Analysis of laminated composite plate/shell structures using a stabilized nodal-integrated quadrilateral element

Abstract

A new simple and accurate four-node quadrilateral element is developed for linear static and dynamic analysis of thin to moderately thick laminated, anisotropic plate/shell structures within the first-order shear deformation theory (FSDT). The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the conventional bilinear four-node quadrilateral finite element (Q4). The membrane and bending stiffness matrices are calculated on the boundaries of the smoothing cells while the shear term is evaluated by 2×2 Gaussian quadrature. This boundary integration, which is done on the smoothing element boundaries for the bending and membrane term, contributes to the preservation of high accuracy of the method even when elements are extremely distorted, for example, when two nodes are collapsed so that the quadrilateral becomes a triangle. Through several structural analysis examples, the simplicity, efficiency and reliability of the element are demonstrated. Convergence and comparison studies with the other existing solutions in the literature suggest that the present element is robust, computationally inexpensive, free of locking and could be the simplest displacement type element of its class. Its convergence properties are insensitive to mesh distortion, thickness-to-span ratio, stacking sequence and degree of anisotropy.