculations 3–8 times larger than observed failure loads, a discrepancy later attributed to imperfection-sensitivity and post-buckling behavior [52,53,54,55]. Modern experimental techniques utilize tools like Digital Image Correlation (DIC) for real-time buckling tracking and strain gauges for local stress measurement [56,57,58,59]. Experiments on composite structures highlight the influence of material anisotropy, fiber-matrix interaction, geometric imperfections, and environmental effects on buckling behavior [60,61,62,63,64,65,66]. For instance, tests on composite ring-stiffened steel cylinders showed good agreement between experimental and numerical data, with reinforcement significantly increasing loading capacity [49].

Numerical methods, particularly Finite Element Analysis (FEA), have revolutionized shell buckling analysis. Early FE codes like STAGS played a significant role in accurately depicting buckling mechanisms and recognizing structural mode-jumping [67]. High-fidelity nonlinear FEA, which incorporates real cylinder imperfection measurements, can accurately predict the nonlinear buckling response of thin shell structures. Numerical studies have explored the impact of manufacturing-induced imperfections, including shell wall thickness variations, lamina ply-gaps, and mid-surface imperfections [35,68,69,70]. For composite shells, numerical analysis has demonstrated that incorporating nanoparticles can significantly increase critical buckling temperature [71]. The use of numerical methods extends to optimizing sandwich composite deep submarine pressure hulls, considering failure criteria and buckling strength, with FEM being a primary tool for such complex analyses [72].

The study [73] presents a comprehensive combined experimental and numerical investigation of sandwich composite semi-ellipsoidal shells, addressing geometric and material nonlinearities via arc-length analysis and validating the models through physical testing.

3.3. The Critical Role of Imperfections in Buckling

The stability of slender and thin-walled structures is highly sensitive to imperfections, making buckling behavior notoriously difficult to predict accurately. While classical theories assume ideal geometries and homogeneous materials, real structures invariably contain deviations that significantly reduce the critical buckling load [35,40,74,75,76]. These imperfections can be geometric, such as initial out-of-flatness or ovality, or material-related, including fiber misalignment, voids, and matrix inhomogeneities, especially in composite materials [77,78].

Geometrical imperfections, such as deviations in shape, dimensions, or overall geometry, strongly affect the shell’s load-carrying capacity [79]. The location, dent-amplitude, shape, and size of these imperfections have a significant influence on the buckling load. For instance, a thicker shell may exhibit axisymmetric or asymmetric buckling [80,81], while a thin shell tends to buckle in a chessboard pattern [82].

The paper [83] provides a rigorous analysis of imperfection sensitivity in the post-buckling regime of thin spherical shells under uniform external pressure.

Material imperfections are particularly critical in composite laminates, where the manufacturing process often introduces fiber waviness, resin-rich zones, or porosity. These defects create local stiffness reductions and act as stress concentration zones, promoting early onset of instability. The study [84] experimentally investigated how in-plane fiber waviness defects affect the compressive properties of quasi-isotropic (QI) C/PEEK composites. Laminates were manufactured with 1–3 wavy 0° plies (out of 24 total), with waviness angles ranging from 23° to 60°. While global laminate stiffness was unaffected, compression tests showed that waviness triggered early damage initiation via kinking, leading to significantly reduced ultimate strength compared to defect-free specimens. Notably, the strength did not vary significantly with the waviness angle within the studied range, but decreased proportionally with the number of wavy plies aligned with the load direction. Similarly, Drummer et al. [85] examined the impact of fiber misalignment defects—specifically folds, waves, and in-plane undulations—on the compressive behavior of GFRP cross-ply laminates produced via resin transfer molding. Compression tests were conducted at four temperatures to assess the influence of matrix properties. Results showed that fiber misalignment significantly reduced composite strength, especially at lower temperatures, with effects greater than their volume fraction would suggest. As temperature increased, the failure mode shifted from fiber-dominated to matrix-dominated, reducing the influence of fiber misalignment on mechanical performance.

In practice, the presence of imperfections necessitates conservative design approaches using knockdown factors or imperfection-sensitivity analyses. For critical applications, such as aerospace and high-performance civil structures, accounting for material imperfections is essential to ensure structural integrity under compressive loads.

3.4. Advances in Shell Buckling Theories and Sustainability-Oriented Implications

The stability of thin-walled and composite shell structures has been the subject of sustained theoretical development for over a century, evolving from classical isotropic models to refined formulations that capture anisotropy, layerwise behavior, and nonlinear effects. Classical shell theories, based on Love–Kirchhoff assumptions, provide closed-form solutions for isotropic cylinders and spheres under uniform loading. While these models offer valuable insights into global stability boundaries, they systematically overestimate buckling loads when compared to experiments, particularly for thin shells. This discrepancy was historically rationalized by the strong imperfection sensitivity of shells, which necessitated the introduction of empirical knock-down factors (e.g., NASA SP-8007) [86].

