The Domain-Boundary Element Method (DBEM) for hyperelastic and elastoplastic finite deformation: axisymmetric and 2D/3D problems

This paper presents the solution of geometrically nonlinear problems in sol id mechanics by the Domain-Boundary Element Method. Because of the Total-La grange approach, the arising domain and boundary integrals are evaluated in the undeformed configuration. Therefore, the system matrices remain unchan ged during the solution procedure, and their time-consuming computation nee ds to be performed only once. While the integral equations for axisymmetric finite deformation problems will be derived in detail, the basic ideas of the formulation in two and three dimensions can be found in [ 1]. The prese nt formulation includes torsional problems with finite deformations, where additional terms arise due to the curvilinear coordinate system. A Newton-R aphson scheme is used to solve the nonlinear set of equations. This involve s the solution of a large system of linear equations, which has been a very time-consuming task in former implementations, [1, 2]. In this work, an it erative solver, i.e. the generalized minimum residual method, is used withi n the Newton-Raphson algorithm, which leads to a significant reduction of t he computation time. Finally, numerical examples will be given for axisymme tric and two/three-dimensional problems.