Search Results (27)

In this paper, the nonlinear vibration (NV) response of carbon nanotube-reinforced composite (CNTRC) marine panels (MPs) fitted with symmetric multi-vibration absorbers (MVAs) subjected to steady, velocity-dependent hydrodynamic loads is investigated. To model actual marine conditions more realistically, the lift and drag forces varying with flow velocity were taken into account using experimentally supported Matveev-based formulations for a specific ship. Within the shell, three carbon nanotube (CNT) distribution schemes are considered: one uniformly distributed (UD) CNT configuration and two functionally graded (FG) CNT patterns, namely FG-V and FG-X. The analytical framework is further constructed using classical shell theory (CST) by incorporating geometric nonlinear terms, and the Galerkin technique is employed to obtain a reduced-order model. Thereafter, the NV response of the CNTRC-MPs is predicted through the P-T method, which relies on the joint application of the piecewise constant argument and Taylor series expansion. The results indicate that symmetric MVAs can effectively suppress NV behavior and significantly decrease the maximum NV amplitude of the panel. Moreover, the effectiveness of the proposed configuration is shown to depend on both the absorber characteristics and the reinforcement pattern of CNTs. The study demonstrates that the use of symmetric absorber systems offers a practical and efficient passive vibration-control solution for advanced marine composite panels. Full article

This paper delves into the free vibration analysis of a rotating non-uniform functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam with symmetric material distribution, taking into account boundary relaxation. Three common carbon nanotube (CNT) distributions, namely FG-X, UD, and FG-O, are considered. The governing equations of a rotating FG-CNTRC beam with variable cross-section and boundary relaxation are formulated via Hamilton’s principle. Some factors, including the centrifugal force induced by rotation, boundary relaxation, cross-section gradient, and others, substantially complicate the boundary conditions, making it challenging to directly obtain an analytical solution with variable coefficients. To address this, a novel power series solution based on the differential transformation method (DTM) is introduced to discretize the vibration equation and obtain the natural frequency of the rotating FG-CNTRC beam, which forms the core novelty of this study. Comprehensive numerical calculations are carried out, and the reliability of the DTM results is fully verified via comparisons with finite element (FEM) outputs and published reference data. Full article

This paper analyzes the vibrational characteristics of a novel sandwich plate configuration composed of an auxetic honeycomb (AH) core and laminated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets, hereafter referred to as the SD-AuCNT plate. Based on Reddy’s third-order shear deformation theory (SDT), which accurately accounts for transverse shear effects without requiring shear correction factors, the equations of motion are derived using Hamilton’s principle and subsequently solved using a pb-2 Ritz formulation combined with the Newmark time integration scheme for dynamic response analysis. By combining an auxetic core with negative Poisson’s ratio characteristics and laminated FG-CNTRC face sheets featuring tailored CNT distribution patterns and orientations, the hybrid SD-AuCNT plate can improve structural stiffness, energy absorption, and dynamic performance; however, it has not been thoroughly investigated in the existing literature. After verifying the accuracy of the proposed computational procedure, the effects of auxetic core geometry, CNT distribution patterns, thickness ratios, and boundary conditions on the natural frequencies and transient responses of the plate are comprehensively investigated. The results provide new insights into the dynamic behavior of advanced sandwich plates and offer practical guidance for the design of high-performance lightweight structures in aerospace, marine, defense, and other engineering applications. Full article

Functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are a novel breed of polymer nanocomposite, in which the nonuniform distribution of the carbon nanotube (CNT) reinforcement is adopted to maximize the macro-mechanical performance of the polymer with a lower content of CNTs. Composite conical–cylindrical combined shells (CCCSs) are widely utilized as loading-bearing components in various engineering applications, and a comprehensive understanding of the vibration characteristics of these shells under different external excitations and boundary conditions is crucial for engineering applications. In this study, the free vibration behaviors of FG-CNTRC CCCSs supported by an elastic foundation are examined using the Haar wavelet discretization method (HWDM). First, by means of the HWDM, the equations of motion of each shell segment, the continuity and boundary conditions are converted into a system of algebraic equations. Subsequently, the natural frequencies and modes of the CCCSs are achieved by calculating the resultant algebraic equations. The convergence and accuracy are evaluated, and the results demonstrate that the proposed method has stable convergence, high efficiency, and excellent accuracy. Furthermore, an exhaustive parametric investigation is conducted to reveal the effects of foundation stiffnesses, boundary conditions, material mechanical properties, and geometric parameters on the vibration characteristics of the FG-CNTRC CCCS. Full article