To address the specificities of composite shells, higher-order shear deformation and zigzag theories were developed. These formulations relax the assumption of linear through-thickness kinematics, allowing for discontinuities in in-plane displacements at ply interfaces. Their inclusion improves the prediction of both pre-buckling stiffness and the post-buckling response, particularly in laminates with strongly heterogeneous layups or sandwich configurations. Importantly, these theories highlight how the localization of buckling modes, often driven by layup asymmetry or thickness variations, modifies the sensitivity to imperfections. For example, zigzag theories predict earlier mode interaction phenomena, which can reduce post-buckling reserves in comparison with isotropic models [87,88].

The question of when fully nonlinear large-displacement formulations are required is essential for design. Linear eigenvalue analyses, while computationally inexpensive, provide only an upper bound to the critical load and do not account for mode interaction or amplitude-dependent stiffness degradation. Fully nonlinear geometrically formulations, incorporating both prebuckling deformations and post-buckling equilibrium paths, are necessary when shells are extremely slender, load eccentricities generate membrane-bending coupling, nonuniform laminate layups induce bending-stretching coupling, or the structure is expected to sustain significant load beyond initial instability [89,90]. These nonlinear analyses enable the identification of stable post-buckling paths that can be safely exploited, reducing conservatism and thereby material usage.

The treatment of imperfections has evolved from deterministic knock-down factors to stochastic imperfection spectra approaches. Rather than applying a universal reduction, modern design frameworks model imperfections as random fields characterized by amplitude, wavelength, and spatial correlation. This perspective permits reliability-based knock-downs, directly linking structural safety to the probability of occurrence of unfavorable imperfection patterns [89,91,92]. For composite shells, where manufacturing defects may be highly directional, such approaches provide a more rational balance between safety and efficiency [93].

From a sustainability-driven design standpoint, these theoretical developments translate into concrete benefits. Overly conservative knock-downs, while ensuring safety, promote excessive material consumption and higher embodied energy. Conversely, the integration of higher-order theories, nonlinear formulations, and probabilistic imperfection modeling allows engineers to replace prescriptive margins with informed, structure-specific predictions. This enables lighter and more efficient shell structures, reducing raw material demand and extending service life through better reliability assessment [94].

Recent studies demonstrate that stability-informed topology and shape optimization can directly contribute to sustainability by reducing embodied carbon. By integrating buckling and imperfection-sensitivity constraints, designers achieve material-efficient geometries that use less raw material while still meeting performance requirements. For example, shape-optimized truss structures have been shown to reduce material usage by over 50% when optimized early in the design phase, directly translating into significant embodied carbon savings [95]. Moreover, topology optimization frameworks that incorporate buckling resistance—such as those applied to fiber-reinforced composites—achieve a balance between material efficiency and structural stability [96].

Beyond these, stability has also been investigated in more advanced contexts where design-dependent loads are considered. In such cases, a model of buckling constraints in topology optimization was developed using the Kreisselmeier–Steinhauser aggregation function and a gradient-based algorithm, with numerical examples confirming both the effectiveness and reliability of the approach [97].

Nonlinear buckling optimization has also been introduced as a method for laminate optimization of generalized composite shell structures. By combining geometrically nonlinear analyses with mathematical programming, this approach maximizes the buckling load while explicitly accounting for imperfection sensitivity. Importantly, the method incorporates the concept of “worst” imperfections, enabling identification of the most detrimental geometric deviations under amplitude constraints. Numerical studies illustrate that such formulations provide valuable insight into the interaction between laminate design and imperfection sensitivity, ultimately leading to designs that balance weight efficiency with robustness to geometric imperfections [98]. These findings highlight that lightweight optimal laminates, while efficient in material use, may otherwise exhibit unacceptably high imperfection sensitivity without stability-informed safeguards.

4. Material-Efficient Design Strategies

4.1. Optimization Tools (Topology, Shape, Multi-Objective)

Design optimization has become a fundamental concept in the development of structural systems, driving improvements in efficiency, safety, and sustainability, particularly in the context of minimizing material usage while meeting stringent performance requirements [99]. Computational approaches are essential for addressing diverse design objectives such as weight reduction, material efficiency, and structural resilience. These techniques are broadly categorized into heuristic optimization methods, topology optimization, and multi-objective optimization [99,100] (Figure 3).

Heuristic Optimization Methods employ approximative search algorithms that iterate through potential design configurations to find solutions for complex problems [83]. Genetic Algorithms (GAs), are widely applied for optimizing material distribution and structural shapes, proving effective for complex, multi-constraint problems like truss design [101,102,103]. Particle Swarm Optimization (PSO), is useful for multi-dimensional problems, often seen in bridge and high-rise structure design [104,105]. Simulated Annealing (SA), drawing inspiration from metallurgy, is applied to complex nonlinear optimization challenges, such as minimizing steel frame weight [106,107,108].

