Статьи в журналах
Dudko O.V., LaptevaA.A., Ragozina V.E. Solving nonstationary boundary value problems with piecewise linear boundary conditions for one-dimensional dynamics of deformable heteromodular elastic solid, AIP Conference Proceedings 2448, 020003 (2021)
Process of propagating one-dimensional deformations in a heteromodular isotropic elastic half-space under nonstationary boundary loading is under consideration. Nonstationary boundary problems are solved with using an algorithm based on piecewise linear approximation of nonlinear boundary conditions. It is shown that this approach preserves the physical nonlinearity of model and at the same time allows us to pass to a related sequence of simpler problems with analytical solutions; all these solutions together are an approximation of a continuous solution of the original problem. Earlier the question concerned with freedom of choice of the number and position of the nodes of the approximating function was investigated for various forms of boundary conditions. The paper presents the solution of one-dimensional boundary value problem for nonstationary loading the heteromodular half-space in the “tension – compression – stop” mode. It is shown that the solution can have several non-intersecting branches due to the various positions of nodes in the piecewise linear function of boundary motion.