An Analysis of the Stability and Convergence Properties of a Crank-Nicholson Algorithm for Nonlinear Elasto-Dynamics Problems
The stability of nonlinear step by step computing schemes for solid mechanics problems can be insured by either requiring that the energy of the approximation be conserved or by insisting that the energy be bounded for all time. While techniques exist for analyzing conserving procedures, few analysis methods exist which are capable of establishing the boundedness of the energy of nonconserving computing schemes. In this paper an analysis procedure for demonstrating the stability and convergence of nonconserving step by step solution algorithms is introduced. As a typical example this technique is used to analyze a Crank-Nicholson-Galerkin algorithm for nonlinear elastodynamics problems.
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