Topology Optimization (TO) is a powerful structural design method that determines the optimal configuration by efficiently distributing materials within a given design domain, satisfying specified load, performance, and volume constraints [99]. Unlike size and shape optimization, TO is independent of the initial design, offering a broader design space [109]. The Solid Isotropic Material with Penalization (SIMP) method is widely used, effectively removing unnecessary material to maximize structural efficiency and stiffness-to-weight ratios [110]. Structural optimization enabled a 40% weight reduction in a bridge’s superstructure by adding elliptical cavities, allowing seismic code compliance without costly foundation upgrades [111].

Shape Optimization refines the external boundaries or internal surfaces of a structure to improve performance metrics like stress concentration and deformation. This method aims to find the ideal geometry for a chosen design space, targeting objectives such as minimizing total weight, volume, or stress, or maximizing stiffness. For shells, optimization variables typically include coordinates and thicknesses of selected design or structural nodes [112]. The process can incorporate geometric nonlinearities and imperfection sensitivity, which is crucial given shells’ high sensitivity to deviations from ideal shapes.

Multi-Objective Optimization (MOO) techniques aim to balance multiple, often conflicting objectives, such as cost, weight, and resilience [99]. Pareto Optimization identifies a set of “Pareto optimal” solutions where no objective can be improved without compromising another, proving valuable for balancing trade-offs like cost versus structural resilience [113]. MOO has been successfully applied to concrete thin shell structures, minimizing weight, deflection, and elastic energy change simultaneously [114].

4.2. Advanced Structural Modeling Techniques (FEA, AI/ML, Digital Twins)

Advanced structural modeling techniques are revolutionizing material efficiency in building design by enabling the creation of load-optimized structures that minimize material usage without sacrificing safety or performance [115].

Finite Element Analysis (FEA) plays a central role. Nonlinear FEA, in particular, is essential for slender, shell, or long-span structures, as it incorporates geometric nonlinearity, material plasticity, and significant deformation effects [116,117,118,119,120,121]. This allows for more accurate predictions of load redistribution and energy dissipation, which in turn leads to reduced overdesign and substantial material savings. FEA is also fundamental for validating analytical models and experimental data in shell buckling analysis, with high-fidelity nonlinear analyses being able to accurately predict the buckling response of thin shell structures by incorporating real imperfection measurements [122].

AI-driven Modeling Strategies and Machine Learning (ML) are increasingly integrated into structural design processes, opening new frontiers in optimization and material efficiency. ML-enhanced form-finding strategies can adapt to complex design constraints, offering improved structural efficiency and material savings. ML supports predictive modeling of stress-strain responses, real-time simulation in digital twins, and automated detection of optimal design regions in topology optimization [123,124]. The integration of machine learning can reduce computational costs and improve accuracy in predicting structural responses, especially in complex configurations, thereby contributing to material efficiency through more precise designs. For instance, a machine learning-based method is introduced in [124] to accurately predict and optimize the nonlinear mechanical behavior of bistable curved shell structures by mapping structural parameters to performance outcomes, particularly backward snapping forces, offering a powerful tool for designing variable-thickness shells and guiding the modular development of advanced metamaterials with specific functionalities

Digital Twins (DTs) are virtual replicas of physical structures that are continuously updated with real-time data [125]. When combined with real-time structural simulation, DTs enable dynamic feedback, predictive analysis, and continuous optimization of material use based on actual structural behavior [125,126,127]. The paper [127] presents a three-level Digital Twin (DT) approach for rapid and accurate prediction of stress fields in deep-diving spherical shells, using a simulation database and validated finite element models. The method achieves high accuracy (errors < 9.4% experimentally and <1% with optimization) and enables real-time stress state monitoring through sensor integration and dynamic model updating.

5. Integration of Recycled and Bio-Based Materials

The integration of recycled and bio-based materials into shell structures is driven by the dual engineering objectives of maintaining structural performance and reducing environmental impact. From a structural engineering standpoint, shells are inherently material-efficient, and incorporating sustainable materials further amplifies this advantage by lowering embodied energy, reducing CO₂ emissions, and promoting resource circularity. Recycled materials—such as reclaimed aggregates, repurposed polymers, and fiber-reinforced composites—can be engineered to meet or exceed strength, stiffness, and durability requirements, making them suitable for load-bearing skins, core layers, or stiffening elements in shell forms. Bio-based materials, including natural fiber composites, engineered wood, and plant-derived polymers, offer favorable strength-to-weight ratios and energy absorption characteristics, with proper treatments enhancing moisture resistance and long-term performance. The adoption of these materials aligns with circular economy principles, enabling shells to serve as structurally efficient, environmentally responsible solutions in civil, industrial, and infrastructure applications.

