IMPLEMENTATION OF THE BOUNDARY-ELEMENT METHOD IN THE DYNAMICS OF FLEXIBLE BODIES

This paper presents the implementation of the Boundary Element Method in the dynamics of flexible multibody systems. Kane's equations are us ed to formulate the governing boundary initial value problem for an ar bitrary three-dimensional elastic body subjected to large overall base motion. Using continuum mechanics principles, direct boundary element incremental formulations are derived. The Galerkin approach was emplo yed to generate the weighted residual statement which serves as a tran sitory point between continuum mechanics and boundary integral equatio ns. By adapting the updated Langrangian formulation for large displace ments analysis and using the Maxwell-Betti reciprocal theorem, integra l representations for geometric stiffening were also derived. The non- linear terms were found to be functions of the time-variant stresses a ssociated with the inertial forces at the reference configuration. The domain integrals arising from body forces (such as gravitational load s, inertia loads and thermal loads, etc.) are presented as DRM integra ls (Dual-Reciprocity Method). Using the substructuring technique the e lastic body is divided into several regions leading to a system of equ ations whose matrices are sparse (block-banded). The linearized equati ons of motion were discretized along the boundary of the body, and an algorithm for the integration involving the Houbolt method was used to establish an algebraic system of pseudo-static equilibrium equations. A Newton-Raphson-type iteration scheme was used to solve these discre tized balance equations. To take advantage of the sparsity of the matr ices, special routines were used to decompose and solve the resulting linear system of equations. An illustrative example is presented to de monstrate the validity of the method as well as how the effects of geo metric stiffening effects are captured. The example consists of spin-u p manoeuvre of a tapered beam attached to a moving base. The beam was modelled as two-dimensional plane strain problem divided into a number of substructures. Numerical simulation results show how the phenomeno n of dynamic stiffening is captured by the present approach.