GURTIN-TYPE QUASI-VARIATIONAL PRINCIPLE FOR LARGE DEFORMATION ELASTO-DYNAMICS BASED ON BASE FORCES THEORY

摘要

Considering that “gap function” is a nuisance term that contains both the stress and the quadratic function of displacement, it is difficult to establish Gurtin-type variational principles for large deformation elasto-dynamics. Luo En, Finlayson B. A. and Scriven L. established Gurtin-type variational principles by restricted variational idea. Based on base forces theory framework, the basic equations for large deformation elasto-dynamics are defined. Using the concept of base forces, Gurtin-type quasi-variational principle for large deformation elasto-dynamics can be established by variational integral method directly. When the base forces and the conjugate variable “displacement gradients” are taken as the basic unknowns, there is no “gap function” in the functional of Gurtin-type quasi-variational principle. Then quasi-stationary value conditions of Gurtin-type quasi-variational principle are derived. One of the quasi-stationary value conditions is the famous wave equation. Finally, some correlative problems are discussed.