Controlling errors in the process of automating boundary element method analysis

An hpr-mesh refinement algorithm for BEM

“…The error in stress concentration factor also rapidly decreases from a 8.18% for the coarse starting mesh to an error of 0.03% for the refined mesh after two mesh refinement. Further mesh refinements decrease the mesh error e R but the error in stress concentration factor increases, emphasizing that the mesh error is only one source of error among the many in BEM analysis as was discussed by Vable [13]. Thus, caution must be exercised in interpretation of results, as low mesh error does not imply low error in BEM analysis at all points.…”

“…In iteration 3 the error changes sign with a slight decrease in magnitude at most but not at all points. Once more the results emphasize that after first few mesh refinement, the other sources of error in BEM [13] become important and thus additional mesh refinements are probably not worth it.…”

“…The various formulations of BEM, the errors that arise from the discretization, and the algorithms that reduce these errors are discussed elsewhere by Vable [13] and are not repeated here. A program called BEAMUP 1 has been built at Michigan Technological University that incorporates the various algorithms that reduce the errors of discretization.…”

Development of circular arc boundary elements method

“…So after numerical implementation we obtain the linear equation where i and j refer to collocation points and integrated boundary elements, respectively) and the sizes of matrices q,u and 0 are N Â 1, where N is the number of collocation points [1,2]. There are three main sources of errors in BEM implementation (also see [10]):…”

Integrating Fracture Mechanics Into Undergraduate Design

“…The key to replicating past century's success in incorporating mechanics research into undergraduate education as elaborated in the above paragraph is the automation of stress analysis. The process of automating stress analysis by Boundary Element Method (BEM) was described by the author in reference [33]. A brief description of the BEM software is given in Section 3.…”