Weakly singular stress-BEM for 2D elastostatics

✍ Scribed by J.D. Richardson; T.A. Cruse

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 200 KB
• Volume: 45
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19990510)45:1<13::aid-nme576>3.0.co;2-w

✦ Synopsis

A weakly singular stress-BEM is presented in which the linear state regularizing ÿeld is extended over the entire surface. The algorithm employs standard conforming C 0 elements with Lagrangian interpolations and exclusively uses Gaussian integration without any transformation of the integrands other than the usual mapping into the intrinsic space. The linear state stress-BIE on which the algorithm is based has no free term so that the BEM treatment of external corners requires no special consideration other than to admit traction discontinuities. The self-regularizing nature of the Somigliana stress identity is demonstrated to produce a very simple and e ective method for computing stresses which gives excellent numerical results for all points in the body including boundary points and interior points which may be arbitrarily close to a boundary. A key observation is the relation between BIE density functions and successful interpolation orders. Numerical results for two dimensions show that the use of quartic interpolations is required for algorithms employing regularization over an entire surface to show comparable accuracy to algorithms using local regularization and quadratic interpolations. Additionally, the numerical results show that there is no general correlation between discontinuities in elemental displacement gradients and solution accuracy either in terms of unknown boundary data or interior solutions near element junctions.