5.1. Recycled Materials in Shell Structures

The integration of recycled materials into shell structures represents a promising direction for sustainable construction, combining structural performance with environmental responsibility. Recent research has demonstrated the feasibility and advantages of such approaches across various applications. For example, sandwich beams with recycled wood cores encased in GFRP skins have shown effective flexural performance, offering a viable lightweight alternative for curved or shell-like structural elements [128]. In concrete-based shell systems, the use of recycled aggregate concrete (RAC) within steel tubes has proven structurally sound, particularly when enhanced with CFRP confinement, which improves load-bearing capacity and ductility [129]. Thin-walled steel tube columns filled with RAC have also demonstrated stable axial compression behavior, suggesting their applicability in shell forms subjected to compressive loading [130]. Beyond load-bearing elements, recycled materials have found use in innovative panel systems, which are increasingly relevant for shell envelopes due to their thermal and acoustic properties and favorable life cycle impacts [131,132]. Expanding the concept of thin-walled sustainability to impact-resistant applications, Liu et al. [133] proposed a cost-effective and eco-friendly energy absorber using recycled beverage cans. Their study revealed that empty cans fail via local buckling under axial loads, behaving as Type-II absorbers, while filling the cans with polyurethane foam (PUF) significantly improves energy absorption through a progressive folding mechanism.

5.2. Bio-Based Materials in Shell Structures

Bio-based materials, derived from renewable sources like wood, bamboo, and natural fibers, offer promising alternatives to traditional construction materials due to their environmental benefits and unique mechanical properties [134]. These materials contribute to lightweight and resilient designs, crucial for sustainable shell structures.

Bio-based structural members exhibit high strength and resilience, making them viable alternatives in specific applications when treated and engineered to meet durability standards [134]. Engineered wood products, such as cross-laminated timber (CLT), can provide strength and stability comparable to concrete or steel for multi-story structures [135,136]. Bio-based composites, particularly those reinforced with natural fibers like flax or hemp, demonstrate promising stiffness and impact resistance due to their inherent flexibility and energy-absorbing properties [134]. For instance, flax fiber-reinforced polymer (FRP) facings combined with paper honeycomb cores in sandwich beams show substantial potential for building applications with a reduced environmental footprint, offering comparable performance to synthetic counterparts while being lighter [137]. Foam-filling these paper honeycomb cores can significantly enhance their shear modulus and strength (with 24 and 60% respectively), further improving the performance of the sandwich beams [137].

However, bio-based materials face durability challenges, primarily moisture absorption, temperature sensitivity, and degradation over time. Moisture can lead to swelling, warping, and microbial growth, weakening fiber-matrix adhesion and accelerating degradation [138]. Elevated temperatures can degrade polymeric matrices and reduce adhesion, while low temperatures may cause brittleness [134]. Prolonged exposure to environmental factors like UV radiation can also lead to physical and chemical changes [134].

Significant advancements are being made to enhance the performance and durability of bio-based materials. Surface treatments (e.g., chemical modification, plasma treatment) and protective coatings can significantly improve tensile strength and impact resistance [134]. Hybrid composites, combining natural fibers with biodegradable resins or bio-based polymers, are developed to achieve improved mechanical properties and lightweight characteristics [134]. Nanotechnology, involving the integration of nanomaterials like nanoparticles or nanotubes, further enhances strength, durability, and environmental resistance [134]. For example, incorporating nanoparticles can improve Young’s and shear moduli of glass/epoxy composites and increase critical buckling temperature [71].

In the context of shell structures, bio-based composites are being explored for their buckling behavior. Factors affecting composite buckling, such as material anisotropy, fiber-matrix interaction, geometric imperfections, and environmental effects, are critical considerations in their design [60]. The study [139] explores the flexural and buckling behavior of sandwich panels with a sawdust-based mortar core and polymeric skins. Material characterization and testing of 42 panels showed good structural performance, with failure mainly by core shear/crimping and no core–skin debonding, confirming their potential as eco-friendly alternatives.

Research on bio-based and modular metastructures, composed of bamboo rods and plant-based polymeric joints (soybean and castor oil), demonstrates their potential as sustainable alternatives for load-bearing structures capable of supporting significant compression [140]. These innovative designs, combining natural materials and sustainable polymers, result in fully renewable composite structures that exemplify environmental stewardship and advanced composite design [140]. Furthermore, knitting techniques are being investigated for fabricating shell-based cellular structures, where the knit can function as a formwork or as a composite structure combined with bio-based resin, aiming for minimal production waste and industrial scalability [141]. The use of bio-based polymers in phase change materials (PCMs) also contributes to minimizing environmental impact in the building sector by reducing carbon footprint and enabling sustainable thermal management [142].

