AN EFFICIENT BOUNDARY-ELEMENT METHOD FOR COMPUTING ACCURATE STRESSES IN 2-DIMENSIONAL ANISOTROPIC PROBLEMS

The stresses calculated by the boundary element method are accurate ev erywhere except in a narrow region near the boundaries. This ''boundar y layer effect'' is due to the presence of hypersingularities in the r elevant kernals. An efficient method that eliminates the boundary laye r effect and yields accurate stresses everywhere in two-dimensional an isotropic material problems is presented. This method, the modified di splacement gradient method, utilizes two identities-Somigliana's ident ity and a second identity in terms of displacement gradients and tract ions. In this method, the Somigliana's identity is used as in the trad itional BEM to determine the displacements and tractions at all nodes on the boundary. All the boundary data is then used to determine the d isplacement gradients at each of the boundary nodes. These displacemen t gradients and tractions are then used in the second identity to calc ulate the displacement gradients (and hence strains) at interior point s. The stresses are then calculated using the constitutive relationshi ps. The modified displacement gradient method is applied to several tw o-dimensional elasticity problems with isotropic and orthotropic mater ials with circular or elliptic cutouts. Numerical studies indicate tha t the present method gives accurate stresses even in the boundary laye r region and is computationally efficient and attractive. In conjuncti on with the modified displacement gradient method, three approaches th at use different evaluation procedures and locations for determining d isplacement gradients are used. In the first approach, the averaging a pproach, displacement gradients are averaged at nodes common to adjace nt elements. In the second approach, the non-averaging approach, displ acement gradients are not averaged but are stored element-wise. In the last approach, the discontinuous element approach, the gradients are evaluated at the nodes of discontinuous elements. Numerical studies in dicate that all three approaches yield nearly same stress results, and hence, any one approach can be used.