Compurers d Swucrures Vol. 31, No. 6. pp. 907-912, 1989 Printed in Great Britain. 004577949/89 S3.00 + 0.00 0 1989 Pergamon Press plc A FINITE-ELEMENT MODEL FOR THE ANALYSIS OF THICK, ANISOTROPIC, BIMODULAR, FIBROUS-COMPOSITE PLATES FARAMARZ GORDANINEJAD Mechanical Engineering Department, University of Nevada-Reno, Reno, NV 89557, U.S.A. zyxwvutsrqponmlk (Received 22 March 1988) Abstract-A finite-element model is developed to analyze the behavior of a shear-deformable, bimodular, anisotropic plate with a uniform rectangular cross-section. The effect of shear-deformation is taken into account by assuming a linear variation for normal strains through the thickness of the plate. Results for transverse deflection and position of neutral surface are presented for a simply-supported plate under uniformly distributed load. The bending behavior is studied for different angles of fiber orientation, plate aspect ratios, and bimodularity ratios. NOMENCLATURE stretching stiffness (i, j = 1,2,6) shear stiffness (i, j = 4,s) length of plate bending-stretching stiffness width of plate bending stiffness Young’s moduli in directions x and y nodal force components longitudinal-transverse, longitudinal-thick- ness and transverse thickness shear moduli of orthotropic material thickness of plate shear correction factor elements of stiffness matrix number of nodes per element plane-stress-reduced stiffnesses distributed transverse pressure finite-element matrix coefficient total displacements in x, y, and z direction, respectively midsurface displacements in x, y, and z direction, respectively dimensionless transverse deflection plate coordinate system position of neutral surface generalized displacements strain in the fiber direction normal strains shear strains longitudinal-transverse Poisson’s ratio of orthotropic material angle of fiber orientation twisting curvature normal stresses shear stresses interpolation functions plate’s bending slopes in x and y direction, respectively 1. INTRODUCTION Within the last two decades, analysis of structures constructed from bimodular (or bimodulus) materials has received considerable attention. Bimodular material is referred to as a material which behaves differently under tension and compression loadings, and its nonlinear stress-strain curve is approximated by two straight lines: one in tension and the other in compression. Many man-made fibrous composites such as, graphite/epoxy and tire-cord rubber exhibit this behavior. Due to a large increase in the application of these materials, more sophisticated analysis becomes neces- sary to predict the behavior of structures constructed from Bimodular Composite Materials (BCM). The purpose of this study is to address the problem of anisotropy in the mechanics of bimodular fibrous composite plates. But first, we briefly review previous investigations on the analysis of BCM plates. Kamiya [l, 21 studied large deformation of thin, isotropic, clamped circular and rectangular plates by using finite difference and Galerkin methods, respect- ively. Singh et al. [3], also, reported the results for bending of a thin, isotropic bimodular plate as applied to rock mechanics. They determined the position of neutral surface of the plate by setting the total in-plane shear force equal to zero. Bert, Reddy and their co-workers extended Kamiya’s work to the analysis of thick, orthotropic laminated bimodular plate [4-71. They utilized fiber-governed compliance theory introduced by Bert [8] in their analysis to determine the position of neutral surface. Later, they extended their studies to thermal stress [9], vibration [lo] and transient response [l l] of orthotropic lami- nated BCM plates. Doong and Chen [12] addressed the problem of vibration of thick, orthotropic plates under combined bending and extensional stresses. Gordaninejad [13] studied the effect of shear-defor- mation on bending of orthotropic laminated BCM by implementing Reddy’s higher-order consistent shear-deformation theory [ 141. 907