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This study addresses a critical gap in the literature by investigating the static and natural frequency characteristics of functionally graded (FG) auxetic metamaterial annular plates reinforced with graphene origami (GOri), a novel area previously unexplored in the context of composite constructions, particularly for circular plates. The governing equations are derived utilizing higher-order shear deformation theory along with Hamilton’s principle, and solved using the finite element approach. For the first time, a comprehensive parametric study including the folding degree and mass fraction, and distribution pattern of GOri, is investigated on the static and natural frequency properties of annular plates. It is found that the natural frequency generally increased with higher mass fractions and decreased with greater folding degrees, though the X and V patterns at a 3% mass fraction showed an atypical increase in frequency with higher folding degrees. The impact of distribution patterns varied with weight fraction: the X-pattern caused the highest deflection at 1% weight fraction but the lowest at 3%, while the O-pattern caused the least deflection overall.

Large amplitude vibration problem of laminated composite spherical shell panel under combined temperature and moisture environment is analyzed in this paper. A general nonlinear mathematical model of laminated composite panel is developed based on higher-order shear deformation theory (HSDT) by taking the geometric nonlinearity in the Green–Lagrange sense. The sets of nonlinear governing differential equations are obtained using Hamilton’s principle and discretized via finite element steps. The nonlinear vibration responses are computed using a direct iterative method by incorporating hygral and/or temperature dependent material properties for laminated composite. The convergence behavior of the developed model has been checked and validated by comparing the responses with those available published results. Finally, some new examples are computed for different parameters (geometry, support condition and lamination scheme, etc.) and their effects on nonlinear free vibration responses under uneven environment are discussed.

The dynamic behavior of singly and doubly curved panels of the rectangular planar form subjected to different types of loadings is presented. The mathematical formulation is based on the higher order shear deformation theory, and the principle of virtual work is used to derive the equations of motion. The fast converging finite double Chebyshev series and Houbolt time-marching scheme are used for evaluating the dynamic response of the panel. The effect of the magnitude and duration of pulse loadings on the transverse central displacement and bending moment responses is evaluated for different parameters. The accuracy of the present solution methodology is established by the convergence study of non-dimensional central deflection and central moments and comparison of the present results with those available in the literature. Some new results are presented for the hyperboloid panels.

In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.

In this work, the dynamic behavior of the spherical magnetorheological elastomer (MRE) sandwich shell panel with multiwalled carbon nanotubes (MWCNT) reinforced composite face sheets is studied. The governing differential equation of motion for the (doubly curved) spherical sandwich shell panel is derived based on the Higher-Order Shear Deformation Theory (HSDT) kinematics. In the finite element framework, nine noded iso-parametric elements with nine Degrees of Freedom (DOFs) at each node are considered for solving the numerical problem. The finite element model of the multifunctional MR elastomer core spherical sandwich shell panel is validated against the existing works in terms of natural frequencies on different boundary conditions and magnetic field environment. The influence of MWCNT in the face sheet of the MR elastomer spherical sandwich shell panel is also studied through the structural rigidity. Detailed parametric investigations are performed to study the stiffness and damping characteristics of the shell panel with respect to the magnetic field intensities, thickness ratio, aspect ratio, ply orientation, and boundary conditions on the multifunctional MR elastomer core spherical sandwich shell panel. Also, the transverse vibration study of the MWCNT reinforced spherical sandwich shell with MR elastomer is carried out for different magnetic field intensities and curvatures to assess their effects on the structural performance. This study shows the applicability of the MR elastomer in sandwich shell structure for control of vibration and damping.

The research work presented in this paper is focused on the investigation of dynamic characteristics and optimum design of rotating laminated composite multi-walled carbon nanotubes-reinforced magnetorheological elastomer (MWCNT-MRE) sandwich plate. Higher-order shear deformation theory (HSDT) and finite element (FE) formulations are employed to derive the governing equations of the composite MWCNT-MRE sandwich plate. The performance of the derived numerical model is validated by comparing it with the results available in the published literature. The free and forced vibrations of the composite MWCNT-MRE sandwich plate are examined at different magnetic fields and rotating speeds. Also, the optimal ply orientations of the MWCNT-MRE sandwich plate are identified using the developed numerical model coupled with a genetic algorithm (GA) to enhance the natural frequencies and loss factors.

