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Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties. (English) Zbl 0961.74073
Summary: We present the local boundary integral formulation for an elastic body with nonhomogeneous material properties. All nodal points are surrounded by a simple surface centered at the collocation point. Only one nodal point is included in each sub-domain. On the surface of a sub-domain, both displacements and traction vectors are unknown generally. If we choose a modified fundamental solution for governing equation, which vanishes on the local boundary, the traction value is eliminated from the local boundary integral equations for all interior points. For every sub-domain, the material constants correspond to those at the collocation point at the center of sub-domain. Meshless and polynomial element approximations of displacements on local boundaries are considered in the numerical analysis.

74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74E05 Inhomogeneity in solid mechanics
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