EPJ Web of Conferences
Volume 94, 2015DYMAT 2015 - 11th International Conference on the Mechanical and Physical Behaviour of Materials under Dynamic Loading
|Number of page(s)||6|
|Section||Modeling and Numerical Simulation|
|Published online||07 September 2015|
A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity
Research Institute for Mechanics, Lobachevsky State University of Nizhni Novgorod, 23 Prospekt Gagarina, Bld. 6, 603950 Nizhni Novgorod, Russia
a Corresponding author: Igumnov@mech.unn.ru
Published online: 7 September 2015
The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.
© Owned by the authors, published by EDP Sciences, 2015
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