Thermal frequency responses of the hybrid laminated composite panel are theoretically computed using the finite element model and for the first time compared with in-house experimental data. The structural model for hybrid panel is derived using higher-order displacement polynomial functions (to maintain the necessary stress/strain continuity) and discretized through the isoparametric finite elements. Moreover, the elastic properties of the composite are evaluated suitably including thermal and physical parameters of the advanced fibers (Glass/Carbon/Kevlar) with the help of experimentations and numerical tool (via ABAQUS using mean-field homogenization). The variation of modal responses due to the change in temperature increment is computed through a generic computer code generated via the higher-order mathematical model. The numerical frequency values are compared with the earlier published numerical results and the experimentally recorded eigen frequencies. The experimental verifications related to the end boundaries indicate that the incorporation of the clamped boundary for one edge doubles the frequency, whereas the fraction of Kevlar fiber does not influence the stiffness (due to longitudinal modulus) parameter irrespective of the temperature change. Further, the conclusive understandings of the hybrid composite structural panel due to the inclusion of different advanced fibers and other design parameters (geometry, boundary and temperature) are deliberated in detail.

Based on a quasi-3D beam formulation, study on frequencies of bidirectional functionally graded (BDFG) curved porous beam in thermal environment is carried out. In severe thermal conditions, where BDFGs are considered to be highly efficient, temperature affects the properties of the BDFG beams. Consequently, this study focuses on the free vibration of porous BDFG curved beams by considering the effective temperature-dependent properties as a function of position across the thickness and thermal rise. The displacement field used contains indeterminate terms and involves a few variables to define. The mechanical characteristics of the curved beam are supposed to be temperature-dependent and graded in both axial and transverse direction depending on various porosity patterns. The governing equations of the simply supported curved porous beam are derived using the principal of virtual works and are then solved utilizing the Navier solution. The accuracy of the current formulation is tested by checking its results with other relevant publications found in the literature. Through a parametric study, we examine the impact of materials properties temperature-dependence, grading indexes, porosity distribution, radius of curvature and other parameters on the frequencies of curved bidirectional functionally graded porous beams. The results reveal that these parameters have a great influence on the free vibration response of porous BDFG curved beams. These results can serve as reference solutions for future investigations.

In this paper, the geometrically nonlinear transverse bending behavior of the shear deformable laminated composite spherical shell panel under hygro-thermo-mechanical loading is investigated. The laminated composite panel model has been developed mathematically based on the higher-order shear deformation theory and Green–Lagrange nonlinear strain kinematics. The material model is introduced through the micromechanical approach explicitly in terms of the matrix properties, the fiber properties, and the fiber volume fractions. Theoretical formulation is developed based on the hygrothermal dependent composite material properties to evaluate the corrugated behavior of the laminated structure. In addition to that, all the nonlinear higher-order terms arising in the strain displacement relation are included in the present formulation for accurate prediction of the flexural behavior. The desired nonlinear governing equations are obtained using the variational method and discretized with the help of suitable finite element steps. The desired responses are computed by solving the nonlinear equations numerically using the direct iterative method. The convergence behavior of the developed nonlinear numerical model has been checked and validated by comparing the responses with those available published literature. Finally, the effect of hygrothermal environment, geometrical and material parameters and the support conditions on the transverse bending behavior of the laminated composite curved shell panel have been highlighted by solving different numerical examples.

In the present paper, the flexural behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate is investigated under the combined thermo-mechanical load. The carbon nanotube reinforced composite plate has been modeled mathematically based on the higher order shear deformation theory. The governing differential equation of the FG-CNTRC plate is obtained using the variational method and discretized using the suitable isoparametric finite element steps and solved numerically through a computer code developed in MATLAB environment. The material properties of the carbon nanotube reinforced composite plate are assumed to be temperature dependent and graded in the thickness direction using different grading rules. The validity and the convergence behavior of the presently proposed numerical model have been checked by comparing the responses with results available in published literature and subsequent simulation model developed in ANSYS. The effect of various design parameters (aspect ratios, support conditions, thickness ratios, volume fractions, temperature load and types of grading) on the static, stress and deformation behavior of the FG-CNTRC plate are examined under the influence of different types of loading (uniformly distributed load, sinusoidally distributed load, uniformly distributed line load, sinusoidally distributed line load and point load) and discussed detail.

