New three-dimensional time-stepping transient fundamental solutions with applications

In this paper, alternative static-like fundamental solutions for transient dynamic analysis of three-dimensional elasticity are developed. The new formulation is based on modification of Navier's equations of elastodynamics by expressing the acceleration in terms of the displacements at different time steps using suitable finite difference scheme. The new fundamental solutions are derived via operator decoupling technique. The displacements from the previous steps are used to form the new generalized inertia terms. The new fundamental solutions are used to solve non-homogeneous media by dividing the continuous media into multi regions. The stiffness and load vector of each region are calculated using the boundary integral equation approach. Then, the whole multi-region system is solved as super finite elements. Numerical examples are solved to demonstrate the validation of the proposed solutions. The results of the proposed solutions are more stable and accurate than those of previous time domain and dual reciprocity formulations.

Automated summary

In this paper, alternative static-like fundamental solutions for transient dynamic analysis of three-dimensional elasticity are developed by modifying Navier's equations of elastodynamics and using a suitable finite difference scheme. The new fundamental solutions are derived using operator decoupling technique and are used to solve non-homogeneous media by dividing them into multi regions. The stiffness and load vector of each region are calculated using the boundary integral equation approach. The proposed solutions are more stable and accurate than previous time domain and dual reciprocity formulations, as demonstrated by numerical examples.