An adaptive algorithm for unilateral viscoelastic contact problems for beams and plates. (English) Zbl 0778.73072
Summary: An adaptive algorithm is given for the bending of viscoelastic beams and plates resting on viscoelastic, unilateral, frictionless foundations. An a posteriori error indicator proposed here is obtained by making use of upper and lower bounds generated by the saddle functional being a potential for the system of equations and inequalities which govern the contact problem.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74K20 | Plates |
Keywords:
bending; unilateral frictionless foundations; a posteriori error indicator; upper and lower bounds; saddle functionalReferences:
| [1] | Oden, J. T., Qualitative Methods in Nonlinear Mechanics (1986), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0578.70001 |
| [2] | Sewell, M. J., Maximum and Minimum Principles (1990), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0652.49001 |
| [3] | Demkowicz, L.; Świerczek, M., An adaptive finite element method for a class of variational inequalities, (Kosinsky, W.; Manacorda, T.; Morro, A.; Ruggeri, T., Proc. Italian-Polish Symposium of Continuum Mechanics. Proc. Italian-Polish Symposium of Continuum Mechanics, Bologna (1987)), 1-18 |
| [4] | Haslinger, J.; Neittaanmäki, P.; Salmenjoki, K., On optimal mesh design for FEM in unilateral boundary value problems, (Whiteman, J. R., MAFELAP 1987 (1988), Academic Press: Academic Press London), 103-113 · Zbl 0687.73075 |
| [5] | Lee, C. Y.; Oden, J. T.; Ainsworth, M., Local a posteriori error estimates and numerical results for contact problems and problems of flow through porous media, (Wriggers, P.; Wagner, W., Nonlinear Computational Mechanics (1991), Springer: Springer Berlin), 671-689 |
| [6] | Świtka, R.; Husiar, B., Discrete analysis of Theological models, Mech. Teor. Stos., 22, 209-233 (1984), (in Polish). · Zbl 0574.73049 |
| [7] | Świtka, R., A discretization method of rheological problems, (Proc. Conf. Rheology of Wood. Proc. Conf. Rheology of Wood, Poznań (1982)), 211-218, (in Polish). |
| [8] | Kuczma, M. S., The problem of unilateral contact of beams and plates on viscoelastic foundations (in Polish), Transactions of Poznań Technical University: Rozprawy No. 255 (1991), Poznań |
| [9] | Kuczma, M. S.; Świtka, R., Bending of elastic beams on Winkler-type viscoelastic foundations with unilateral constraints, Comput. & Structures, 34, 125-136 (1990) · Zbl 0703.73073 |
| [10] | Olejniczak, M., Analysis of one- and two-phase viscoelastic disks (in Polish), (Ph.D. Thesis (1990), Poznań Technical University: Poznań Technical University Poznań) |
| [11] | Kikuchi, N.; Oden, J. T., Contact Problems in Elasticity: A study of Variational Inequalities and Finite Element Methods (1988), SIAM: SIAM Philadelphia, PA · Zbl 0685.73002 |
| [12] | Stein, E.; Bischoff, D.; Brand, G.; Plank, L., Adaptive multi-grid methods for finite element systems with biand unilateral constraints, Comput. Methods Appl. Mech. Engrg., 52, 873-888 (1985) · Zbl 0589.73072 |
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.
