Solution of dynamic plasticity problems by using of the variables separation method based on the variational formulation

Method for solving dynamic problems of the mechanics of solids is proposed, which allows one to determine stress fields more accurately and thus offers better calculation of material damage. The essence of the method is the separation of variables. The spatial quasi-static problem is solved by the variational principle based on the weakening of constitutive equations and on the simultaneous variation of stress and kinematic fields. Tune-dependent parameters are found from a set of ordinary differential equations obtained with the application of a direct variational method. Solution of sample problem of perforation of a plate by a ball is fulfilled with the method proposed.