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Analysis of shell‐like structures by the Boundary Element Method based on 3‐D elasticity: formulation and verification
Author(s) -
Liu Yijun
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980215)41:3<541::aid-nme298>3.0.co;2-k
Subject(s) - boundary element method , elasticity (physics) , degenerate energy levels , shell (structure) , finite element method , mathematical analysis , ellipsoid , integral equation , boundary value problem , mathematics , geometry , structural engineering , physics , materials science , engineering , mechanical engineering , composite material , quantum mechanics , astronomy
Abstract In this paper, the Boundary Element Method (BEM) for 3‐D elastostatic problems is studied for the analysis of shell or shell‐like structures. It is shown that the conventional boundary integral equation (CBIE) for 3‐D elasticity does not degenerate when applied to shell‐like structures, contrary to the case when it is applied to crack‐like problems where it does degenerate due to the closeness of the two crack surfaces. The treatment of the nearly singular integrals, which is a crucial step in the applications of BIEs to thin shapes, is presented in detail. To verify the theory, numerical examples of spherical and ellipsoidal vessels are presented using the BEM approach developed in this paper. It is found that the system of equations using the CBIE is well conditioned for all the thickness studied for the vessels. The advantages, disadvantages and potential applications of the proposed BEM approach to shell‐like structures, as compared with the FEM regarding modelling and accuracy, are discussed in the last section. Applications of this BEM approach to shell‐like structures with non‐uniform thickness, stiffeners and layers will be reported in a subsequent paper. © 1998 John Wiley & Sons, Ltd.