Boundary Element Method with Runge-Kutta Convolution Quadrature for Three-Dimensional Dynamic Poroelasticity

Abstract:

The paper contains a brief introduction to the state of the art in poroelasticity models, in BIE & BEM methods application to solve dynamic problems in Laplace domain. Convolution Quadrature Method is formulated, as well as Runge-Kutta convolution quadrature modification and scheme with a key based on the highly oscillatory quadrature principles. Several approaches to Laplace transform inversion, including based on traditional Euler stepping scheme and Runge-Kutta stepping schemes, are numerically compared. A BIE system of direct approach in Laplace domain is used together with the discretization technique based on the collocation method. The boundary is discretized with the quadrilateral 8-node biquadratic elements. Generalized boundary functions are approximated with the help of the Goldshteyn’s displacement-stress matched model. The time-stepping scheme can rely on the application of convolution theorem as well as integration theorem. By means of the developed software the following 3d poroelastodynamic problem were numerically treated: a Heaviside-shaped longitudinal load acting on the face of a column.

• Periodical: Applied Mechanics and Materials (Volume 709)
• Pages: 101-104
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.709.101
• Online since: December 2014
• Authors: L.A. Igumnov, I.V. Vorobtsov, Svetlana Litvinchuk
• Keywords: 3D, BEM, Convolution Quadrature, Dynamic, Poroelasticity, Runge-Kutta Methods

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