Large Deformation Theory Using Truncated Rotations

by Daniel A. Miller, Air Force Inst of Technology, Dayton, United States,
Anthony N. Palazotto, Air Force Inst of Technology, Dayton, United States,

Document Type: Proceeding Paper

Part of: Engineering, Construction, and Operations in Space IV


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. Couple a more complex material with some geometrically complex structures and a significant engineering challenge arises. This research has been directed to capturing large cross-sectional rotation incorporating a geometrically nonlinear finite element composite arch model. An existing FORTRAN code was initially used and modified. It was simplified and derived from 2-D shell theory that has been demonstrated to be accurate for large displacements and 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. This tangent function is modeled by using a series representation 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. 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.

Subject Headings: Composite materials | Finite element method | Rotation | Deformation (mechanics) | Nonlinear finite element analysis | Fiber reinforced composites | Construction materials

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