A finite-difference approximation of elastic forces on spaced Lagrangian grids is constructed, based on the method of support operators. For displacement vectors on irregular grids, on the topological and geometric structure of which minimal reasonable restrictions are imposed, the approximations of vector analysis operations are constructed in relation to difference schemes for problems of elasticity theory. Taking into account the energy balance of the medium, the constructed families of integrally consistent approximations of vector analysis operations are sufficient for discrete modeling of these processes. The schemes are considered, both using the stress tensor in an explicit form, and dividing it into spherical and shear components (pressure and deviator). The latter is used to construct homogeneous algorithms applicable to both the solid and the vaporized phase. The linear theory of elasticity is used for constructing approximations. The resulting forces in spatial geometry are obtained explicitly. Calculations of the sound waves propagation in a three-dimensional orthogonal aluminum plate due to end impact are presented. These calculations confirm the good quality of the difference schemes constructed in work.

support operator method, two- and three-dimensional conservative difference schemes, spaced Lagrangian grid

Mathematical modelling in actual problems of science and technics

Poveschenko Yuri Andreevich,  ,  orcid.org/0000-0001-9211-9057,  KIAM RAS

Krukovskiy Alexander Yur’evich,  ,  orcid.org/0000-0003-4188-6904,  KIAM RAS

Boykov Dmitri Sergeevich,  ,  orcid.org/0000-0001-8587-4994,  KIAM RAS

Podryga Victoria Olegovna,  ,  orcid.org/0000-0001-7874-6978,  KIAM RAS

Rahimly Parvin Ilgar gizi,  ,  orcid.org/0000-0002-9271-5956,  KIAM RAS