The buckling-like mechanical behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) structures is increasingly attracting research attention. However, buckling behavior has previously been studied separately as thermal buckling and mechanical buckling. In this context, this study investigates the buckling behavior of FG-GPLRC plates under combined thermal and mechanical loads. The coupled buckling problem is formulated according to the minimum potential energy theorem using first-order shear deformation theory (FSDT). In addition, the problem is approximated by the 2-D natural element method (NEM), and the resulting coupled eigen matrix equations are derived to compute the critical buckling temperature rise (CBTR) and the mechanical buckling load. The developed numerical method can solve thermal, mechanical, and coupled thermo-mechanical buckling problems, and its reliability is examined through convergence and benchmark tests. Using the developed numerical method, the buckling behavior of FG-GPLRC plates under thermal and mechanical buckling loads is examined in depth with respect to the key parameters. In addition, a comparison with functionally graded CNT-reinforced composite (FG-CNTRC) plates is also presented. Full article

This study introduces a novel analytical framework for investigating the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) elliptical cylindrical shells under arbitrary boundary conditions. Unlike previous studies that focused on simplified geometries or specific boundary conditions, this work combines the least-squares weighted residual method (LSWRM) with an adapted variational principle, addressing high-order vibration errors and ensuring continuity across structural segments. The material properties are modeled using an extended rule of mixtures, capturing the effects of carbon nanotube volume fractions and distribution types on structural dynamics. Additionally, virtual boundary techniques are employed to generalize elastic boundary conditions, enabling the analysis of complex boundary-constrained structures. Numerical validation against existing methods confirms the high accuracy of the proposed framework. Furthermore, the influence of geometric parameters, material characteristics, and boundary stiffness on vibration behavior is comprehensively explored, offering a robust and versatile tool for designing advanced FG-CNTRC structures. This innovative approach provides significant insights into the optimization of nanoscale reinforced composites, making it a valuable reference for engineers and researchers in aerospace, marine, and construction industries. Full article

This paper presents numerical investigations into the free vibration properties of a sandwich composite plate with two fiber-reinforced plastic (FRP) face sheets and a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) core made of functionally graded carbon nanotube-reinforced composite resting on Winkler/Pasternak elastic foundation. The material properties of the FG-CNTRC core are gradient change along the thickness direction with four distinct carbon nanotubes reinforcement distribution patterns. The Hamilton energy concept is used to develop the equations of motion, which are based on the high-order shear deformation theory (HSDT). The Navier method is then used to obtain the free vibration solutions. By contrasting the acquired results with those using finite elements and with the previous literature, the accuracy of the present approach is confirmed. Moreover, the effects of the modulus of elasticity, the carbon nanotube (CNT) volume fractions, the CNT distribution patterns, the gradient index p, the geometric parameters and the dimensionless natural frequencies’ elastic basis characteristics are examined. The results show that the FG-CNTRC sandwich composite plate has higher dimensionless frequencies than the functionally graded material (FGM) plate or sandwich plate. And the volume fraction of carbon nanotubes and other geometric factors significantly affect the dimensionless frequency of the sandwich composite plate. Full article

A phase-field crack model is developed for numerical analysis of thermal buckling and postbuckling behavior of a functionally graded (FG) graphene platelet-reinforced composite (FG-GPLRC) plate with a central crack. The inclined central crack is represented according to a stable, effective phase-field formulation (PFF) by introducing a virtual crack rotation. The problem is formulated using first-order shear deformation theory (SDT) incorporated with von Kármán geometric nonlinearity. And it is approximated by combining regular Laplace interpolation functions and crack-tip singular functions in the framework of the 2D extended natural element method (XNEM). Troublesome shear locking is suppressed by applying the concept of the MITC (mixed-interpolated tensorial components)3+ shell element to the present numerical method. The results demonstrate the effectiveness of this method in accurately predicting the critical buckling temperature rise (CBTR) and the thermal postbuckling path. In addition, the parametric results reveal that the CBTR and postbuckling path of the FG-GPLRC plate are distinct from those of the FG carbon nanotube-reinforced composite (FG-CNTRC) plate and remarkably affected by the parameters associated with the crack and graphene platelet (GPL). Full article

