Geometrically nonlinear formulation for the curved shell elements

Abstract

Abstract This paper presents a geometrically nonlinear formulation using total lagrangian approach for the three‐dimensional curved shell elements. The basic element geometry is constructed using the coordinates of the middle surface nodes and the mid‐surface nodal point normals. The element displacement field is described using three translations of the mid‐surface nodes and the two rotations about the local axes. The existing shell element formulations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper nonlinear functions representing the effects of nodal rotations. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements.