ISSN:
1460-2695
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Abstract— The boundary value problem for an arbitrarily shaped plane crack embedded in a 3D linear elastic solid can be reduced to a governing hyper-singular integral equation. A discretizing procedure based on a triangulation of the crack area has been offered in Part I of this work. The main goal of Part I is to introduce the analytical results for the 18 resulting finite-part integrals defined over a triangular mesh area. The finite-part integrals occur in those triangles where the source point coincides with one of the element nodes. Mostly the source point lies outside of the considered triangle. In these cases the occurring area integrals are regular.The aim of Part II is, therefore, the derivation of the closed form expressions for the relevant 18 regular area integrals. The resulting relations are of algebraic form which can easily be coded in compact form. Their numerical proof by two different methods shows the highest accuracy and, therefore, the correctness of the final solutions. The relevant numerical results are offered in Appendix I.With the formulae provided in Part I and Part II of the paper the determination of the coefficient matrix, necessary for the calculation of COD values from a linear equation system, is precise and needs only minimum computer time.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1460-2695.1997.tb01506.x
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