Boundary element formulations in fracture mechanics: a review M.H Aliabadi, C.A. Brebbia Wessex Institute of Technology Ashurst Lodge, Ashurst, Southampton, UK 1 Introduction The modern Boundary Element Method (BEM) originated from work carried out by a few research groups in the 1960's on the application of boundary integral equations for the solution of engineering problems. These researchers were seeking a different solution from the Finite Element Method (FEM) which was starting to become more widely established for computational analysis of engineering problems. Boundary integral methods in structural analysis were known inthe western countries through the work ofRussian authors such as Muskelishvili, Mikhlin and Kupradze. These methods at that time were considered to be difficult to implement numerically. The "direct" boundary element formulation can be traced back to Kupradze. Early work by Jaswon[l] provided the foundation for subsequent direct formulation in engi- neering. Later Rizzo[2] presented the direct formulation for elastostatic problems by the application of Betti's and Somiglina's formulae. During the same period Shaw[3] and Cruse[4] presented an indirect and direct formulations respectively for elastodynamic problems. During the 1960's a small group at Southampton University started working on the application of integral equations to solve stress analysis problems. The work was con- tinued through a series dealing mainly with elastostatic problems under supervision of Carlos Brebbia. Lachat's work in Brebbia's group was thefirst contribution of the use of higher order elements for elastostatics[14). This capability marked an important de- velopment, as until then, integral equations were restricted to constant sources and were assumed to be concentrated as a series of points on the external surface of the body. The constant source approach gave poor results in many practical applications and in particular those involving bending. In 1977 J aswon and Symm[5] published a book on integral equation methods. Their book, which contained considerable original material also illustrated the equivalence be- tween Rizzo's elastostatic formulation and Kupradze's. In 1978 thefirstbook with Boundary Elements as its title, written by Brebbia, was published [6]. The importance of this book is that it pointed out the relationship be- tween the BEM an other methods such as FEM. Brebbia was also thefirstto present a derivation of the boundary integral equation from a weighted residual formulation. More mathematical aspects of the method were presented by Brebbia and Walker[7]. Later, in early 80's as the BEM was rapidly advancing there was a need to define the state of the art on the subject and a more comprehensive and definitive book was written by Brebbia, Telles and Wrobel[8]. This paper reviews advances in the application of the boundary element method (BEM) to fracture mechanics that have taken place over the last 25 years. Over this Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533
Boundary element formulations in fracture mechanics: a review
Jun 14, 2023
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