A Variable-Step Central Difference Method for Structural Dynamics Analysis. Part I. Theoretical Aspects. Part II. Implementation and Performance Evaluation,
Abstract
Part I: Three major theoretical aspects of variable-step explicit integration procedures are proposed and analyzed. These include basic fixed-step integration formulas for no damping, diagonal damping and nondiagonal damping problems; the adjustment of the basic formulas to accommodate step changes; and, step size selection criteria. It is shown that the truncation error concept is not adequate to detect numerical instability for general structural dynamics analysis when low accuracy is requested. The 'apparent frequency' concept is introduced to maximize stable step sizes and is shown to be stable when low accuracy is requested. Part II: The variable-step central difference method developed in Part I is implemented as a stand-alone software package that is easily accessed by existing structural dynamics analyzers (i.e., finite-element, -difference discrete element computer codes) through a common data strucutre, input/output (I/O) manager and a few user-supplied control and interface routines. The performance of this package is evaluated through a computer study of four sample problems that embody a large class of response characteristics: linear to highly nonlinear; wave to structural to uncoupled component response; narrow to wide frequency spread; no damping to over-damping and accuracy-critical to numerical-stability-critical response. The present method is successful in meeting these response characteristics with effectiveness in all the above cases with the single exception of pure wave propagation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1979
- Accession Number
- ADA068598
Entities
People
- K. C. Park
- P. G. Underwood
Organizations
- Lockheed Martin Missiles and Space