6. Results of Bibliometric Analysis

The refined dataset served as the basis for a structured bibliometric mapping aimed at understanding the conceptual organization of research concerning shell structures, buckling phenomena, and their intersection with optimization and sustainability. To achieve this, a co-occurrence analysis of author keywords was performed in VOSviewer (version 1.6.20) using the full counting method. A minimum threshold of 20 occurrences was applied to ensure the inclusion of only consistently recurring terms, resulting in a selection of keywords that are central to the discourse.

The generated network visualization is presented in Figure 4. Each node in the map represents a frequently used keyword, while the links between them reflect the frequency with which these terms co-appear in the same publications. The algorithmic clustering procedure grouped the terms into distinct thematic clusters, each differentiated by color, revealing areas of concentrated research attention as well as the conceptual bridges between them.

The keyword co-occurrence map reveals a structured network composed of four major thematic clusters, each corresponding to a distinct but interrelated research direction. The red cluster, positioned in the left region of the map, is centered around terms such as “design”, “optimization”, “performance”, “behavior” and “strength”. This group reflects the engineering-driven focus on enhancing the mechanical behavior of structures, often involving simulation-based design and performance assessment under various loading conditions.

Moving toward the right, the green cluster captures topics tied to algorithmic and computational strategies, including “topology optimization”, “design optimization”, “structural optimization”, and various metaheuristics such as “particle swarm optimization” and “differential evolution”. This grouping represents a strong emphasis on the development of optimization frameworks applicable to complex geometries and material distributions.

The blue cluster, located in the lower-right quadrant, is more closely aligned with theoretical and analytical investigations into “buckling analysis”, “composite plates”, “vibration”, and “post-buckling”. These terms point to foundational studies that underpin structural stability assessments, particularly in thin-walled and laminated systems.

The yellow subcluster bridges terms across all thematic zones—most notably “buckling”, “stability”, and “load”—indicating its integrative role and relevance across both design and analysis contexts.

Together, these clusters trace the conceptual landscape of the field, emphasizing the dynamic interplay between structural mechanics, optimization strategies, and the growing integration of sustainability considerations. The network structure suggests a mature research domain with strong internal cohesion, yet it also opens space for further interdisciplinary convergence, particularly between computational optimization and ecological imperatives in structural design.

Building on the structural overview provided in Figure 4, which outlined the main thematic clusters within the research field, Figure 5 introduces a temporal dimension to the analysis. This overlay visualization enriches the static map by revealing how the prominence of individual keywords has shifted over time. Each term is color-coded according to its average publication year, with darker blue shades indicating earlier appearances and yellow tones reflecting more recent emergence. Although the dataset covers publications from 2016 to 2025, the color scale in the overlay visualization was deliberately adjusted to enhance contrast.

As expected, two of the main search terms—“optimization” and “buckling”—appear as central, high-frequency nodes, shaded in darker tones. Their early average occurrence underscores their role as longstanding pillars of the field, anchoring both the theoretical foundations and methodological developments. Similarly, terms such as “plates”, “compression”, “optimum design”, and “geometry” also appear in darker hues, reflecting their early and consistent use across the literature. These concepts are closely tied to classical formulations in structural mechanics and optimization, forming the analytical backbone of many studies addressing stability under compressive loads.

Terms like “layout optimization”, “additive manufacturing”, “prediction” and “continuum structures” suggest a growing interest in computationally driven design approaches that leverage algorithmic modeling, data-informed performance estimation, and manufacturing-aware configurations. Their relatively recent appearance, as indicated by lighter hues, points to an emerging shift from purely theoretical formulations toward applications that integrate fabrication constraints, material distribution logic, and predictive control—hallmarks of a more adaptive, digitally integrated structural design paradigm.

Although “sustainability” was explicitly included in the query string, the term did not meet the minimum occurrence threshold required for visualization in VOSviewer. We conducted additional sensitivity analyses by lowering the occurrence threshold to 5 and by testing fractional counting, but “sustainability” still did not reach the inclusion criteria. This finding indicates that, within the 2016–2025 dataset, sustainability has not yet become a consolidated keyword in the research stream on shells, buckling, and optimization. This absence points to a limited integration of sustainability considerations in this niche domain. Consequently, the gap highlights an opportunity for future research to more systematically embed sustainability criteria into structural optimization studies, thereby bridging performance-driven approaches with environmental and societal imperatives.

Figure 6 presents the density visualization of the keyword co-occurrence network, offering an alternative view that highlights the intensity of term usage within the field. In this representation, brighter areas correspond to higher densities of keyword co-occurrence, reflecting regions where terms are not only frequent but also closely interconnected in the literature. In contrast, darker areas indicate lower conceptual density, where keywords are either less frequently used or more loosely integrated into the core discourse.

