About | ECITTT | Conference Programme | Poster Abstracts (4.)
A NEW GENERALIZATION OF BOUNDARY ELEMENT METHODS
Dr-Ing Fabian Duddeck
FOR THE MODELLING OF COMPLEX MATERIALS
Lehrstuhl für Baumechanik, Technical University of Munich
Arcisstr 21, D-80469 Munich, Germany
Tel.: +49 (0)89-289-23994, Fax: +49 (0)89-289-28665
Complementary to FEM, Boundary Element Methods (BEM) have been established as a numerical tool for engineering problems. In contrast to FEM, only the boundary has to be discretized. Hence the modelling needs a comparatively low number of degrees of freedom, remeshing for crack propagation is relatively easy, and coupling of BEM-tools to CAE-programs is rather straightforward. If the newly developed Galerkin-version of the BEM is chosen, the coupling to FEM can easily be achieved.
One of the main drawbacks of the BEM lies in their restriction to simple material models (e.g. problems of 3D-anisotropy can not be modelled in a reasonable manner). Thus, we have developed a totally new BEM-approach via the Fourier transform which enables us to extend the Galerkin-BEM to almost all cases of physical interest. The method is based on the Fourier transform of the fundamental solution (which is known for all homogeneous problems) and not on the fundamental solution itself, unfortunately unknown for complicated materials and necessary for traditional BEM. We present the general approach for the heat conduction problem in 2D and 3D in detail. The transfer to linear isotropic and anisotropic elasticity and to plasticity is as well given as a Fourier-BEM for transient elastic and thermo-elastic problems. Further examples are taken from plate theory (Kirchhoff and Reissner) and piezo-electricity.