Application of a fundamental solution to a problem operator for modeling vibrations of elastically supported load-bearing structures

Abstract

The work is devoted to the construction of effective computational algorithms for modeling vibrations of elastically supported load-bearing systems. An approach is developed based on the representation of a mathematical model in the form of partial differential equations for generalized functions. With this approach, the presence of elements with a very high stiffness in the design made it necessary to carry out the calculation with a very small time step. To build a computational algorithm, a fundamental solution to the problem operator is used, which allows one to obtain a solution at the next time step for each point of the spatial grid independently. The need to carry out the calculation with a very small time step arises only in nodes that coincide with the location of structural elements with very high stiffness. The proposed approach allows simulating impact forces and instantaneous change of boundary conditions. The possibility of using the model with an absolutely rigid restraining support as a limit transition from a model of elastic bond of high rigidity was researched on.