Trefftz and RBF-based formulations for concrete beams analysis using damage models

• Autorzy: Tiago C. M. , Castro Luis M.S.S. , Leităo Victor M. A.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

In this work a hybrid-Trefftz formulation and a meshless approach based on the use of radial basis functions (RBF) are applied to the analysis of reinforced concrete beams. Resorting to the Mazars model, the concrete is represented by an elastic medium with progressive damage. In the hybrid-Trefftz formulation a stress field that satisfies a priori the equilibrium equations on the domain is used. The displacements on the static boundary are independently approximated, resulting in a governing system where the operators have to be integrated over the domain of the problem. In what concerns the meshless approach, radial basis functions are used to approximate the displacement fields but, as a collocation procedure is used, no integrations are required. A numerical example illustrates the results obtained with both techniques.

Słowa kluczowe

EN

reinforced concrete; Trefftz method

PL

beton zbrojony; metoda Trefftza

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 641--660
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Tiago C. M.

• Departamento de Engenharia Civil, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

autor

Castro Luis M.S.S.

• Departamento de Engenharia Civil, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

autor

Leităo Victor M. A.

• Departamento de Engenharia Civil, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Bibliografia

• [1] J.A. Teixeira de Freitas, Z.Y. .Ji. Hybrid-Trefftz stress elements for plate bending analysis. Int. J. Num. Meth. Eng., 39: 569-584, 1996.
• [2] J.A. Teixeira de Freitas, Z.M. Wang. Hybrid-Trefftz stress elements for elastoplasticity. Int. J. Num. Meth. Eng., 43: 655-683, 1998.
• [3] E.M.B. Ribeiro Pereira. Analise fisicamente não linear de pórticos tridimensionais de betão armado (in portuguese). Master's thesis, 1ST-Technical University of Lisbon, 1989.
• [4] J.J. Monaghan, R.A. Gingold. Shock Simulation by the Particle Method SPH. J. Camp. Phys., 52: 374-389, 1983.
• [5] B. Nayroles, G. Touzot, P. Villon. Generalizing the finite element method: Diffuse approximation and diffuse elements. Comput. Mech., 10: 307-318, 1992.
• [6] W.K. Liu, Y. Chen, J.S. Jun, T. Belytschko, C. Pan , R.A . Uras, C.T. Chang. Overview and applications of the Reproducing Kernel Particle Methods. Arch. of Comput. Meth. in Eng., 3{1): 3-80, 1996.
• [7] I. Babuska, .J.M. Melenk. The Partition of Unity Method. Int. J. Num. Meth. Eng., 40: 727-758, 1997.
• [8] T. Belytschko, Y. Lu, L. Gu. Element-Free Galerkin Methods. Int. J. Num. Meth. Eng., 37: 229-256, 1994.
• [9] C.A. Duarte. The Hp Cloud Method. PhD thesis, Faculty of the Graduate School of the University of Texas at Austin, 1996.
• [10] E.J. Kansa. Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics- ii: Solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput. Math. Applic., 19: 149-161, 1990.
• [11] G.E. Fasshauer. Solving partial differential equations by collocation with radial basis functions. In: A. Le Mehaute, C. Rabut, L.L. Schumaker, editors, Proceedings of Chamonix 1996, pages 1-8. 1997 by Vanderbilt University Press, Nashville, TN, 1996.
• [12] V.M.A. Leitão. A meshless method for Kirchhoff plate bending problems. Int. J. Num. Meth. Eng., 52: 1107-1130, 2001.
• [13] J. Mazars. Application de Ia mécanique de l'endommagement au comportement non lineaire et à Ia rupture du béton de structure. PhD thesis, Universite Paris 6, 1984.
• [14] J.A. Teixeira de Freitas, Z.Y. Ji. Hybrid-Trefftz boundary integral formulation for simulation of singular stress fields. Int. J. Num. Meth. Eng., 39: 281-308, 1996.
• [15] J.A. Teixeira de Freitas, J.P. Moitinho de Almeida, E.M.B. Ribeiro Pereira. Non-conventional formulations for the finite element method. Comput. Mech., 23(5-6): 488-501, 1999.
• [16] The MathWorks Inc. MATLAB, The Language of Technical Computing. Version 6.0, 2000.
• [17] M.S. Alvares. Estudo de urn modelo de dano para o concreto: formulação, identificação paramétrica e aplicação com o emprego do método dos elementos finitos (in portuguese). Master's thesis, Escola de Engenharia de São Carlos, Universidade de São Paulo, 1993.
• [18] F.B. Barros. Métodos Sem Malha e Método dos Elementos Finitos Generalizados em Análise Não-Linear de Estruturas (in portuguese). PhD thesis, Escola de Engenharia de São Carlos, Universidade de São Paulo, 2002.