The bending responses of the delaminated composite curved (single and doubly) shallow shell panel computed numerically and validated with subsequent experimental results. The laminated shell panel model is developed mathematically with the help of two higher-order mid-plane theories and finite element method. The generalized governing equations of the shell panel model is obtained via the variational method and solved numerically using a home-made computer code developed in MATLAB. The consistency of the developed models has been established through the convergence test and validated by comparing the present numerical results with available published data including experimental values. The experimental bending results are obtained via three-point bend test of the fabricated woven Glass/Epoxy composite plate including the delamination (different size and location) and utilized for the comparison purpose. The numerical and experimental comparison reveals the necessity of the current higher-order models for the delaminated structure. In order to report the comprehensive conclusions related to the flexural strength of laminated structure with internal damage, a detailed parametric study has been carried out numerically and discussed in detail including the effect delamination (size, position and location).

The linear and nonlinear flexure analysis of laminated plates with twenty theories with the five variable higher order shear deformation theory (HSDT) is investigated using multiquadratic radial basis function based meshfree method. The mathematical formulation of the actual physical problem of the plate subjected to transverse loading is presented utilizing von Karman nonlinear kinematics. These non-linear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. The different results for deflection and stresses are obtained for thin to a thick plate and compared with some published results. It is observed that some of the theories taken here are well suited for analysis of thin as well as a thick plate while some theories are suited only for thin plates.

The effect of random system properties on thermal post-buckling temperature of laminated composite cylindrical shell panel with temperature independent (TID) and dependent (TD) material properties subjected to uniform temperature distribution is examined in this study. System properties such as material properties, thermal expansion coefficients and lamina plate thickness are modeled as independent basic random variables. The basic formulation is based on higher-order shear deformation (HSDT) theory with von-Karman nonlinearity using modified C⁰ continuty. A direct iterative-based C⁰ nonlinear finite element method (FEM) combined with Taylor series-based mean-centered first-order perturbation technique (FOPT) developed by the authors for composite plate is extended for shell panel with reasonable accuracy to compute second-order statistics of post-buckling temperature of cylindrical shell panel. Typical numerical results for second order statistics (mean and coefficient of variance) of thermal post-buckling temperature of laminated cylindrical shell panel are obtained through numerical examples for various support conditions, amplitude ratios, shell thickness ratios, aspect ratios, lamination lay-up sequences, curvature to length ratios, types of material properties with the effect of random system parameters. The performance of outlined approach has been validated with those results available in the literatures and independent MCS.

Dynamic instability analysis of laminated composite skew plate for different skew angles subjected to different type of linearly varying in-plane loadings is investigated. The analysis also includes the instability of skew plate under uniform bi-axial in-plane loading. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is mapped into a square plate over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Different boundary conditions of skew plate have been correctly incorporated by using Rayleigh–Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials (BCOPs). The boundaries of dynamic instability regions are traced by the periodic solution of governing differential equations (Mathieu type equations) with period T and 2T. The width of instability region for uniform loading is higher than various types of linearly varying loadings (keeping the same peak intensity). Effect of various parameters like skew angle, aspect ratio, span-to-thickness ratio, boundary conditions and static load factor on dynamic instability has been investigated.

The free vibration and flexural behavior of functionally graded carbon nanotube reinforced composite curved panel is investigated under uniform and linear thermal environment. The carbon nanotube reinforced composite curved panel has been modeled mathematically based on the higher-order shear deformation theory. The nanotube properties are assumed to be depended on the temperature and graded in the thickness direction using different grading rules. The governing equations for the static and vibration analysis of the functionally graded carbon nanotube reinforced composite panel are obtained using the variational method. Further, isoparametric finite element steps are implemented for the discretization of the governing equation and solved numerically via a specialized computer code developed in MATLAB environment. The rate of convergence and the validity of the presently developed numerical model have been checked. Finally, the effect of different geometrical and material parameters (thickness ratios, support conditions, volume fractions, thermal load, aspect ratios, and type of grading) on the free vibration and flexural behavior of functionally graded carbon nanotube reinforced composite are examined and discussed detail under thermal environment.

