Mathematical Support for The Study of Three-Layer Rods Under Spatial Loads
Аннотация
This article is devoted to the development of mathematical support (software) for the study of three-layer rods under spatial loads. Variations in kinetic and potential energy and the work of external volumetric and surface forces of a three-layer rod are determined. The Ostrogradsky–Hamilton principle was applied to determine the variation of kinetic and potential energy and the work of external volumetric and surface forces. A system of equations for a three-layer rod vibration with corresponding generalized initial and natural boundary conditions is obtained. The problem is solved for six unknowns. To solve it, the authors used the central finite-difference relations of the implicit scheme of the finite-difference method of the second-order accuracy, considering the features of the boundary and initial conditions. By setting specific boundary conditions, several practical problems can be solved. A methodology and computational algorithm for calculating static and dynamic deformation processes of spatially loaded three-layer rods are presented. The results were obtained under specific boundary conditions. All results obtained are presented in the form of graphs.