Search Results (206)

This study examines the forced vibration behavior of a hydroelastic system composed of a functionally graded material (FGM) plate, a barotropic compressible Newtonian viscous fluid, and an adjacent rigid wall. The fluid occupies the gap between the plate and the wall. A time-harmonic force, applied in and along the free surface of the FGM plate, excites vibrations within the system. The plate’s motion is modeled using the exact equations of elastodynamics, while the fluid dynamics are described by the linearized Navier–Stokes equations for compressible viscous flow. The governing equations, which feature variable coefficients, are solved using a discrete analytical approach. Boundary conditions enforce impermeability at the rigid wall and continuity of both forces and velocities at the fluid–plate interface. The investigation focuses on the plane strain state of the plate coupled with the corresponding two-dimensional fluid flow. Numerical analyses are conducted to evaluate normal stresses and velocity distributions along the interface. The primary objective is to assess how the graded material properties of the plate influence the frequency-dependent responses of stresses and velocities at the plate–fluid boundary. Full article

An analysis of free vibrations for thin functionally graded plate bands is presented in this work. On the microlevel these plate bands have a tolerance-periodic microstructure in planes parallel to the mid-plane. Partial differential equations with tolerance-periodic, highly oscillating, non-continuous coefficients describe the vibrations of such plates. Here, the influence of microstructure inhomogeneity is shown on free vibration frequencies of these plate bands with different boundary conditions. This analysis was carried out within the framework of two models of these plates. The models are represented by equations with smooth, slowly varying coefficients. One of these models, called the tolerance model, takes into account the effect of the microstructure size. Hence, it leads not only to formulas of fundamental lower-order vibration frequencies, but also to formulas of higher-order vibration frequencies, which are related to the microstructure. The analyses of free vibration frequencies for thin functionally graded plate bands with different boundary conditions are presented. The formulas of frequencies are obtained using the Ritz method. A comparison of some calculated results to the results obtained by the FEM is also shown. Full article

This paper provides an overview of various size-dependent theories based on modified/consistent couple stress and strain gradient theories (CSTs and SGTs), highlighting the development of two-dimensional (2D) refined and advanced shear deformation theories (SDTs) and three-dimensional (3D) pure analytical and semi-analytical numerical methods, including their applications, for analyzing the static and dynamic behaviors of microscale plates and shells made from advanced materials such as fiber-reinforced composites, functionally graded (FG) materials, and carbon nanotube/graphene platelet-reinforced composite materials. The strong and weak formulations of the 3D consistent CST, along with their corresponding boundary conditions for FG microplates, are derived and presented for illustration. A comparison study is provided to show the differences in the results of a simply supported FG microplate’s central deflection, stress, and lowest natural frequency obtained using various 2D size-dependent SDTs and 3D analytical and numerical methods based on the consistent CST. A parametric study is conducted to examine how primary factors, such as the effects of dilatational and deviatoric strain gradients and couple stress, impact the static bending and free vibration behaviors of a simply supported FG microplate using a size-dependent local Petrov–Galerkin meshless method based on the consistent SGT. Influences such as the inhomogeneity index and length-to-thickness ratio are considered. It is shown that the significance of the impact of various material length-scale parameters on the central deflection and its lowest natural frequency (in the flexural mode) of the FG microplate is ranked, from greatest to least, as follows: the couple stress effect, the deviatoric strain gradient effect, and finally the dilatational strain gradient effect. Additionally, when the microplate’s thickness is less than 10⁻⁷ m, the couple stress effect on its static and dynamic behaviors becomes saturated. Conversely, the impact of the dilatational and deviatoric strain gradients consistently influences the microplate’s static and dynamic behaviors. Full article

The reconstruction of segmental bone defects requires patient-specific scaffolds that combine mechanical safety, biological functionality, and rapid manufacturing. We converted CT-derived mandibular geometry into a functionally graded Ti-6Al-4V lattice and optimised porosity, screw layout, and strut thickness through a cyber-physical loop that joins high-fidelity FEM, millisecond ANN, and a BN for uncertainty quantification. Fifteen candidate scaffolds were fabricated by direct metal laser sintering and hot isostatic pressing and were mechanically tested. FEM predicted stress and stiffness with 98% accuracy; the ANN reproduced these outputs with 94% fidelity while evaluating 10,000 designs in real time, and the BN limited failure probability to <3% under worst-case loads. The selected 55–65% porosity design reduced titanium use by 15%, shortened development time by 25% and raised multi-objective optimisation efficiency by 20% relative to a solid-plate baseline, while resisting a 600 N bite with a peak von Mises stress of 225 MPa and micromotion < 150 µm. Integrating physics-based simulation, AI speed, and probabilistic rigour yields a validated, additively manufactured scaffold that meets surgical timelines and biomechanical requirements, offering a transferable blueprint for functional scaffolds in bone and joint surgery. Full article

