Abstract
The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures, because only boundary and crack-surface elements are needed. However, for engineering structures subjected to body forces such as rotational inertia and gravitational loads, additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain. In this study, weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed. By using divergence theorem or alternatively the radial integration method, the domain integral terms caused by body forces are transformed into boundary integrals. And due to the weak singularity of the formulated boundary integral equations, a simple Gauss-Legendre quadrature with a few integral points is suffcient for numerically evaluating the SGBEM equations. Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.
Highlights
The Symmetric Galerkin Boundary Element Method (SGBEM) [1–3] has gained increasing popularity in fracture and crack-growth analysis of solid structures due to its attractive features of symmetric coef cient matrices, weak-singularity, and that only boundary & crack-surface elements are needed
For the fracture mechanics problems such as turbine discs and turbine blades of aircraft engines, concrete gravity dam, etc., SGBEM may lose its advantages, because evaluation of domain integral terms resulting from body forces such as rotational inertia and gravitational loads leads to the meshing of the interior of the domain
This paper presents the weakly singular traction boundary integral equation for solids undergoing rotational inertia and gravitational Loads
Summary
The Symmetric Galerkin Boundary Element Method (SGBEM) [1–3] has gained increasing popularity in fracture and crack-growth analysis of solid structures due to its attractive features of symmetric coef cient matrices, weak-singularity, and that only boundary & crack-surface elements are needed. This paper presents the weakly singular traction boundary integral equation for solids undergoing rotational inertia and gravitational Loads. By using the divergence theorem (div) or the radial integration method (RIM), domain integrals induced by rotational inertia or gravitational forces are transformed into boundary integrals correspondingly. The developed SGBEM with only weakly-singular boundary integrals are applied to simulate various examples of 3D solids with/without considering rotational inertia and gravitational loads. Appearing in traction boundary integral Eq (2) considering rotational inertia and gravitational loads is transformed into weakly singular boundary integral, using the divergence theorem or the radial integration method. In Subsections 2.1 and 2.2, the domain integral terms with rotational inertia and gravitational loads in tBIE are transformed into weakly singular boundary integral terms by two methods of divergence theorem and radial integration method, respectively
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