A linear complementarity approach to the time integration of dynamic elastic–plastic structural problems

A new procedure for dealing with elastoplasticity during the time integration of multi degree of freedom (MDOF) structural problems in dynamics is developed and numerically implemented. It is shown here how the solution of MDOF elastic–plastic dynamics structural problems formulated in generalized variables, when piecewise linear yield functions are usually available, can be obtained utilizing any time integration technique—here the Newmark scheme is adopted—in conjunction with a linear complementarity problem (LCP) approach for dealing with plasticity. The same method could be extended to general 3D continuum dynamics problems with general yield conditions exploiting techniques developed in the past for the quasi-static case. The paper summarizes first the quasi-static problem in terms of a finite step LCP formulation; the elastic–plastic dynamic integration scheme is then formulated as an extension of the quasi-static LCP formulation. Two simple examples illustrate the effectiveness of the approach.