The buckling behavior of a functionally graded graphene-platelet-reinforced composite (FG-GPLRC) was traditionally investigated, mostly with respect to its undamaged structures. In this context, the current study investigated the buckling behavior of an FG-GPLRC cylindrical panel with an anti-symmetric central crack by introducing a 2-D extended natural element method (XNEM). The displacement was basically expressed with the first-order shear deformation theory (FSDT) and approximated using Laplace interpolation functions (for the non-singular displacement part) and crack-tip singular functions (for the singular displacement part) without grid refinement around the crack tips. The complex numerical manipulation on the curved shell surface was resolved by geometrically transforming the curved shell surface to a 2-D planar rectangular NEM grid. The painstaking numerical locking was suppressed by adopting the concept of a stabilized MITC3+ shell element. The validity of the developed numerical method was examined through a benchmark test, and the fundamental buckling loads of cracked FG-GPLRC cylindrical panels were investigated in depth by changing the major parameters. The numerical results also included a comparison with the FG-CNTRC. The numerical results indicated that the developed numerical method effectively predicts the buckling loads with reasonable accuracy, and that the fundamental buckling load of cracked FG-GPLRC cylindrical panels are remarkably influenced by the inclination angle and length of the crack as well as the other associated parameters. Full article

Functionally graded CNT (carbon nanotube)-reinforced composites (FG-CNTRCs) are intensively studied because the mechanical behaviors of conventional composites can be dramatically improved. Only a small amount of CNTs are appropriately distributed through the thickness. However, the studies on conical shell panels have been poorly reported when compared with beams, plates and cylindrical shells, even though more parameters are associated with the mechanical behaviors of conical shell panels. In this context, this study intends to profoundly investigate the free vibration of FG-CNTRC conical shell panels by developing an effective and reliable 2-D (two-dimensional) numerical method. The displacement field is expressed using the first-order shear deformation shell theory, and it is approximated by the 2-D planar natural element method (NEM). The conical shell surface is transformed into the 2-D planar NEM grid, and the approach for MITC3+shell element is employed to suppress the shear locking. The developed numerical method is validated through the benchmark experiments, and the free vibration responses of FG-CNTRC conical shell panels are investigated with respect to all the associated parameters. It is found from the numerical results that the free vibration of FG-CNTRC conical shell panels is significantly influenced by the volume fraction and distribution pattern of CNTs, the geometry parameters of the conical shell, and the boundary condition. Full article

This paper is concerned with the multi-objective optimization of thickness-wise CNT distribution in functionally graded porous CNT-reinforced composite (FG-porous CNTRC) beams. The mechanical behaviors of FG-porous CNTRC structures are strongly influenced by the thickness-wise distributions of CNTs and porosity. Nevertheless, several linear functions were simply adopted to represent the thickness-wise CNT distribution without considering the porosity distribution, so these assumed linear primitive CNT distribution patterns are not sufficient to respond to arbitrary loading and boundary conditions. In this context, this study presents the multi-objective optimization of thickness-wise CNT distribution in FG-CNTRC porous beams to simultaneously minimize the peak effective stress and the peak deflection. The multi-objective function is defined by the larger value between two normalized quantities and the design variable vector is composed of the layer-wise CNT volume fractions. The constrained multi-objective optimization problem is formulated by making use of the exterior penalty-function method and the aspiration-level adjustment. The proposed optimization method is demonstrated through the numerical experiments, and the optimization solutions are investigated with respect to the porosity distribution and the combination of aspiration levels for two single-objective functions. It is found from the numerical results that the optimum CNT distribution is significantly affected by the porosity distribution. Furthermore, the proposed method can be successfully used to seek an optimum CNT distribution within FG-porous CNTRC structures which simultaneously enhances the multi-objective functions. Full article

