Time Integration Procedures with Hybrid-Mixed Stress Finite Elements

This paper reports the implementation of an alternative time integration procedure for the dynamic analysis of structures based on the use of hybrid-mixed stress finite element models. In recent years, this approach has been successfully applied to the linear analysis of civil engineering structures [5,16], to the dynamic analysis of hydrated soft tissues [17] and to the elastodynamic analysis of saturated porous media [11]. The time integration algorithm discussed in this work corresponds to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthonormal Legendre polynomials are used to define the time approximation basis required by the model. A classical example with known analytical solution is presented to validate the model. The numerical efficiency of the numerical technique being discussed is then assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear [6,7,13] and nonlinear dynamics [10].