Numerical solving dynamic problems of elastoplastic deformation of solids

Numerical schemes for solving two-dimensional dynamic problems of elasticity theory based upon several local approximations for each of the required functions are discussed. The schemes contain free parameters (dissipation constants). An explicit form of artificial dissipation of the solutions allows us to control its size and to effectively construct both explicit and implicit schemes. The principle of producing such schemes is applied to a plane dynamic problem of elasticity theory as an example. We describe a class of problems for which numerical algorithms using several local approximations for each of the required functions are constructed. Examples of solving practical problems are given.