A new approach to dynamic condensation for FEM

Abstract

A new dynamic condensation model reduction (CMR) theory is implemented into a linear finite element environment, and applied to transient two-dimensional elasticity problems. This approach, which utilizes projection operators, avoids both the periodic media and global boundary layer restrictions which limit popular methods of homogenization/smoothing. This method is a general purpose approach that is applicable to heterogeneous media and allows dynamic degree of freedom (d.o.f.) reduction in a straightforward fashion without the introduction of additional approximations. The CMR algorithm is directly applicable to general second-order (in time) linear differential equations and has been coupled with both explicit and implicit FEM solvers in this work. The CMR method contains Guyan reduction as a special case. Numerical results and direct comparisons to Guyan reduction for two-dimensional wave propagation problems are made. In addition, the results indicate a relaxation of the Courant stability limit for explicit analysis, allowing larger time steps in the reduced models.