This paper combines third-order shear deformation theory (TSDT) and modified couple stress theory (MCST) with the principle of total potential energy to analyze the size-dependent buckling behavior of a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular microplate of variable thickness subject to non-uniform biaxial compression when resting on an elastic medium. To determine the thickness qualities of the material, the extended rule of mixture was applied. In the context of microplate buckling in the presence of small length scale effects, the three kinds of Carbon Nanotube (CNT) distribution—(a) UD, (b) FG-O, and (c) FG-X—were used and compared. The equations governing various combinations of simply supported or clamped boundary conditions have been solved using the differential quadrature method (DQM). The correctness and precision of the solutions have been compared to another study. A numerical study was conducted to examine the dependence of buckling load on several parameters, including percentage change of thickness, length scale parameter, nonuniform edge loads, boundary conditions, volume percentage of the CNTs, CNT distribution, and elastic medium parameter. The results of their effects are presented in this paper. Full article

This paper is concerned with the numerical optimization of the thickness-wise CNT (carbon nanotube) distribution in functionally graded CNT-reinforced composite (FG-CNTRC) beams to secure the structural safety. The FG-CNTRC in which CNTs are inserted according to the specific thickness-wise distribution pattern are extensively investigated for high-performance engineering applications. The mechanical behaviors of FG-CNTRC structures are definitely affected by the distribution pattern of CNTs through the thickness. Hence, the tailoring of suitable CNT distribution pattern is an essential subject in the design of FG-CNTRC structure for a given boundary and loading conditions. Nevertheless, the thickness-wise CNT distribution pattern has been assumed by several linear functions so that these assumed primitive patterns cannot appropriately respond to arbitrary loading and boundary conditions. In this context, this paper aims to introduce a numerical method for optimally tailoring the CNT distribution pattern of FG-CNTRC beams. As a preliminary stage, the effective stress is defined as the objective function and the layer-wise CNT volume fractions are chosen as the design variables. The exterior penalty-function method and golden section method are adopted for the optimization formulation, together with finite difference scheme for the design sensitivity analysis. The proposed optimization method is illustrated and validated through the benchmark experiments, such that it successfully provides an optimum CNT distribution which can significantly minimize the effective stress, with a stable and rapid convergence in the iterative optimization process. Full article

The combination of auxetic honeycomb and CNT reinforcement composite is expected to further improve the impact protection performance of sandwich structures. This paper studies the low-velocity impact response of sandwich plates with functionally graded carbon nanotubes reinforced composite (FG-CNTRC) face sheets and negative Poisson’s ratio (NPR) auxetic honeycomb core. The material properties of FG-CNTRC were obtained by the rule of mixture theory. The auxetic honeycomb core is made of Ti-6Al-4V. The governing equations are derived based on the first-order shear deformation theory and Hamilton’s principle. The nonlinear Hertz contact law is used to calculate the impact parameters. The Ritz method with Newmark’s time integration schemes is used to solve the response of the sandwich plates. The (20/−20/20)s, (45/−45/45)s and (70/−70/70)s stacking sequences of FG-CNTRC are considered. The effects of the gradient forms of FG-CNTRC surfaces, volume fractions of CNTs, impact velocities, temperatures, ratio of plate length, width and thickness of surface layers on the value of the plate center displacement, the recovery time of deformation, contact force and contact time of low-velocity impact were analyzed in detail. Full article

In this paper, the mechanical behavior of a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate is numerically investigated. According to the concept of a hierarchical model, the displacement is decomposed into the in-field functions and the assumed thickness-wise monomial. The former is defined on the plate midsurface and is approximated by the 2-D meshfree natural element method (NEM). The FG-CNTRC plate is modeled as a homogenized orthotropic body, and its effective elastic properties are determined by referring to MD simulation and the linear rule of mixtures. Regarding the thickness-wise distribution of CNTs, one uniform and three functionally gradient distributions are taken. Through comparative numerical experiments, the reliability of the numerical method is justified with the maximum relative difference of 6.12%. The effects of the volume fraction and vertical distribution of CNTs, the plate width-thickness and aspect ratios, and the boundary conditions on the bending, free vibration, and buckling behaviors of FG-CNTRC plates are examined. It is found that the mechanical behavior of FG-CNTRC plates is significantly dependent of these major parameters. Full article