zbMATH — the first resource for mathematics

Application of local boundary integral equation method into micropolar elasticity. (English) Zbl 1021.74047
Summary: We present a new meshless method for solving boundary value problems in micropolar elasticity. The method is based on the local boundary integral equation (LBIE) method with the moving least squares approximation of physical quantities. Randomly scattered nodes are utilized for interpolation of field data. Every node is surrounded by a simple surface centered at the collocation point in the LBIE method. On the surface of subdomains the LBIEs are written, and fundamental solutions corresponding to uncoupled governing equations are derived. To eliminate the traction vector in the LBIE, the modified fundamental solution is introduced.

MSC:
 74S15 Boundary element methods applied to problems in solid mechanics 74A35 Polar materials
Full Text:
References:
 [1] Eringen, A.C., Mechanics of micromorphic continua, (), 18-35 · Zbl 0181.53802 [2] Eringen, A.C.; Suhubi, E.S., Nonlinear theory of simple micropolar solids. I, Int J engng sci, 2, 189-203, (1964) · Zbl 0138.21202 [3] Balas, J.; Sladek, J.; Sladek, V., Stress analysis by boundary element methods, (1989), Elsevier Amsterdam · Zbl 0681.73001 [4] Zhu, T.; Zhang, J.D.; Atluri, S.N., A local boundary integral equation method in computational mechanics, and a meshless discretization approach, Comput mech, 21, 223-235, (1998) · Zbl 0920.76054 [5] Atluri, S.N.; Sladek, J.; Sladek, V.; Zhu, T., The local boundary integral equation (LBIE) and It’s meshless implementation for linear elasticity, Comput mech, 25, 180-198, (2000) · Zbl 1020.74048 [6] Sladek, V.; Sladek, J.; Atluri, S.N.; Van Keer, R., Numerical integration of singularities in meshless implementation of local boundary integral equations, Comput mech, 25, 394-403, (2000) · Zbl 0973.74086 [7] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods, Int J numer meth engng, 37, 229-256, (1994) · Zbl 0796.73077 [8] Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P., Meshless methods; an overview and recent developments, Comput meth appl mech engng, 139, 3-47, (1996) · Zbl 0891.73075 [9] Atkinson, C.; Leppington, F.G., The effect of couple stresses on the tip of a crack, Int J solids struct, 13, 1103-1122, (1977) · Zbl 0368.73083 [10] Sladek, J.; Sladek, V.; Atluri, S.N., Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties, Comput mech, 24, 456-462, (2000) · Zbl 0961.74073 [11] Sladek, V.; Sladek, J., Some computational aspects associated with singular kernels, () · Zbl 0961.74072 [12] Kaloni, P.; Ariman, T., Stress concentration effects in micropolar elasticity, Z angew math phys, 18, 136-141, (1967) [13] Eringen, A.C., Theory of micropolar elasticity, () · Zbl 0145.21302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.