NONLINEAR FINITE-ELEMENT ANALYSIS OF COMPOSITE BEAMS AND ARCHES USINGA LARGE ROTATION THEORY

Today's aerospace industry has advanced to the point of using optimum design techniques in virtually all applications. In structural element s, orthotropic fiber composite materials have emerged as lighter, stro nger and a more easily manufactured solution to the material applicati on aspect of design. Composites have the distinct advantage of being d esigned and built to many different desired specifications by varying materials, amount of matrix/fiber and orientation. As with many high p erformance applications, the analysis techniques of fiber composites a re more complicated than for the simpler counterparts. This research h as been directed to capturing large cross-sectional rotation incorpora ting a geometrically nonlinear finite element composite arch model. Th e model was derived and simplified from a (two-dimensional) 2-D shell theory that has been demonstrated to be accurate for large displacemen ts and only moderate rotations. The current effort uses a similar pote ntial energy based finite element model with through-the-thickness she ar. Large rotation kinematics are derived in a vector format which inc ludes a tangent function in the in-plane displacement relationship. Pr eviously published research (Creaghan and Palazotto, 1994; Palazotto a nd Dennis, 1992) used a small angle approximation to simplify stiffnes s expressions, limiting those theories to moderate cross-sectional rot ation angles. This tangent function is modeled by a series representat ion of the angle and thereby preserving the existing degrees of freedo m. The approach decomposes the Green strain components into convenient forms for inclusion in the potential energy function which is then ex tended to a nonlinear finite element solution method. The potential en ergy is simplified by substituting the new rotation function for the p revious rotation angle. Riks and displacement control are used to show solutions to several nonlinear arch problems. Other published analyti cal and experimental results are compared with the current research. T his work is a simple extension of a previously published large displac ement/moderate rotation theory (Creaghan and Palazotto, 1994), but the results show significant improvement when large cross sectional bendi ng angles are present.