Time-integrated mixed lagrangian formulation for time-discontinuous or impulsive loadingsand responses of structures

Different phenomena in mechanics often possess sharp gradients in time. In the analysis of such phenomena, traditional time integration schemes often require a very small time increment. In this paper, the equations of motion and the compatibility equations of rate of deformations, which were used to form the mixed Lagrangian formulation (MLF), are integrated with respect to time. This produces the momentum equations and the compatibility of deformations equations. The use of these equations in a framework similar to the MLF enables an accurate and stable analysis of various discontinuous phenomena using relatively large time increments.