Abstract
A three-dimensional dynamic model of a thermoelastic transversely isotropic medium is used to describe the thermoelastic deformation of materials with anisotropy of elastic properties with a selected direction of anisotropy. Such materials are layered and composite materials used in construction, mechanical engineering, aircraft and shipbuilding, soils in permafrost conditions, glaciers, as well as rocks (basalt, sandstone, marble, limestone, shale, and others). The study of this model, in particular, is relevant in connection with the use of 3D printers in construction. This is due to the fact that it is necessary to select the heating mode of the 3D printer head, in which cracks will not form during the cooling of the polystyrene concrete layers.We study this model using the group analysis methods, which is one of the most powerful and effective tools for obtaining exact solutions. The group stratification of the system of second-order differential equations defining this model is carried out. A system of first-order differential equations is obtained, which is equivalent to the equations of the original model. The solution describing a traveling wave for this system is obtained, that depends on arbitrary elements: parameters and function. For the specific sets of these elements, we study a deformation of a sphere and cube located inside a thermoelastic transversely isotropic medium with increasing time is found. The corresponding graphs are given.
Three-Dimensional Wave-Field Simulation in Heterogeneous Transversely Isotropic Medium with Irregular Free Surface