As expected, the highest-density zones appear around “optimization”, “design”, “buckling”, and “behavior” confirming their central role in shaping the intellectual architecture of the field. These regions correspond closely to the dominant clusters observed in the previous figures, reinforcing the conclusion that the domain remains anchored in classical mechanics, structural analysis, and computational design.

Peripheral regions of the map—such as those containing terms like “additive manufacturing”, “microstructure”, “differential evolution”, or “curvilinear fiber format”—exhibit lower density levels. This suggests that while these topics are emerging in relevance, they have not yet coalesced into high-connectivity zones within the bibliographic network. In other words, they represent nascent or specialized subfields, whose conceptual integration into the mainstream remains in progress.

To complement the keyword-based co-occurrence analysis, a broader lexical mapping was conducted using terms extracted from the titles and abstracts of the publications. This approach extends the scope of the analysis by capturing not only the predefined author keywords but also the language patterns authors use to frame their research narratives. The resulting map, shown in Figure 7, is based on binary counting, with a threshold of 35 minimum occurrences, and highlights frequently used terms across the textual metadata of the corpus.

The resulting visualization reveals three dominant clusters. The red cluster, concentrated on the right side of the map, continues to emphasize experimental and application-driven research. Terms such as “strength”, “capacity”, “deformation”, “test”, “experiment”, and “mechanical property” highlight a strong focus on structural performance, material behavior, and empirical validation—central concerns in engineering practice.

The blue cluster at the top left is centered around computational and optimization-oriented terminology, including “topology optimization”, “constraint”, “optimization process”, “function”, and “design variable”. This indicates an analytical and algorithmic approach, where the formulation and solution of optimization problems—often multi-objective—are central to the methodological framework.

The green cluster, spanning the lower-left quadrant, is dominated by terms such as “laminate”, “buckling load”, “panel”, “fiber orientation”, “plate”, and “formulation”. This cluster captures the theoretical and material modeling aspects of the field, especially in the context of composite structures and layered materials. It bridges mechanics, geometry, and material science, reflecting efforts to integrate physical realism into structural simulation.

In the center of the map, we observe transversal terms like “problem”, “function”, “formulation”, and “panel”, acting as semantic connectors between the analytical, experimental, and material clusters. These linkages suggest a high degree of interdisciplinary interplay, where optimization formulations are grounded in physical principles and ultimately validated through testing.

Compared to the keyword-based visualizations, this map emphasizes the semantic texture of the research field—showing how authors narratively position their work and which concepts serve as conceptual anchors. It also reveals a more pronounced presence of core mechanics and materials science terminology, indicating that even in optimization-driven studies, the grounding in physical modeling remains strong.

To complement the thematic and conceptual analyses, a co-authorship network based on country affiliations is presented in Figure 8. This map offers a macro-level view of international collaboration patterns within the field, based on the country information extracted from author affiliations. Each node represents a country, with the size of the node reflecting its total link strength (i.e., its overall number of co-authored publications), while the color gradient denotes the average year of activity.

According to the co-authorship network, China has the highest degree centrality and the largest number of publications. The United States, Iran, India, Germany, and Turkey also represent significant hubs, with dense bilateral and multilateral connections as reflected by high link strength values.

The overlay color coding reveals recent increases in research activity from countries like Mexico, Turkey, Ecuador, Jordan, and Belarus, suggesting a growing diversification of contributors in the domain.

The structure of the network reflects both traditional power centers of scientific production and newly active regions entering discourse. The visible density of connections in Asia, Europe, and the Middle East underscores the globalized character of research in structural optimization and stability, while also pointing toward opportunities for strengthening participation from underrepresented regions such as sub-Saharan Africa or Southeast Asia.

The co-authorship network highlights clusters in Asia, with China, India, Iran, and South Korea at the core, and in Europe, with Germany, France, Poland, the UK, Switzerland, Spain, and Greece as visible contributors. Latin American countries such as Brazil, Mexico, Colombia, and Ecuador also appear, albeit with lower connectivity, usually linked through collaborations with larger hubs. Other regions, including Sub-Saharan Africa and Southeast Asia, remain only marginally represented, which reflects persistent asymmetries in global research participation.

To further contextualize the conceptual landscape and highlight the sources that shape the current discourse, a bibliographic coupling analysis by source was performed. The resulting visualization is shown in Figure 9, where each node represents a journal or conference proceeding, and the links between them reflect the number of shared references. The node size corresponds to the number of documents indexed in the dataset from that particular source, while the color gradient indicates the average year of publication—from earlier (blue) to more recent (yellow).

The map shows that Composite Structures, Thin-Walled Structures, and Engineering Structures have the largest node sizes and strongest connections, highlighting their role in the field.

Surrounding journals such as Applied Composite Materials, Computers & Structures, Engineering Optimization, and Materials & Design maintain substantial linkages, bridging computational approaches with application-oriented studies. Peripheral sources, such as the Journal of Bridge Engineering, Earthquake Engineering and Structural Dynamics, and the SPE Journal, are positioned toward the margins, reflecting narrower thematic scopes but preserved integration into the wider network.

