A geometric and material nonlinear plate and shell element

Abstract

A displacement-based versatile and effective finite element is presented for linear and geometric and material nonlinear analysis of plates and shells. The element is formulated by interpolating the element geometry using the mid-surface nodal point coordinates and mid-surface nodal point normals. A total and an updated Lagrangian formulation are presented, that allow very large displacements and rotations. In linear analysis of plates, the element reduces to well-established plate bending elements based on classical plate theory, whereas in linear analysis of shells and geometrically nonlinear analysis of plates and shells by use of the element, in essence, a very general shell theory is employed. The element has been implemented as a variable-number-nodes element and can also be employed as a fully compatible transition element to model shell intersections and shell-solid regions. In the paper various sample solutions are presented that illustrate the effectiveness of the element in practical analysis.