Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions

Abstract

The intent of the present study is to employ the extended Kantorovich method for semi-analytical solutions of laminated composite plates with arbitrary lamination and boundary conditions subjected to transverse loads. The method based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation theory, a laminated plate theory is developed. Using the principle of minimum total potential energy, two systems of coupled ordinary differential equations with constant coefficients are obtained. The equations are solved analytically by using the state-space approach. The results obtained are compared with the Levy-type solutions of cross-ply and antisymmetric angle-ply laminates with various admissible boundary conditions to verify the validity and accuracy of the present theory. Also, for other laminations and boundary conditions that there exist no Levy-type solutions the present results are compared with those obtained by other investigators and finite element method. It is found that the present results have very good agreements with those obtained by other methods.

Application of Adomian‐type method to solve rectangular laminated thick plates in bending

“…Results for and regarding uniform loading and SSSS boundary condition set are shown in Table . Comparing the results from the present methodology and those found in [], good agreement is found.…”

“…As one may observe, excellent agreement was found even for lower polynomial degrees in the interpolation functions, specially for high slenderness ratios (Table ). Figures – show graphically the convergence for another slenderness ratio () in CCCC plates and for all cases analysed, the convergence oscillations are inside the truncation error of Nik & Tahani . Table presented the results of plates with for several boundary conditions.…”

“…Umashee & Bhaskar have used the idea of superposing three different solutions so as to determine a fully clamped cross‐ply rectangular plate. Nik & Tahani have derived semi‐analytical solutions for thick laminated plates using the extended Kantorovich method and the state‐space approach. The obtained solution have well‐agreed to other laminated plate solutions.…”

Coupled stretching–bending analysis of laminated plates with corners via boundary elements

“…Good agreement was also observed in Fig. 6 between BEM4 and that presented in [28] by using the extended Kantorovich method. [20] and those calculated by the commercial finite element ANSYS using 256 shell elements was observed for BEM4.…”

Thermal Bending Analysis of Doubly Curved Composite Laminated Shell Panels with General Boundary Conditions and Laminations

“…Recent studies show that the multi-term extended Kantorovich method (MTEKM) has a great potential to solve two-dimensional elasticity problems with general boundary conditions and laminations (e.g., see [21][22][23]). For instance, the MTEKM successfully offers solutions for stress analysis of rectangular plates [21] and annular sector plates [22,23]. In this study, the MTEKM is used to find semi-analytical solutions for thermal bending of laminated shell panels with general boundary conditions and laminations.…”