This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel shape functions are introduced to accurately model transverse shear deformation across the plate thickness without employing shear correction factors. These functions are constructed to satisfy shear stress boundary conditions and capture nonlinear effects induced by material gradation and porosity. A variational formulation is developed to describe the dynamic response of FGM plates in a thermo-mechanical environment, incorporating temperature-dependent material properties and three porosity distributions: uniform, linear, and trigonometric. Numerical solutions are obtained using in-house MATLAB codes, allowing complete control over the formulation and interpretation of the results. The model is validated through detailed comparisons with existing literature, demonstrating high accuracy. The findings reveal that the porosity distribution pattern and gradient intensity significantly influence natural frequencies and mode shapes. The trigonometric porosity distribution exhibits favorable dynamic performance due to preserved stiffness in the surface regions. Additionally, the Kerr-type elastic foundation enables fine tuning of the dynamic response, depending on its specific parameters. The proposed approach provides a reliable and efficient tool for analyzing FGM structures under complex loading conditions and lays the groundwork for future extensions involving nonlinear, time-dependent, and multiphysics analyses. Full article

Background: Plantar plate injuries represent a common yet frequently underdiagnosed etiology of forefoot pain and metatarsophalangeal joint instability. Diagnostic accuracy is often compromised by nonspecific clinical presentations and significant symptom overlap with other forefoot pathologies, including Morton’s neuroma and synovitis. Early and accurate identification is essential to prevent progression to irreversible deformity. Methods: This narrative review synthesizes recent literature on the clinical evaluation, imaging modalities, and differential diagnosis of plantar plate injuries. A comprehensive literature search in a narrative review format of key databases and relevant journals was performed to critically appraise the diagnostic accuracy, advantages, limitations, and clinical implications of various diagnostic techniques. Results: Physical examination maneuvers—including the drawer test, toe purchase test, and Kelikian push-up test—provide important diagnostic insights but are constrained by operator dependency and lack of standardization. Among imaging modalities, MRI and dynamic ultrasound offer high diagnostic utility, with MRI providing superior specificity and ultrasound enabling functional, real-time assessment. Emerging techniques such as dorsiflexion-stress MRI and dual-energy CT show promising diagnostic potential, though broader clinical validation is lacking. Differential diagnosis remains a major challenge, given the clinical and radiological similarities shared with other forefoot conditions. Conclusions: Accurate diagnosis of plantar plate injuries necessitates a multimodal strategy that combines clinical suspicion, structured physical examination, and advanced imaging. Acknowledging the limitations of each diagnostic modality and integrating findings within the broader clinical context are essential for timely and accurate diagnosis. Future research should prioritize validation of diagnostic criteria, enhanced access to dynamic imaging, and the development of consensus-based grading systems to improve diagnostic precision and patient outcomes. Full article

Elastic solutions of a differential system of vibrational responses of a bidirectional porous functionally graded plate (BPFG) are described by employing high-order normal and shear deformation theory, in the present study. Natural frequency values are computed for the plates with simply supported boundary conditions and taking into consideration the thickness stretching effect. Grading of the effective material property for the BPFG plate is defined according to a power-law distribution. Navier’s approach is applied to determine the governing differential equations solution of the studied model derived by Hamilton’s principle. To confirm the reliability of the solution and the model accuracy, a comparison study with various studies that are presented in the literature is carried out. Numerical illustrations are presented to discuss the influences of the plate geometry, the porosity, the volume fraction distribution, and the nonlocality on the vibration behaviors of the model. The dynamic responses of unidirectional and bidirectional porous functionally graded nanoplates are analyzed in detail, employing two parametric numerical examples. Numerical results show the sensitivity of frequencies to the studied parametric factors and their dependence on porosity and nonlocality coefficients. Frequencies of BPFG with uneven/even distribution porosity decrease when increasing the transverse and axial power-law indexes ($P\ne 0$), and the same effect appears when increasing the nonlocal parameter. Full article

This study develops a vibration model for functionally graded material (FGM) plates with embedded planar cracks. Based on thin plate theory and von Kármán-type geometric nonlinear strain assumptions, the kinetic and potential energies of each region are derived. Displacement field trial functions are constructed according to boundary conditions, and the Ritz method is employed to determine natural frequencies and vibration modes under small deformation conditions. The investigation focuses on how crack parameters and material gradient coefficients affect vibration characteristics in exponentially graded FGM plates. The results show that natural frequencies decrease with increasing crack length, while crack presence alters nodal line patterns and mode symmetry. During free vibration, the upper and lower surfaces of the crack region exhibit relative displacement. Material gradient effects induce thickness–direction asymmetry, causing non-uniform displacements between the plate’s upper and lower sections. Full article

Osteosarcoma is one of the most common primary bone malignancies, typically occurring around the knee. However, the forearm is a rare site, with tumors in the proximal ulna being extremely uncommon. Primary sarcoma in this location presents a surgical challenge due to the complex anatomy and limited reconstructive options. We report a rare case of a 19-year-old female with non-metastatic, high-grade giant cell-rich osteosarcoma involving the right proximal ulna. To our knowledge, this is only the second reported adult case of this histological subtype in this location. The patient was treated at a specialized oncology center with neoadjuvant and adjuvant chemotherapy, along with wide intra-articular resection for local tumor control. Reconstruction was achieved using a novel, customized 3D-printed articulating cement spacer mold with plate osteosynthesis. Artificial elbow ligamentous reconstruction was performed using FiberTape and FiberWire sutures passed through drill holes, and the triceps tendon was reattached to the cement mold using an endobutton. This cost-effective and personalized surgical approach allowed successful joint reconstruction while maintaining elbow stability and function. Our case highlights a feasible reconstructive option for rare and anatomically challenging osteosarcoma presentations, contributing to the limited literature on proximal ulna giant cell-rich osteosarcoma. Full article

An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundaries. The differential and integral operators can be discretized into matrix representations employing the differential quadrature method (DQM) and Taylor series expansion techniques. The discretization of dynamics equations stems directly from a weak formulation that circumvents the need for any transformation or discretization of higher-order derivatives encountered in the corresponding strong equations. Utilizing the matrix elementary transformation technique, the displacements of boundary and internal nodes are segregated, subsequently leading to the derivation of the generalized eigenvalue problem pertaining to the free vibration analysis of the Functionally Graded Material (FGM) rectangular plate. Furthermore, the study examines the impact of the gradient parameter, aspect ratio, and elastic constraints on the dimensionless frequency characteristics of the FGM rectangular plate. Ultimately, the modal properties of an in-plane FGM rectangular plate are investigated. Full article

Background/Objectives: Distal forearm fractures are the most common fractures in children. Three surgical techniques are most commonly used at the level of the radial diametaphysis on the distal forearm in children: K-wire, ascending ESIN (elastic stable intramedullary nail) or plate osteosynthesis. The aim of this study was to compare these procedures in children with distal diametaphyseal radius fractures regarding operative and functional outcome. Methods: A retrospective study was conducted in two level 1 trauma centers. Children and adolescents aged 2 to 15 years were included. The study period was from January 2010 to December 2022. The hospital information system was used to record patient age, gender, height, weight, fracture location, degree of angular deformity postoperatively, surgical procedure and postoperative complications, which were described in the medical records of the hospital information system. Complications graded by modified Clavien–Dindo–Sink served as the primary outcome. Reduction accuracy, operative and fluoroscopy times, immobilization length and postoperative motion were the secondary endpoints. Results: A total of 213 children were included in the study. K-wire osteosynthesis was performed in 25%, nailing in 19% and volar plate osteosynthesis in 55%. All ESIN were inserted in ascending technique. Complications occurred in 22% of patients and did not differ overall between techniques (p = 0.20). Severe complications were significantly more frequent after ESIN (20%) than after K-wires (7%) or plates (4%) (p = 0.04). Plate fixation achieved the most accurate alignment (≤5° angular deformity in 93% vs. 57% K-wires and 61% ESIN; p < 0.0001) and the fewest late motion restrictions (p = 0.02). K-wire surgery was fastest technique and required the least fluoroscopy, but necessitated the longest postoperative cast. Conclusions: Volar plating combines reliable anatomical reduction with a low rate of major complications and early mobilization, supporting its use in older children whose remodeling potential is limited. K-wires are a swift, minimally invasive option for younger patients, albeit with less precise reduction and prolonged immobilization. Conventional ESIN showed the highest burden of severe complications. Full article

