Abstract
Integral representations for deformation (velocity) gradients in elastic or elastic-plastic solids undergoing small or large deformations are presented. Compared to the cases wherein direct differentiation of the integral representations for displacements (or velocities) were carried out to obtain velocity gradients, the present integral representations have lower order singularities which are quite tractable from a numerical point of view. Moreover, the present representations allow the source point to be taken, in the limit, to the boundary, without any difficulties. This obviates the need for a two tier system of evaluation of deformation gradients in the interior of the domain, on one hand, and at the boundary of the domain, on the other. It is expected that the present formulations would yield more accurate and stable deformation gradients in problems dominated by geometric and material nonlinearities. The present results are also useful in directly establishing traction boundary-integral equations in linear and non-linear solid mechanics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atluri, S. N. (1980): On some new general and complementary energy theorems for the rate problems of finite strain, classical elastoplasticity. J. Struct. Mech. 8, 61–92
Guiggiani, M.; Casalini, P. (1987): Direct computation of Cauchy principal value integrals in advanced boundary elements. Int. J. Numer. Methods Eng. 24, 1711–1720
Hess, J. L.; Smith, A. M. O. (1967): Calculation of potential flow about arbitrary bodies. In: Küchemann, D. (ed.): Progress in aeronautical sciences, vol. 8. London: Pergamon
Im, S.; Atluri, S. N. (1987a): A study of two finite strain plasticity models: an internal time theory using Mandel's director concept, and a general isotropic/kinematic hardening theory. Int. J. Plasticity 3, 163–191
Im, S.; Atluri, S. N. (1987b): Endochronic constitutive modeling of finite deformation plasticity and creep: a field-boundary element computational algorithm. In: Nakaga, S.; Williams, K. (eds.): Recent advances in computational methods for inelastic analysis. New York: ASME
Jaswon, M. A. (1963): Integral equation methods in potential theory I, Proc. R. Soc. London Ser. A 275, 23–32
Massonnat, C. E. (1966): Numerical use of integral procedures, in stress analysis. In: Zienkiewicz, O. C.; Hollister, G. S. (eds.): Stress analysis. London: Wiley
O'Donoghue, P. E.; Atluri, S. N. (1987): Field/boundary element approach to the large deflections of thin plates. Comput. Struct. 2, 427–435
Symm, G. T. (1963): Integral equation methods in potential theory II, Proc. R. Soc. London Ser. A 275, 33–46
Watanabe, O.; Atluri, S. N. (1986): Internal time, general internal variable, and multi-yield surface theories of plasticity and creep: a unification of concepts. Int. J. Plasticity 2, 107–134
Zhang, J.-D.; Atluri, S. N. (1986): A boundary/interior element method for quasistatic and transient response analysis of shallow shells. Comput. Struct. 24, 213–224
Zhang, J.-D.; Atluri, S. N. (1988): Post-buckling analysis of shallow shells by the field-boundary element method: Int. J. Numer. Methods Eng. 26, 571–587
Author information
Authors and Affiliations
Additional information
Communicated by G. Yagawa, July 1, 1987
Rights and permissions
About this article
Cite this article
Okada, H., Rajiyah, H. & Atluri, S.N. Non-hyper-singular integral-representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations). Computational Mechanics 4, 165–175 (1989). https://doi.org/10.1007/BF00296664
Issue Date:
DOI: https://doi.org/10.1007/BF00296664