Polynomial shape functions and numerical methods for flexible multibody dynamics

摘要

The use of Taylor polynomials as shape functions in a Rayleigh-Ritz discretization of flexible beams in dynamic multi-body systems has been previously investigated (1,2). This approach is relatively simple, but it was found to cause some ill-conditioning problems in the numerical solution of the system equations. In this paper, two solutions to these problems are presented. First, better-behaved system equations can be obtained by using orthogonal Chebyshev or Legendre polynomials in place of Taylor polynomials. Secondly, a judicious choice of numerical solver can reduce or eliminate the ill-conditioning problems. Two examples are used to demonstrate these findings.