A parallel computing procedure for lower and upper bounds on linear functionals of solutions to PDE: Appliction to stress intensity factors in bimaterials

A computing procedure for the bounds on stress intensity factors in bimaterial is presented based on the a-posteriori error estimate in output of finite element solutions. The stress intensity factors on coarse finite element mesh are first obtained by two points extrapolation method with the displacements of two nodes (or node pairs) on the crack edges computed by finite element method. Then a-posteriori bounding procedure based on the finite element error estimate is utilized to compute the bounds to stress intensity factors. The computation of the error estimate is performed by solving independent elemental Neumann subproblems decomposed from the finite element model, thus the computing procedure is parallel and potential to solve large scale structural problems. The lower and upper bounds on stress intensity factors of a bimaterial interface crack problem are computed with the present method to verify the procedure.