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Abstrakty
This paper presents the basis of an adaptive mesh refinement technique aimed at reducing a local error, i.e. the error in a local quantity, which is defined as the integral of a stress or a displacement in a given subregion. Two pairs of dual solutions, one corresponding to the applied load and the other to the virtual action, dual of the local quantity, are used to bound the local error and to provide the element error indicators for the adaptive process. A test case is used to exemplify the behaviour of the technique.
Słowa kluczowe
Rocznik
Tom
Strony
565--574
Opis fizyczny
Bibliogr. 24 poz., rys., wykr.
Twórcy
autor
- Departamento de Engenharia Civil, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
autor
- Departamento de Engenharia Civil, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Bibliografia
- [1] R. Albanese, R. Fresa. Upper and lower bounds for local electromagnetic quantities. Int. J. Num. Meth. Eng., 42: 499-515, 1998.
- [2] J.P.M. Almeida, J.A.T. Freitas. Alternative approach to the formulation of hybrid equilibrium finite elements. Computers & Structures, 40(4): 1043-1047, 1991.
- [3] J.P.M. Almeida, J.A.T. Freitas. Continuity conditions for finite element analysis of solids. Int. J. Num. Meth. Eng., 33: 845-853, 1992.
- [4] I. Babuska, A. Miller. The post-processing approach in the finite element method (parts 1, 2 and 3). Int. J. Num. Meth. Eng., 20: 1085-1129, 2311-2324, 1984.
- [5] I. Babuska, W.C. Rheinbolt. A posteriori error estimates for the finite element method. Int. J. Num. Meth. Eng, 12: 1597-1615, 1978.
- [6] P. Beckers, H.G . Zhong. Mesh adaptation for two dimensional stress analysis. In: M. Papadrakakis, B.H. V. Topping, eds., Advances in post and preprocessing for finite element technology, pages 47-59. CivilComp, Edinburgh, 1994.
- [7] B.M.F. deVeubeke. Displacement and equilibrium models in the finite element method. In: O.C. Zienkiewicz, G.S. Holister, eds., Stress Analysis. Wiley, 1965.
- [8] J.A.T. Freitas, J.P.M. Almeida, E.M.B.R. Pereira. Non-conventional formulations for the finite element method. Computational Mechanics, 23: 488-501, 1999.
- [9] H.J. Greenberg. The determination of upper and lower bounds for the solution of the Dirichlet problem. J. Math. Phys., 27: 161-182, 1948.
- [10] B. Jakobsen. The Sleipner accident and its causes. In: J. Robinson, ed., FEM Today and the Future, pages 102-108. Robinson and Associates, 1993.
- [11] R.E. Jones. A generalization of the direct-stiffness method of structural analysis. AIAA Journal, 2(5): 821-826, 1964.
- [12] D.W. Kelly, J.P.S.R. Gago, O.C. Zienkiewicz. A posteriori error analysis and adaptive processes in the finite element method: Part I - error analysis. Int. J. Num. Meth. Eng, 19: 1593-1619, 1983.
- [13] P. Ladeveze, D Leguillon. Error estimate procedure in the finite element method and applications. SIAM J. Num. Anal., 20(3): 483-509, 1983.
- [14] O.J.B.A. Pereira, J.P.M. Almeida. Majorantes do erro em grandezas locais obtidas a partir de soluções duais de elementos finitos. In: J.M . Goicolea, C. Mota Soares, M. Pastor, G. Bugeda, eds., Métodos Numéricos en Ingeniería V. SEMNI, 2002.
- [15] O.J.B.A. Pereira, J.P.M. Almeida, E.A.W. Maunder. Adaptive methods for hybrid equilibrium finite element models. Camp. Methods in Applied Mechanics and Engineering, 176: 19-39, 1999.
- [16] O.J.B.A. Pereira, G. Bugeda. Mesh optimality criteria and remeshing strategies for singular point problems. In: M. Papadrakakis, ed., Innovative Computational Methods for Structural Mechanics, Edinburgh, 1998. Saxe-Coburg Publications.
- [17] T.H.H. Pian, P. Tong. Basis of finite element methods for solid continua. Int. J . Num. Meth. Eng., 1: 3-28, 1969.
- [18] W. Prager, J.L. Synge. Approximations in elasticity based on the concept of function space. Quart. Appl. Math., 5(3): 241-269, 1947.
- [19] M.J. Turner, R.W. Clough, H.C. Martin, L.J. Topp. Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences, 23(9): 805-854, Sep. 1956.
- [20] K. Washizu. Bounds for solutions of boundary value problems in elasticity. J. Math. Phys., 32: 117-128, 1953.
- [21] M.L. Williams. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics, 19: 526-528, 1952.
- [22] D.J. Yang, W.D. Kelly, J.D. Isles. A posteriori pointwise upper bound estimates in the finite element error. Int. J. Num. Meth. Eng., 36: 1279-1298, 1993.
- [23] O.C. Zienkiewicz, J.Z. Zhu. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Num. Meth. Eng, 24: 337-357, 1987.
- [24] O.C. Zienkiewicz, J.Z. Zhu. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Camp. Methods in Applied Mechanics and Engineering, 101: 207-224, 1992.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0009-0066