8-NODED ZIGZAG ELEMENT FOR DEFLECTION AND STRESS-ANALYSIS OF PLATES WITH GENERAL LAY-UP

Based on the kinematics of a third-order zig-zag plate model accountin g for the zero transverse shear stress conditions at upper and lower f ree surfaces irrespective for the lay-up, a eight-noded, 56 d.o.f. cur vilinear plate element is formulated and tested. Nodal parameters are membrane displacements, transverse shear rotations, deflections, slope s and curvatures for corner nodes, membrane displacements and transver se shear rotations for mid-side nodes. Suitably defining the parameter s appearing in the plate model, some higher-order plate elements, comp rising previous zig-zag elements and some smeared-laminate plate eleme nts, are obtained as particular cases. The benchmark problem is the cy lindrical bending of simply-supported, symmetric and antisymmetric cro ss-ply plates under a sinusoidally distributed transverse loading. The body of numerical results is as follows. Closed-form solutions for th e present plate model, together with the ones that can be particulariz ed in it, are given that provide analytical comparison results. Finite element results by the present element and by the ones that are parti cularized in it are compared with closed-form solutions and with the e xact three-dimensional elasticity solution, available for this benchma rk problem. A great importance of stress-free conditions appears when plates are thick and unsymmetric. This justify development of present element accounting for unsymmetry in the lay-up. The quadratic approxi mation makes the present element able to accurately predict stresses b y integrating local equilibrium equations. Inclusion of the layerwise kinematics of zig-zag models allows for satisfactory predictions of tr ansverse shear stresses via constitutive equations. Use of C-2 approxi mation for deflections, instead of C-1 approximation required for obta ining conforming elements, appear to little improve accuracy. (C) 1998 Elsevier Science Limited. All rights reserved.