On computational stability of explicit schemes in nonlinear engineering dynamics

On computational stability of explicit schemes in nonlinear engineering dynamics

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Physical analysis of problems of engineering dynamics leads typically to hyperbolic systems of partial differential equations of evolution of 2nd order with some nonlinear terms, supplied with Dirichlet and Neumann boundary conditions together with some interface ones and with Cauchy initial conditions. Their numerical treatment needs coupling the finite element (or similar) method with the method of discretization in time. The preference of distributed and parallel computations for large problems, e. g. of multiple contacts of moving deformable bodies, stimulates the analysis of convergence and stability properties of explicit integration schemes, as simple, eective and robust as possible. This paper demonstrates such research direction, significant for practical calculations, on the conditional stability of a model simple explicit algorithm, motivated by the central difference method, implemented ad hoc e. g. in the LS-DYNA software package.

Physical analysis of problems of engineering dynamics leads typically to hyperbolic systems of partial differential equations of evolution of 2nd order with some nonlinear terms, supplied with Dirichlet and Neumann boundary conditions together with some interface ones and with Cauchy initial conditions. Their numerical treatment needs coupling the finite element (or similar) method with the method of discretization in time. The preference of distributed and parallel computations for large problems, e. g. of multiple contacts of moving deformable bodies, stimulates the analysis of convergence and stability properties of explicit integration schemes, as simple, eective and robust as possible. This paper demonstrates such research direction, significant for practical calculations, on the conditional stability of a model simple explicit algorithm, motivated by the central difference method, implemented ad hoc e. g. in the LS-DYNA software package.

finite difference method; computational dynamics

finite difference method; computational dynamics

VALA, J.; JAROŠOVÁ, P.

2024

01.09.2023

American Institute of Physics

Melville (USA)

978-0-7354-4182-8

ICNAAM 2021 Proceedings

2849

1

370004-1

370004-4

4

https://pubs.aip.org/aip/acp/article/2849/1/370004/2909204/