Numerical Time Integration In Dynamics

S Shyam Sunder

doi:10.1117/12.939279

5 January 1984 Numerical Time Integration In Dynamics

S Shyam Sunder

Proceedings Volume 0450, Structural Mechanics of Optical Systems I; (1984) https://doi.org/10.1117/12.939279
Event: 1983 Cambridge Symposium, 1983, Cambridge, United States

Abstract

Numerical time integration methods for solving sets of simultaneous dynamic equilibrium equations are reviewed. Both mathematical and physical approximations are used in generating numerical solutions to the governing second-order differential equations. The resulting algorithms are classified into two basic categories: explicit (predictor) and implicit (corrector). Explicit methods are computationally efficient, but all explicit second-order accurate methods are only conditionally stable. On the other hand, many implicit methods are unconditionally stable, but may require iteration for convergence at each time step. For linear problems, implicit methods usually can be reduced to explicit form and iteration can be avoided. Methods which are unconditionally stable for linear problems may become unstable for nonlinear problems depending upon the manner in which nonlinearities are evaluated: exactly, or approximately using a pseudo-force or tangent modulus idealization. Methods which introduce numerical (or algorithmic) damping are used to eliminate "spurious" high frequency noise present in nonlinear, and sometimes even linear, structural dynamics problems. The question still remains whether the manner and extent of filtering at high frequencies is realistic. While attempts to develop new time integration algorithms synthesizing the better features of both explicit and implicit methods continue to be made, a basic controversy over the relative advantages and disadvantages of explicit and implicit schemes still exists.

Citation Download Citation

S Shyam Sunder "Numerical Time Integration In Dynamics", Proc. SPIE 0450, Structural Mechanics of Optical Systems I, (5 January 1984); https://doi.org/10.1117/12.939279

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KEYWORDS

Astatine

Algorithm development

Modal analysis

Nonlinear filtering

Numerical integration

Error analysis

Numerical analysis

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