The Simulation of Deformable Mechanical Systems Using Vector Processors.

This thesis presents a formulation for simulating systems of deformable bodies undergoing large, nonlinear motion using vector processors. For algorithms tailored to them, vector processors, such as the Cray-1 and Cyber-205, offer better computational rates than scalar processors. The equations of motion in three dimensions are derived from Cauchy's first law of motion by using the finite element method. By introducing an appropriate set of quasi-coordinates and the canonical momenta as variables, arbitrary mechanical systems are represented with a mixture of simple algebraic and first order differential equations. The general formulation is specialized and simplified by representing linearly elastic bodies as truncated series of their vibrational modes. A generalized program, named DAVES, for three-dimensional problems based on the formulation for linearly elastic and rigid bodies is documented. The program is self formulating in the sense that the equations are automatically generated from a description of the bodies, joints, and applied forces in the system. Numerical solutions are obtained by using Gear's stiff integration method with an explicit Jacobian. At the end of the thesis, example problems are solved and compared to the solutions in the literature.PhDMechanical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/159701/1/8402240.pd