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The purpose of this study is the comprehensive numerical assessment of multidirectional (1D/2D/3D) functionally graded composite panel structures with different material gradation patterns and degrees of material heterogeneity. Here, deformation characteristics are obtained under different loading and support conditions.

The finite element solutions of multidirectional functionally graded composite panels subjected to uniform and sinusoidal transverse loads are presented under different support conditions. Here, different functionally graded composites, such as unidirectional (1D) and multidirectional (2D/3D), are considered by distributing constituent materials in one, two and three directions, respectively, using single and multivariable power-law functions. A constitutive model with fully spatial-dependent elastic stiffness is developed, whereas the kinematics of the present structure is defined using equivalent single-layer higher-order theory. The weak form, based on the principle of virtual work, is established and solved consequently using isoparametric finite element approximations via quadrilateral Lagrangian elements.

The appropriate mesh-refinement process is carried out to achieve the mesh convergence; whereas, the correctness of proposed heterogeneous model is confirmed through a verification test. The comprehensive numerical assessment of multidirectional functionally graded panels under various loading and support conditions depicts the importance of degree of material heterogeneity with different gradation patterns and volume-fraction exponents.

A comprehensive analysis on the deformation behaviour of 1D-functionally graded materials (FGMs) (X-FGM, Y-FGM and Z-FGM), 2D-FGMs (XY-FGM, YZ-FGM and XZ-FGM) and 3D-FGM composite panels FGM structures is presented. Multifaceted heterogeneous FGMs are modelled by varying constituent materials in one, two and three directions, using power-law functions. The constitutive model of multi-directional FGM is developed using fully spatial-dependent elastic matrix and higher-order kinematics. Isoparametric 2D finite element formulation is adopted using quadrilateral Lagrangian elements to model 1D/2D/3D-FGM structures and to obtain their deflection responses under different loading and support conditions.

The purpose of this paper is to analyse the nonlinear flexural behaviour of laminated curved panel under uniformly distributed load. The study has been extended to analyse different types of shell panels by employing the newly developed nonlinear mathematical model.

The authors have developed a novel nonlinear mathematical model based on the higher order shear deformation theory for laminated curved panel by taking the geometric nonlinearity in Green-Lagrange sense. In addition to that all the nonlinear higher order terms are considered in the present formulation for more accurate prediction of the flexural behaviour of laminated panels. The sets of nonlinear governing equations are obtained using variational principle and discretised using nonlinear finite element steps. Finally, the nonlinear responses are computed through the direct iterative method for shell panels of various geometries (spherical/cylindrical/hyperboloid/elliptical).

The importance of the present numerical model for small strain large deformation problems has been demonstrated through the convergence and the comparison studies. The results give insight into the laminated composite panel behaviour under mechanical loading and their deformation behaviour. The effects of different design parameters and the shell geometries on the flexural responses of the laminated curved structures are analysed in detailed. It is also observed that the present numerical model are realistic in nature as compared to other available mathematical model for the nonlinear analysis of the laminated structure.

A novel nonlinear mathematical model is developed first time to address the severe geometrical nonlinearity for curved laminated structures. The outcome from this paper can be utilized for the design of the laminated structures under real life circumstances.