In this paper the authors derive a higher-order shear deformation theory for modeling functionally graded plates accounting for extensibility in the thickness direction. The explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera’s Unified Formulation. The static and eigenproblems are solved by collocation with radial basis functions. The efficiency of the present approach is assessed with numerical results including deflection, stresses, free vibration, and buckling of functionally graded isotropic plates and functionally graded sandwich plates.

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Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique

In this paper, an efficient and simple higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

Recent developments in finite element analysis for laminated composite plates

http://milad-engc.persiangig.com/Recent.pdf

Recent research advances on the dynamic analysis of composite shells: 2000-2009

A review of theories for the modeling and analysis of functionally graded plates and shells

https://www.civil.iitb.ac.in/~tkant/papers/TKant-IITB-JP093.pdf

Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells

https://www.civil.iitb.ac.in/~tkant/papers/TKant-IITB-JP097.pdf

Free vibration of composite and sandwich laminates with a higher-order facet shell element

Closed-form formulations of two-dimensional (2D) higher-order shear deformation theories (HOSTs) for the free vibration analysis of simply supported cross-ply laminated composite and sandwich doubly curved shells are presented. The formulation includes the Sander’s theory for doubly curved shells. Two of the HOSTs account for the effects of both transverse shear strains/stresses and the transverse normal strain/stress, while the third includes only the effects of transverse shear deformation. In these developments a realistic parabolic distribution of transverse shear strains through the shell thickness is assumed. The equations of motion are obtained using Hamilton’s principle. Solutions are obtained in closed-form using Navier’s technique and by solving the eigenvalue equations. Numerical results are presented for the natural frequencies of laminated composite and sandwich shallow shells. The closed-form solutions presented herein for laminated composite plates and shells are compared with the available...

Higher-order Closed-form Solutions for Free Vibration of Laminated Composite and Sandwich Shells

A simple C0 isoparametric finite element formulation based on a higher-order displacement model for the analysis of symmetric and unsymmetric, composite, and sandwich laminates subjected to a thermal gradient across the thickness is presented. The displacement model accounts for the nonlinear distribution of in-plane displacement components through the plate thickness, and the theory requires no shear correction coefficients. The nine-noded quadratic Lagrangian two-dimensional element is used with five and nine degrees of freedom per node. The accuracy of the formulation is verified by analyzing sample problems available in literature. Numerical results are presented in nondimensional form for symmetric, antisymmetric, and cross-ply laminates, both thick and thin.

Finite element thermal stress analysis of composite laminates using a higher-order theory

A simple Co isoparametric finite element model, based on a higher-order shear deformation theory is presented for the free vibration analysis of isotropic, orthotropic, and layered anisotropic composite and sandwich skew laminates. This theory incorporates a realistic nonlinear variation of displacements through the laminate thickness, and eliminates the use of shear correction coefficients. The boundary conditions on the skew edges are imposed through the suitable transformation of element matrices. The accuracy of the present model is demonstrated by comparing with alternative solutions available in the literature. Extensive numerical results are presented for natural frequencies of cross-ply and angle-ply skew laminates with various lamination parameters, skew angles, boundary conditions, and width-to-thickness ratios. New results on skew sandwiches are obtained for different lamination parameters and skew angles.

R. K. Khare

Papers

Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells

Free vibration of composite and sandwich laminates with a higher-order facet shell element

Higher-order Closed-form Solutions for Free Vibration of Laminated Composite and Sandwich Shells

Finite element thermal stress analysis of composite laminates using a higher-order theory

Free Vibration of Skew Fiber-reinforced Composite and Sandwich Laminates using a Shear Deformable Finite Element Model: