Structural inverse problems solved by the T-element approach

• Autorzy: Wróblewski A. , Zieliński A. P.
• Języki publikacji: EN

Abstrakty

EN

Any direct boundary-value problem is defined in a certain area $\Omega$ by a system of differential equations and respective set of boundary conditions. In structural inverse problems the above conditions can be partly unknown. Instead, we can measure certain quantities inside the investigated structure and then approximately define the whole boundary-value problem. Usually, the solutions of inverse problems are connected with the minimization of a certain functionals, which results in optimization procedures. The applications of the trial functions identically fulfilling governing partial differential equations of a discussed problem (the Trefftz approach) can considerably improve these procedures. The original idea of Erich Trefftz was based on modelling objects of simple geometry. In the case of more complex structures the division of the whole object into sub-regions (Trefftz elements) is necessary. This kind of formulation is presented in this paper and is illustrated by numerical examples. The properties of the Trefftz finite elements allow the formulation of effective algorithms, which considerably shorten the time of computer calculations in comparison to standard finite element solutions.

Słowa kluczowe

EN

Trefftz method; finite element method

PL

metoda Trefftza; metoda elementów skończonych

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2006
• Tom: Vol. 13, No. 3
• Strony: 473--480
• Opis fizyczny: Bibliogr. 7 poz., tab., wykr.

Twórcy

autor

Wróblewski A.

autor

Zieliński A. P.

• Cracow University of Technology, [Politechnika Krakowska] ul. Jana Pawła II 37, Kraków, Poland

Bibliografia

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• [2] J. Jirousek, A. Venkatesh. A hybrid-Trefftz plane elasticity elements with p-method capabilities. Int. J. Numer. Meth. Eng., 35: 1443-1472, 1992.
• [3] J. Jirousek, A. Wróblewski. T-elements: State of the art and future trends. Archives of Comp. Mcth. in Engng., 3: 323-434, 1996.
• [4] J. Jirousek, A.P. Zieliński. Survey of Trefftz type element formulations. Comp. Struct., 17: 375-388, 1997.
• [5] M. Karas, A.P. Zieliński. Structural inverse problems solved by the Trefftz approach. Comm. Numer. Methods Engng. (submitted after reviews).
• [6] Q.-H, Qin. The Trefftz Finite and Boundary Element Method. WITPress, Southampton-Boston, 2000.
• [7] N. Tosaka, A. Utani, H. Takahashi. Unknown defect identification in elastic field by boundary element method with filtering procedure. Eng.. Analysis with Bound. Elem., 15: 207-215, 1995.