Background: Hallux rigidus (HR) is a common forefoot disorder, and surgical treatment is typically guided by the severity of the condition, as defined by the Coughlin and Shurnas four-grade classification. This study aimed to compare clinical and functional outcomes in patients undergoing first metatarsophalangeal joint arthrodesis (FMTPJA) with or without the use of an interfragmentary (IF) screw in addition to a dorsal plate. Methods: We retrospectively evaluated a cohort of patients who underwent surgery with a FMTPJA, dividing patients in two groups: patients who underwent FMTPJA through dorsal plate associated with an interfragmentary screw (WIS group) and patients who underwent FMTPJA through dorsal plate without an interfragmentary screw (WOIS group). The primary outcomes were analyzed using the FAAM score and FAAM sport score. Secondary outcomes included VAS, patient satisfaction, recovery time to return to sports, and the level of postoperative sports activity compared to preoperative levels. Results: In paired analyses, the WOIS group showed statistically significant improvements in both the FAAM and FAAM sport scores (p = 0.01). In contrast, the WIS group showed significant improvement only in the FAAM sport score (p = 0.01), while the FAAM score did not reach statistical significance (p = 0.42). Multivariate analysis revealed that a higher preoperative FAAM score predicted a higher postoperative FAAM score (p = 0.75), while the use of an IF screw was associated with a lower expected postoperative FAAM score (p = 0.25). Increased BMI and older age were significantly associated with lower postoperative FAAM scores. Conclusions: Both surgical techniques led to significant clinical improvements. However, patients in the WOIS group showed a trend toward faster recovery and higher postoperative sports activity levels, particularly in the athletic population. Although no statistically significant differences were found between groups overall, these findings suggest potential benefits of avoiding an IF screw in selected patients. Further prospective studies are warranted to better delineate the clinical impact of screw usage in FMTPJA. Full article

In functionally graded polymer foam, mechanical properties and chemical composition vary in a prescribed direction according to a power law distribution. However, most manufacturing methods lack precise control over pore size, limiting their application. In this case, the graded foam structure can be formed from separate layers, with each layer assigned unique values in terms of mechanical properties or chemical composition based on the power law distribution. The hypothesis of the work is that the application of functionally graded (FG) foam materials inside the rotor blades or wings of an unmanned aerial vehicle can provide the ability to vary their stiffness properties. The aim of this work is to conduct an investigation of the static behaviour of a composite box plate with constant and variable heights that simulate the dimensions and changing profile of a helicopter rotor blade. In the numerical analysis, two models of composite box plate are considered and the material properties of graded polymeric foam core are assumed to vary continuously by the power law along the width of cross-sectional structures. It is not possible to model the continuous flow of graded properties through the foam in construction; therefore, the layers of foam are modelled using discontinuous gradients, where the gradient factor changes step by step. The numerical results are obtained using ANSYS software. The results of the numerical calculation showed that the use of graded foam affects the parameters under study. The stiffness of a structure significantly decreases with an increase in the power law index. Full article

The thick-walled thickness effect in layered-symmetrical structure is very important for considering the external thermal heating on the surface of functionally graded material (FGM) plates. Dynamic thermal vibration with advanced shear correction on the FGM plates are presented. The third-order shear deformation theory (TSDT) is included to calculate the values of advanced shear correction for the thick plates based on the displacement assumed in the middle symmetry plane. The values of advanced shear correction coefficient are in nonlinear variation with respect to the power-law index value for FGM. The dynamic stresses are calculated when the displacements and shear rotations are obtained for the given natural frequency of displacements, frequency of applied heat flux and time. The natural frequencies of sinusoidal displacements and shear rotations are obtained by using the determinant of the coefficient matrix in the fully homogeneous equation. Only the numerical dynamic results of displacements and stresses subjected to sinusoidal applied heat loads are investigated. The heating study in symmetry structure of FGMs to induce thermal vibration is interesting in the field of engineering and materials. The center displacements can withstand a higher temperature of 1000 K and a power-law index of 5, for which the length-to-thickness ratio 5 is better than that for 10. Full article

This work shows a three-dimensional (3D) layerwise model for static and free vibration analyses of functionally graded piezomagnetic materials (FGPM) spherical shell structures where magnetic and elastic fields are completely coupled. The 3D magneto-elastic governing equations for spherical shells are made of the three equations of equilibrium in three-dimensional form and the three-dimensional divergence equation for the magnetic induction. Governing equations are written in the orthogonal mixed curvilinear reference system ($\alpha$, $\beta$, z) allowing the analysis of several curved and flat geometries (plates, cylindrical shells and spherical shells) thanks to proper considerations of the radii of curvature. The static cases, actuator and sensor configurations and free vibration investigations are proposed. The resolution method uses the imposition of the Navier’s harmonic forms in the two in-plane directions and the exponential matrix methodology in the transverse normal direction. Single-layered and multilayered simply-supported FGPM structures have been investigated. In order to understand the behavior of FGPM structures, numerical values and trends along the thickness direction for displacements, stresses, magnetic potential, magnetic induction and free vibration modes are proposed. In the results section, a first assessment phase is proposed to demonstrate the validity of the formulation and to fix proper values for the convergence of results. Therefore, a new benchmark section is presented. Different cases are proposed for several material configurations, load boundary conditions and geometries. The possible effects involved in this problem (magneto-elastic coupling and effects related to embedded materials and thickness values of the layers) are discussed in depth for each thickness ratio. The innovative feature proposed in the present paper is the exact 3D study of magneto-elastic coupling effects in FGPM plates and shells for static and free vibration analyses by means of a unique and general formulation. Full article