Completed double layer boundary element method in elasticity. (English) Zbl 0773.73097
Summary: This paper reports an indirect boundary element method is elasticity that is most suitable to deal with particulate solids. The method involves a distribution of a double layer potential and, after a suitable completion and deflation, is amenable to iterative solution techniques. It can therefore accommodate a large number of particles with complex geometries. Convergence of the method is significantly improved by the introduction of a simple domain decomposition to solve the system of equations. The method is illustrated by the translating sphere problem, the load transfer problem between two spheres at near contact, and the shear deformation of a cluster of 125 spheres initially in a simple cubic array.
MSC:
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
Keywords:
convergence; particulate solids; iterative solution; simple domain decomposition; translating sphere problem; load transfer problem; cluster of 125 spheresReferences:
| [1] | Banerjee, P. K.; Butterfield, R., Boundary Element Methods in Engineering Science (1981), McGraw Hill: McGraw Hill London · Zbl 0499.73070 |
| [2] | Batchelor, G. K., The stress system in a suspension of force-free and torque-free particles, J. Fluid Mech., 41, 545-570 (1970) · Zbl 0193.25702 |
| [3] | Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary Element Techniques: Theory and Applications in Engineering (1984), Springer: Springer Berlin · Zbl 0556.73086 |
| [4] | Chan, C. Y.; Beris, A. N.; Advani, S. G., High order boundary element method calculations of hydrodynamic interactions between particles at close proximity, Int. J. Num. Meth. Fluids, 14, 13-28 (1992) |
| [5] | Dvorkin, J.; Mavko, G.; Nur, A., The effect of cementation of the elastic properties of granular material, Mech. Mater., 12, 207-217 (1991) |
| [6] | Jeffrey, D. J., Low-Reynolds-number flow between converging spheres, Mathemutika, 29, 58-66 (1982) · Zbl 0479.76040 |
| [7] | Karrila, S. J.; Fuentes, Y. O.; Kim, S., Parallel computational strategies for hydrodynamic interactions between rigid particles of arbitrary shape in a viscous fluid, J. Rheology, 33, 913-947 (1989) · Zbl 0693.76043 |
| [8] | Karrila, S. J.; Kim, S., Integral equation of the second kind for Stokes flow: direct simulation for physical variables and removal of inherent accuracy limitation, Chem. Engng Commun., 82, 123-161 (1989) |
| [9] | Kim, S.; Karrila, S. J., Microhydrodynamics: Principles and Selected Applications (1991), Butterworth-Heinemann: Butterworth-Heinemann Boston |
| [10] | Lachat, J. C.; Watson, J. O., Effective numerical treatment of boundary integral equations: a formulation for three dimensional elastostatics, Int. J. Num. Meth. Engng, 10, 991-1005 (1976) · Zbl 0332.73022 |
| [11] | Newman, M., Matrix Computations, (todd, J., A Survey of Numerical Analysis (1962), McGraw-Hill: McGraw-Hill London) · Zbl 0101.33601 |
| [12] | Nunan, K. C.; Keller, J. B., Effective elasticity tensor of a periodic composite, J. Mech. Phys. Solids, 32, 259-280 (1984) · Zbl 0549.73003 |
| [13] | Odqvist, P. K.G., Math. Z., 32, 329-375 (1930) · JFM 56.0713.04 |
| [14] | Pakdel, P.; Kim, S., Mobility and stresslet functions of particles with rough surfaces in viscous fluids: a numerical study, J. Rheology, 35, 797-823 (1991) |
| [15] | Phan-Thien, N., Rigid spherical inclusion: the multipole expansion, J. Elasticity (1992), in press · Zbl 0805.73021 |
| [16] | Phan-Thien, N.; Karihaloo, B., Effective moduli of particulate solids, ZAMM, 62, 183-190 (1982) · Zbl 0514.73003 |
| [17] | Phan-Thien, N.; Tullock, D. L.; Ilic, V.; Kim, S., Completed double layer boundary element method:a numerical implementation and some experimental results, Comp. Mech. (1992), in press · Zbl 0775.76108 |
| [18] | Phan-Thien, N.; Tullock, D. L.; Kim, S., Completed double layer in half space: a boundary element method, Comp. Mech., 9, 121-135 (1992) · Zbl 0775.76107 |
| [19] | Power, H.; Miranda, G., Second kind integral equation formulation of Stokes flows past a paticle of arbitrary shape, SIAM J. Appl. Math., 47, 689-698 (1987) · Zbl 0634.76029 |
| [20] | Tullock, D.; Phan-Thien, N., A completed double layer boundary element method with domain decomposition, Albuquerque, New Mexico, June 1992. Albuquerque, New Mexico, June 1992, Proc. BETECH 92 (1992) · Zbl 0775.76107 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