The higher-order kinematic theory in conjunction with Green–Lagrange strain field has been incorporated to compute the nonlinear frequency parameter of the curved (single/doubly) graded (functionally) sandwich panel structure numerically via finite element technique. The current sandwich panel model is derived assuming the functionally graded carbon nanotube face sheets and isotropic (epoxy) core. The current mathematical model is generic in nature, i.e., the grading configurations of the face sheets and sandwich construction including the different geometrical shapes can be achieved easily. The governing equation of the sandwich structure is obtained and the subsequent weak form derived with the help of the isoparametric finite element method. The nonlinear solutions are computed via an original computer code using a robust numerical method (direct iterative method). The consistency and the accuracy of the current finite element solutions are established by executing different types of numerical examples. Also, the concurrence of current numerical solution is established by comparing the results with the available benchmark solutions. Finally, the effect of various design parameters on the nonlinear natural frequency values have been computed under the uniform temperature environment and the inferences provided in detail.

This paper presents the second-order statistics of hygro-thermo-electrically-induced progressive failure in terms of first-ply failure load (FPFL) and last-ply failure load (LPFL) analysis for laminated composite material plate (LCMP) under out of plane mechanical loading with random system properties. Basic governing equation of nonlinear progressive failure analysis is based on shear deformation theory (higher order) with von-Karman nonlinear kinematics using Newton’s Raphson approach through Tsai–Wu failure criteria. The random input variables are assumed as uncorrelated type and are evaluated using second-order perturbation method (SOPT). Laminated composite plate with elliptical cutouts are subjected to uniformly distributed, point and hydrostatic load. The effect of boundary conditions, temperature variation, moisture content and voltage variations by utilizing piezoelectric layer position and various cutout shapes on the mean and corresponding covariance (COV) of FPFL and LPFL load are evaluated. Convergence of numerical analysis is performed, and results are validated with those available in literatures to check the efficiency of present methodology. It is observed that the presence of elliptical hole always causes an increase in the failure load of plates subjected to bending, even further increase for LPFL due to the reduction of stresses.

The free vibration frequency responses of the laminated composite structure with a cut-out of variable shapes (square/circular/elliptical), position (center/eccentric) and orientation (parallel/inclined) are investigated for the first time in this research including geometrical shapes. The eigenvalues are obtained computationally for the cut-out borne structure via a linear isoparametric finite element model of the composite structure in association with cubic-order of displacement kinematics. Also, a coupled code is prepared in MATLAB environment by joining the higher-order formulation and the simulation model (ABAQUS) to achieve the generic form to investigate the influential cut-out parameter (shape, size and position) on their eigenvalues. Further, a series of experimentations are carried out using the cut-out borne composite panel and compared with the computational frequency, including the experimental properties. Finally, the key behavior is surveyed through different kinds of numerical examples for various design constraint parameters including the cut-out relevant factors (shape, position and orientation) to show the subsequent inclusiveness of the proposed model.

The transient deflections of the functionally graded structure considering various types of patterns (power-law, sigmoid and exponential) are computed in this paper numerically using a higher-order shear deformation model. Also, the model includes variable distribution of porosity, i.e., the even and the uneven types, through the thickness direction ($z$-axis) of the graded panel. The transient deflection data are obtained computationally via a customized computer code prepared in MATLAB in association with Newmark’s constant acceleration-type time-integration technique. The model accuracy is checked by comparing the present time-dependent data with the published transient deflection values and the simulated results (modeled through a commercial package, ANSYS). Further, the effects of several design parameters (aspect ratio, thickness ratio, power exponent, porosity index, type of porosity, geometry and end-support conditions) on the transient deflection responses of the graded structure are computed through the derived numerical model.

This study reports the optimal frequencies and damping factor of the honeycomb sandwich composite plates. The sandwich panel face sheets have been considered as layered composite and honeycomb core. The higher-order shear deformation theory has been adopted to formulate the structural model and solve the governing equations of motion of sandwich structures to compute the frequencies. An optimal layout of the honeycomb composite laminated sandwich structure is being utilized to improvise both the fundamental natural frequencies and damping factors using a teaching–learning-centered artificial bee colony (TLABC). An experimental investigation is performed to demonstrate the effectiveness of the current TLABC algorithm to identify the optimal values by comparing them with numerically obtained results. Additionally, for the optimal layer sequences and the fiber orientations of the composite laminated plates, several optimization problems are developed with the objective functions of frequency maximization and modal damping factors (MDF). The TLABC algorithm integrated with finite element method has been utilized to evaluate the said responses. Hence, it is concluded that the efficient design layout of a honeycomb sandwich composite plate configurations would provide the guidelines for the designer to control the vibration effectively.