A BEM-formulation applied to the solution of nonlinear dynamic problems

A semi-analytical time-integration procedure is presented for the integration of discretized dynamic mechanical systems. This method utilizes the advantages of the boundary element method, well known from quasi-static field problems. Motivated by these spatial formulations, the present dynamic method is based on influence functions in time, and gives exact solutions in the linear time-invariant case. Similar to domain-type BEM's for nonlinear field problems, the method is extended for different nonlinear dynamic systems having nonclassical damping. The numerical stability and accuracy of the semi-analytical method is discussed in two steps for the nonclassical damping and for the nonlinear restoring forces. The Duffing oscillator and a system with nonclassical damping are used as representative model problems. A comparison is given to other conventionally used time integration procedures, which shows the efficiency of the present method.