More recent publication activity is visible in journals like Sustainability, Buildings, and several editions of the AIAA SciTech Forum 2024.

This coupling analysis provides valuable insight into where interdisciplinary discourse is intensifying. Taken together, the visualizations presented in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 offer a comprehensive and multi-dimensional understanding of the research landscape surrounding shell structures and buckling phenomena in the context of optimization and sustainability. From the structural clustering of author keywords to the temporal evolution of concepts, from density-based prominence to semantic mapping via title and abstract terms, and finally to global collaboration networks and bibliographic coupling among journals, the analyses reveal a field that is both grounded in classical mechanics and increasingly receptive to computational innovation and sustainability concerns. These findings not only highlight the central research themes and emerging directions but also underscore the interdisciplinary and international character of the domain, pointing toward future opportunities for integration, collaboration, and impact.

7. Research Gaps and Future Directions

Despite significant advancements in the understanding of shell buckling behavior and the development of material-efficient design strategies, several critical research gaps persist, necessitating focused future investigations to fully realize the potential of sustainable shell structures.

7.1. Performance-Based Design for Shell Structures

The current paradigm in structural design often relies on prescriptive codes that, while ensuring safety, may not optimally satisfy multiple objectives such as economy, serviceability, sustainability, and robustness [143]. This approach implicitly assumes that conformance to prescriptive criteria guarantees desired performance, without quantifying true safety margins or exploring superior design solutions. Performance-based design (PBD) offers a transformative alternative by explicitly setting specific performance objectives for the completed structure and prescribing processes in minimal terms [144,145]. This approach encourages creativity and innovation, allowing engineers to identify optimal solutions to multiple, sometimes competing, objectives by leveraging structural and material mechanics principles.

For shell structures, the full integration of PBD is a critical future direction. This involves moving beyond simplified linear bifurcation buckling analyses to high-fidelity nonlinear structural simulations that incorporate real-world imperfections and complex load paths [146]. The NASA Shell Buckling Knockdown Factor (SBKF) Project, for example, aims to develop less-conservative, robust analysis-based knockdown factors for launch vehicle structures, explicitly accounting for shell geometry, manufacturing tolerances, and combined mechanical, pressure, and thermal loads. This initiative highlights the need for validated analysis tools that can reduce reliance on structural testing by enabling high-fidelity predictions of as-built hardware [146].

A significant challenge in PBD is the “performance gap” between calculated energy consumption in the design phase and actual field measurements [147]. Establishing comprehensive calibration models at the design stage, potentially through full-scale mockups and extensive on-site monitoring, is very important. Furthermore, PBD demands a better understanding of risk assessment and management from structural engineers, with peer reviews likely becoming vital for validation [143]. The development of tools that can genuinely predict operational performance early in the design stage is needed to increase transparency about long-term benefits outweighing initial costs [147].

7.2. Advanced Materials and Manufacturing Technologies

The future of sustainable shell structures is inextricably linked to the continued development and integration of advanced materials and manufacturing technologies. While traditional materials like concrete and masonry remain prevalent, modern shell structures increasingly incorporate innovative materials such as fiber-reinforced polymers (FRP) and advanced concrete mixes for improved mechanical properties and sustainability [148]. The potential for new materials that can utilize waste products to build structures with lower environmental and economic costs is particularly compelling [2]. Ideally, future construction could involve materials that help absorb CO₂ and utilize waste from other societal sectors [2].

Research into bio-based materials, such as bamboo and natural fiber-reinforced composites, is fundamental. While these materials offer renewability and reduced environmental footprints, challenges related to moisture absorption, temperature sensitivity, and long-term degradation need further investigation [134]. Advancements in surface treatments, hybrid composites, and nanotechnology are addressing these durability issues, enhancing mechanical properties and environmental resistance [134].

Additive manufacturing, particularly large-area 3D printing (LAAM), presents new opportunities for geometric and material design, enabling the fabrication of complex shell geometries with reduced material waste [149]. Optimization frameworks are connecting sustainability and design in LAAM by minimizing embodied energy, carbon footprint, water footprint, and manufacturing time while maximizing structural integrity [150]. However, generative design, while producing lighter geometries, can introduce manufacturability issues, highlighting the need for future research to integrate manufacturing constraints into design software [150]. The development of new approaches to topology optimization of ribbed slabs and shells, using brick elements with mapping constraints, aims to improve rib continuity and structural performance, though it currently incurs higher computational costs compared to shell element models [151].

