Nonlinear finite element analysis of composite beams and arches using a large rotation theory

Abstract

Today's aerospace industry has advanced to the point of using optimum design techniques in virtually all applications. In structural elements, orthotropic fiber composite materials have emerged as lighter, stronger and a more easily manufactured solution to the material application aspect of design. Composites have the distinct advantage of being designed and built to many different desired specifications by varying materials, amount of matrix/fiber and orientation. As with many high performance applications, the analysis techniques of fiber composites are more complicated than for the simpler counterparts. This research has been directed to capturing large cross-sectional rotation incorporating a geometrically nonlinear finite element composite arch model. The model was derived and simplified from a (two-dimensional) 2-D shell theory that has been demonstrated to be accurate for large displacements and only moderate rotations. The current effort uses a similar potential energy based finite element model with through-the-thickness shear. Large rotation kinematics are derived in a vector format which includes a tangent function in the in-plane displacement relationship. Previously published research (Creaghan and Palazotto, 1994; Palazotto and Dennis, 1992) used a small angle approximation to simplify stiffness expressions, limiting those theories to moderate cross-sectional rotation angles. This tangent function is modeled by a series representation of the angle and thereby preserving the existing degrees of freedom. The approach decomposes the Green strain components into convenient forms for inclusion in the potential energy function which is then extended to a nonlinear finite element solution method. The potential energy is simplified by substituting the new rotation function for the previous rotation angle. Riks and displacement control are used to show solutions to several nonlinear arch problems. Other published analytical and experimental results are compared with the current research. This work is a simple extension of a previously published large displacement/moderate rotation theory (Creaghan and Palazotto, 1994), but the results show significant improvement when large cross sectional bending angles are present.