Polynomial shape functions and numerical methods for flexible multibody dynamics

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