Stability Analysis of Linear and Nonlinear Dynamic Finite Element Method Programs.
Final rept. Oct 72-Jun 73,
ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG MS
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Linear and nonlinear dynamic finite element method FEM solution schemes are analyzed for stability in this report. Because of the diversity in techniques, representative methods are selected. For the linear case, a stability analysis in a way not heretofore done is performed for the extended Wilson linear acceleration, direct integration type scheme. This method is used in the program commonly known as FEAR. The effect of damping of the form C alpha M beta K is also studied. For the nonlinear case, the nonlinear version of FEAR NOFEAR is studied. The linear stability analysis techniques are applied to this solution scheme to determine the extent of usefulness of the linear techniques in the nonlinear realm. FEAR and NOFEAR are U. S. Army Engineer Waterways Experiment Station WES code names for two computer programs written by Wilson and modified by WES that use the direct integration techniques analyzed for stability in this report. The research reported is basic and theoretical in nature.
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