Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method

Abstract

In this article, the buckling and post-buckling behaviours of a laminated composite spherical shallow shell panel embedded with shape memory alloy (SMA) fibres are studied under a thermal environment. System equations for a laminated composite spherical shell panel embedded with SMA fibres are for the first time derived by modelling the geometric non-linearity in the Green—Lagrange sense and the material non-linearity in SMA fibres in the framework of the higher-order shear deformation theory. The shell panel model is discretized by using a non-linear finite-element approach. The governing algebraic equations are then derived by the variational approach and solved using a direct iterative technique. Influences of the thickness ratio, boundary condition, aspect ratio, curvature ratio, lamination scheme, SMA volume fraction, percentage of prestrain, and amplitude ratio on the buckling and post-buckling temperatures of a laminated composite shell panel with and without SMA have been examined in detail. The results are computed using the present model and compared with those available in the literature.

A Lagrange Multiplier-based Technique within the Nonlinear Finite Element Method in Cracked Columns

“…A literature review on the thermal post-buckling subject using the FEM shows that the solution of the nonlinear thermal equilibrium equation is performed through two techniques: A) employing a direct iterative procedure without the linearization of the equation and without the determination of the tangent stiffness matrix [31], B) the linearization of the equilibrium equation and the determination of the tangent stiffness matrix [32]. Relations and results in this research work have been represented based on the second one.…”

Nonlinear stability of CNT-reinforced composite cylindrical panels with elastically restrained straight edges under combined thermomechanical loading conditions

“…Subsequently, putting equations (7) and (10,11) into the equations (17,18), then substituting solutions (27)(28)(29) into the obtained relations give a system of two equations relating to coefficients A 3 ; B 1 ; B 2 and a combination of these two equations and equation (30) yields…”

“…Panda and coworkers [4][5][6][7][8][9][10][11][12][13] used nonlinear finite element method to investigate nonlinear bending, vibration, buckling, and postbuckling behaviors of laminated composite flat and curved panels under thermal, mechanical, and thermomechanical loadings. Katariya et al 14,15 and Panda and Singh 16,17 analyzed the effects of shape memory alloy fibers on the buckling and postbuckling behaviors of laminated sandwich shallow shell structures subjected to mechanical and thermal loads. Nonlinear stability of thin and thick CPs made of ceramic-metal functionally graded (FG) material and subjected to mechanical and thermal loading conditions has been investigated in works 18,19 basing on an analytical approach.…”

The postbuckling behaviour of adhesively bonded stiffened panels subjected to in-plane shear loading

“…In the present model, hardening is introduced by changing the fixed yield stress σ 0 , so that, σ 0 becomes a function of the equivalent plastic strain, which leads to the following expression for yield function, f = σ e − σ 0 (ε ps ) (6) with, ε ps = ε ps dt…”

“…Tel./fax: +55 12 3947 5944. when submitted to large strains and displacements. This can only be achieved by considering the geometrical and material nonlinearities on the models formulation, as discussed by Panda and Singh [3][4][5][6].…”