Eight-noded zig-zag element for deflection and stress analysis of plates with general lay-up

Abstract

Abstract Based on the kinematics of a third-order zig-zag plate model accounting for the zero transverse shear stress conditions at upper and lower free surfaces irrespective for the lay-up, a eight-noded, 56 d.o.f. curvilinear plate element is formulated and tested. Nodal parameters are membrane displacements, transverse shear rotations, deflections, slopes and curvatures for corner nodes, membrane displacements and transverse shear rotations for mid-side nodes. Suitably defining the parameters appearing in the plate model, some higher-order plate elements, comprising previous zig-zag elements and some smeared-laminate plate elements, are obtained as particular cases. The benchmark problem is the cylindrical bending of simply-supported, symmetric and antisymmetric cross-ply plates under a sinusoidally distributed transverse loading. The body of numerical results is as follows. Closed-form solutions for the present plate model, together with the ones that can be particularized in it, are given that provide analytical comparison results. Finite element results by the present element and by the ones that are particularized in it are compared with closed-form solutions and with the exact three-dimensional elasticity solution, available for this benchmark 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 approximation makes the present element able to accurately predict stresses by integrating local equilibrium equations. Inclusion of the layerwise kinematics of zig-zag models allows for satisfactory predictions of transverse shear stresses via constitutive equations. Use of C 2 approximation for deflections, instead of C 1 approximation required for obtaining conforming elements, appear to little improve accuracy.