A new type of high-accuracy BEM and local stress analysis of real beam, plate and shell structures

Abstract A high-accuracy BEM (HABEM) presented by the author is briefly summarized, and then applied to the local stress analysis (LSA) of real clamped thin-plate beam, in 2D and 3D models. The simple examples in 2D have shown the process of discretization error reduction via mesh refinement under guidance of error indicator. The numerical results have shown the feasibility and high accuracy of the presented HABEM. On the other hand the results obtained are valuable for the strength evaluation in engineering. The corresponding 3D HABEA has also been presented. The results agree with the corresponding 2D analysis. But the complexity of the 3D HABEA is much higher than 2D one. The advantage of dimension reduction is also the major advantage of BEM over FEM. For 3D HABEM an improved equal-accuracy Gaussian quadrature for regular including nearly singular integrals, and that for weakly singular integrals is presented and numerically verified in detail. For the local stress analysis of real beam, plate and shell structures the 3D HABEA is necessary, in such case it is encountered with a large-scale BEA problem, and fast algorithm should be introduced. Such approach is defined as high-performance BEM, which will be a new research field in future.