7.3. Enhanced Computational Methods and Simulation

The complexity of shell buckling behavior, especially with advanced composite and imperfect geometries, necessitates continuous enhancement of computational methods and simulation tools. While Finite Element Analysis (FEA) has become a standard, further refinements are needed to accurately predict nonlinear responses, particularly concerning material and geometric nonlinearities and contact phenomena [109]. The integration of AI and machine learning into FEA and other modeling strategies offers promising avenues for predictive modeling, real-time simulation, and automated design optimization, potentially reducing computational costs and improving accuracy [99].

Digital Twins (DTs), virtual replicas of physical structures updated with real-time data, hold immense potential for continuous optimization of material use and extended service life based on actual structural behavior [115]. Future research should focus on standardizing DT frameworks and integrating them with automated design and digital fabrication workflows. The development of multiscale and multiphysics modeling approaches will also be essential, allowing engineers to capture the influence of material behavior at micro- and mesoscales on macroscopic structural performance and account for interactions between mechanical, thermal, and environmental effects.

Specific research gaps in shell buckling analysis include the lack of comprehensive studies on the buckling evolution process, particularly for perforated composite cylindrical shells under hydrostatic pressure, where real-time observation of buckling shape is challenging [152]. Future experimental studies should utilize Digital Image Correlation (DIC) for real-time tracking, employ strain gauges for local stress measurement, and introduce cyclic loading to simulate real-world conditions. Numerically, finer meshes, more accurate imperfection modeling, and validation with extensive experimental data are needed. Analytically, integrating interaction factors for different buckling modes and stiffener effects into design codes will enhance predictive capabilities. A broader outlook that engages with policy, design, economics, and social impacts, in addition to conventional mechanics and engineering science, is essential for structural engineering research to drastically improve the sustainability of the built environment [2].

8. Conclusions

This comprehensive review underscores the essential role of shell structures in advancing sustainable construction, primarily due to their inherent material efficiency. However, this efficiency introduces a critical vulnerability to buckling, creating a fundamental paradox that necessitates advanced design and analytical strategies. The field has witnessed a continuous evolution of theories, from classical isotropic models to sophisticated higher-order zigzag theories for composites, driven by the imperative for accurate buckling prediction in lightweight, high-performance applications.

Bibliometric analysis reveals a dynamic research landscape, with a growing emphasis on structural engineering standards and the critical influence of imperfections on buckling behavior. This highlights a shift towards more rigorous and probabilistic approaches in design, moving away from overly conservative empirical factors. The development of material-efficient design strategies is increasingly reliant on advanced computational optimization tools, including topology, shape, and multi-objective optimization, which enable the creation of load-optimized structures with minimal material waste. These efforts are further amplified by the integration of cutting-edge modeling techniques such as Finite Element Analysis, AI/Machine Learning, and Digital Twins, offering unprecedented precision in predicting structural response and optimizing material use throughout a structure’s lifecycle.

The integration of recycled and bio-based materials represents a significant frontier in sustainable shell construction. While challenges related to mechanical properties and long-term durability persist, ongoing advancements in material science—including surface treatments, hybrid composites, and nanotechnology—are enhancing their performance.

Technical difficulties and research progress in research methods for sustainable shell structures largely stem from the complexity of accurately predicting buckling behavior and optimizing material usage under real-world conditions. Key challenges include: the imperfection-sensitivity of thin-walled shells, which makes experimental results highly dependent on manufacturing accuracy; the gap between analytical predictions and experimental performance, particularly for composite and hybrid materials; and the computational cost of high-fidelity nonlinear simulations, especially when integrating geometric and material nonlinearities, contact effects, and environmental influences. Experimental studies face difficulties in full-scale testing due to cost, safety, and the need for specialized equipment such as large-scale buckling rigs and Digital Image Correlation systems.

Recent research progress has addressed these issues by: refining higher-order and layer-wise theoretical models to improve accuracy for composite shells; developing semi-analytical and hybrid numerical–experimental methods that incorporate measured imperfections; leveraging finite element advancements to enable more precise nonlinear buckling simulations; and integrating machine learning and digital twin frameworks to accelerate parametric studies and real-time monitoring. These developments are narrowing the gap between predictive models and observed structural performance, supporting more reliable and material-efficient designs for sustainable shell structures. Despite these advancements, critical research gaps remain. A key area for future focus is the full implementation of performance-based design for shell structures, which moves beyond prescriptive codes to explicitly target multiple performance objectives, including sustainability and resilience. This requires further development of advanced materials and manufacturing technologies, particularly in areas like large-area 3D printing and bio-based composites, to overcome current limitations in manufacturability and long-term performance. Concurrently, continuous enhancement of computational methods and simulation tools is essential to accurately model complex behaviors, incorporate real-world imperfections, and integrate multi-physics phenomena. The ultimate realization of truly sustainable shell structures hinges on a collaborative, interdisciplinary approach that bridges research, design, and policy, fostering a built environment that is both structurally robust and environmentally responsible.