C0 Fixed Degrees of Freedom Zigzag Model with Variable In-Plane and Out-of-Plane Kinematics and Quadrilateral Plate Element

Abstract

Physically based, multilayered zigzag models have the merit of providing accurate stress predictions with few fixed unknowns, but unfortunately they involve derivatives of functional degrees of freedom (e.g., u,x, w,x, w,xxx, and so on). Here, a variable kinematics zigzag model with up to third-order derivatives always giving accurate predictions is considered in order to apply a technique that enables the conversion of derivatives of the unknowns. Such technique relies on energy updating concepts for finding closed form, modified expressions of displacements constituting the equivalent C0 model. From this model, a simple quadrilateral plate element with standard C0 interpolation functions is developed and tested. The first objective is finding a priori modified displacement fields that make the C0 zigzag model equivalent from the energy standpoint to its initial counterpart containing derivatives. Then a finite element is developed, whose structural model is equivalent from the energy standpoint to its counterpart with derivatives as variables. Comparisons with three-dimensional (3D) elasticity solutions of benchmark test cases and to an experiment show that the present element obtains accurate results.