BEM/FEM non-linear model applied to transient analysis with viscous damping

Abstract

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented

Alternative time marching process for BEM and FEM viscoelastic analysis

“…where K and C give the in uences of viscosity and friction, respectively, on the global movement time di erential equation (32); K, M and G are the usual sti ness, mass and consistent lumping matrices [20]. For ÿnite element formulations applied to dynamic analysis, Equation (32) is usually integrated by adopting the Newmark ÿ method or other equivalent technique.…”

“…By introducing those values into Equation (35) and applying again the divergence theorem, the following integral equation is found [20][21][22]:…”

“…Expression (38) is the well-known boundary integral equation for dynamic problems based on the static fundamental solution [20][21][22], in which the new friction and viscous damping domain integrals have been incorporated. Equation (38) can now be approached by assuming boundary and cell values approximated by:…”

“…The time di erential equation (45) can be integrated in time following the Houbolt scheme, that has already proved to be appropriate for boundary element dynamic analysis [20][21][22]. When the dynamic e ects, for any reasons, do not a ect the solution, matrix M can be neglected.…”

“…where K and C give the in uences of viscosity and friction, respectively, on the global movement time di erential equation (32); K, M and G are the usual sti ness, mass and consistent lumping matrices [20].…”