Abstract
A boundary element formulation for 3D-elastostatics and 3D-elastodynamics is presented which avoids singular boundary integrals. The proposed method is based on a generalized variational principle. A weighted superposition of static fundamental solutions is used for the field approximation in the domain, whereas the displacement and stress field on the boundary are interpolated by well-known polynomial shape functions. By separating time-and space-dependence a symmetric equation of motion is derived with time-independent mass and stiffness matrix. The domain integral over inertia terms, leading to the mass matrix, is analytically transformed to the boundary. Thus, a boundary only formulation is derived. Comparing numerical results with analytical solutions clearly shows that the obtained system of equations is well-suited for dynamic problems.
Support by the Deutsche Forschungsgemeinschaft DFG of the Graduate Collegium ‘Modelling and dis- cretization methods for continua and fluids’ at the University of Stuttgart is gratefully acknowledged.
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Gaul, L., Moser, F. (2002). A Hybrid Boundary Element Approach without Singular Boundary Integrals. In: Kompiš, V. (eds) Selected Topics in Boundary Integral Formulations for Solids and Fluids. International Centre for Mechanical Sciences, vol 433. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2548-9_10
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DOI: https://doi.org/10.1007/978-3-7091-2548-9_10
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83693-4
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