Abstract
This paper presents an efficient numerical technique for stress analysis of three‐dimensional infinite media containing cracks and localized complex regions. To enhance the computational efficiency of the boundary element methods generally found inefficient to treat nonlinearities and non‐homogeneous data present within a domain and the finite element method (FEM) potentially demanding substantial computational cost in the modeling of an unbounded medium containing cracks, a coupling procedure exploiting positive features of both the FEM and a symmetric Galerkin boundary element method (SGBEM) is proposed. The former is utilized to model a finite, small part of the domain containing a complex region whereas the latter is employed to treat the remaining unbounded part possibly containing cracks. Use of boundary integral equations to form the key governing equation for the unbounded region offers essential benefits including the reduction of the spatial dimension and the corresponding discretization effort without the domain truncation. In addition, all involved boundary integral equations contain only weakly singular kernels thus allowing continuous interpolation functions to be utilized in the approximation and also easing the numerical integration. Nonlinearities and other complex behaviors within the localized regions are efficiently modeled by utilizing vast features of the FEM. A selected set of results is then reported to demonstrate the accuracy and capability of the technique.
Highlights
A physical modeling of three-dimensional solid media by an idealized mathematical domain that occupies the full space is standard and widely used when inputs and responses of interest are only localized in a zone with its length scale much smaller than that of the body
Among various strategies utilized to form the BEM, the weakly singular symmetric Galerkin boundary element method SGBEM has become a wellestablished and well-known technique and, during the past two decades, has proven robust for three-dimensional analysis of linear elasticity problems e.g., 15, 16, linearly elastic infinite media containing isolated cracks e.g., 14, 19, 23, and cracks in finite bodies e.g., 16, 18, 20, 21, 23. Superior features of this particular technique over other types of the BEM are due mainly to that all kernels appearing in the governing integral equations are only weakly singular of O 1/r and that a final system of linear algebraic equations resulting from the discretization possesses a symmetric coefficient matrix
The coupling procedure between a standard finite element method FEM and a weakly singular, symmetric Galerkin boundary element method SGBEM has been successfully established for stress analysis of a three-dimensional infinite medium
Summary
A physical modeling of three-dimensional solid media by an idealized mathematical domain that occupies the full space is standard and widely used when inputs and responses of interest are only localized in a zone with its length scale much smaller than that of the body. Among various strategies utilized to form the BEM, the weakly singular symmetric Galerkin boundary element method SGBEM has become a wellestablished and well-known technique and, during the past two decades, has proven robust for three-dimensional analysis of linear elasticity problems e.g., 15, 16 , linearly elastic infinite media containing isolated cracks e.g., 14, 19, 23 , and cracks in finite bodies e.g., 16, 18, 20, 21, 23 Superior features of this particular technique over other types of the BEM are due mainly to that all kernels appearing in the governing integral equations are only weakly singular of O 1/r and that a final system of linear algebraic equations resulting from the discretization possesses a symmetric coefficient matrix. Following sections of this paper present basic equations and the coupling formulation, essential components for numerical implementations, numerical results and discussions, and conclusions and useful remarks
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