Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations

Abstract

This paper develops a computational model for nonlinear static bending analysis of functionally graded (FG) plates using a smoothed four-node quadrilateral element MISQ24 [1, 2] within the context of the first-order shear deformation theory (FSDT). In particular, the construction of the nonlinear geometric equations is based on Total Lagrangian approach in which motion at the present state compared with the initial state is considered large. Small strain–large displacement theory of von Karman will be used in nonlinear formulations of the smoothed quadrilateral element MISQ24 with drilling rotations. The drilling rotations are introduced to improve the coarse mesh accuracy of the MISQ24 element. The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton–Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these structures.