A new variational self-regular traction-BEM formulation for inter-element continuity of displacement derivatives.

*(English)*Zbl 1038.74665Summary: In this work, a non-symmetric variational approach is derived to enforce \(C^{1,\alpha}\) continuity at inter-element nodes for the self-regular traction-BIE. This variational approach uses only Lagrangian \(C^0\) elements. Two separate algorithms are derived. The first one enforces \(C^{1,\alpha}\) continuity at smooth inter-element nodes, and the second enforces continuity of displacement derivatives in global coordinates at corner nodes, where \(C^{1,\alpha}\) continuity cannot be enforced. The variational formulation for the traction-BIE is implemented in this work for two elastostatics problems with various discretizations and polynomial interpolants. Local and global measures of the discretization error are obtained by means of an error estimator recently derived by the authors. Comparisons are also made with the displacement-BIE, which does not require \(C ^{1,\alpha }\) continuity for the displacement. The lack of smoothness of the displacement derivatives at the inter-element nodes is shown to be an important source of both local and global error for the traction-BIE formulation, especially for quadratic elements. The accuracy of the boundary solution obtained from the traction-BIE improves significantly when \(C^{1,\alpha}\) continuity is enforced where possible, i.e., at the smooth inter-element nodes only.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |