Time integration and the Trefftz Method Part I - First-order and parabolic problems

• Autorzy: de Freitas J. A. T.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

The finite element method is applied in the time domain to establish formulations for the integration of second-order and hyperbolic (dynamic) problems. Modal decomposition in the space domain is used to recover the well-established method for uncoupling the equations of motion, which is extended to include general time approximation bases. The limitations of this approach in the implementation of large-scale, non-linear problems while preserving the uncoupling of the equations of motion are overcome by using the alternative concept of modal decomposition in the time domain. Both single- and double-field formulations are presented and the associated Trefftz formulations are established.

Słowa kluczowe

EN

Trefftz method; parabolic problems

PL

metoda Trefftza

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 453--463
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

de Freitas J. A. T.

• Departmento de Engenharia Civil e Arquitectura, Instituto Superior Tecnico Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Bibliografia

• [1] A.P. Zielinski. Trefftz Method. GAMES, 4(3/ 4), 1997.
• [2] J.A.T. Freitas and J.P.M. Almeida. Trefftz method. GAMES, 8(2/3) , 2001.
• [3] K.K. Tamma, X. Zhou, and D. Sha. The time dimension: A theory towards the evolution, classification, characterization and design of computational algorithms for transient/dynamic applications. Archives of Computational Methods in Engineering, 7(2): 67-290, 2000.
• [4] J.A.T. Freitas. Mixed finite element formulation for the solution of parabolic problems. Computer Methods in Applied Mechanics and Engineering, 191: 3425-3457, 2002.
• [5] J. Jirousek and Q.H. Qin. Application of hybrid-Trefftz element approach to transient heat conduction analysis. Computers and Structures , 58(1): 195-201, 1996.
• [6] J.A.T. Freitas. Hybrid-Trefftz displacement and stress elements for elastodynamic analysis in the frequency domain. GAMES, 4: 345-368, 1997.
• [7] J.A.T. Freitas. Hybrid finite element formulations for elastodynamic analysis in the frequency domain. International Journal of Solids and Structures, 36: 1883-1923, 1999.
• [8] M. Braun . Differential Equations and Their Applications. Springer- Verlag Texts in Applied Mathematics. Springer-Verlag, New York, 4th edition, 1991.