An Indirect Trefftz Method to Model a Linear Elastic Halfspace

The linear elastic halfspace is split up into an interior domain, describing the soil in the vicinity to the structure, and an unbounded exterior domain. Both parts are solved in the frequency domain. To model the interior domain, an Indirect-Trefftz-Method is used. The solution for each element is obtained using a suitable set of shape functions, fulfilling the homogenous part of the differential equation a priori. Further constraints for the set involve the completeness regarding the considered problem. The used wave functions additionally ensure a good convergence behavior for the truncated set. Due to the global characteristics of the method, local effects influence all shape functions of a particular element. This requires a special treatment of local singularities as they might occur for external loads acting on a boundary or stress singularities at sharp corners. In contrary to classical Finite Element Approaches, the described Trefftz-Method uses a small number of convex elements, resulting in stiffness matrices that are considerably smaller but complex and fully populated. The exterior domain, describing the surrounding semi-infinite halfspace, is modelled by superposing fundamental systems using the Integral-Transfer-Method (ITM). Subsequently, the exterior ITM solution and the interior Trefftz solution are coupled in an indirect manner.     «

The linear elastic halfspace is split up into an interior domain, describing the soil in the vicinity to the structure, and an unbounded exterior domain. Both parts are solved in the frequency domain. To model the interior domain, an Indirect-Trefftz-Method is used. The solution for each element is obtained using a suitable set of shape functions, fulfilling the homogenous part of the differential equation a priori. Further constraints for the set involve the completeness regarding the consider...     »