Finite displacements in reciprocity-based FE formulation

• Autorzy: Kompiš V. , Novák P. , Handrik M.
• Konferencja: 8th International Conference on Numerical Methods in Continuum Mechanics (September 19-24, 2000 ; Liptovsky Ján, Low Tatras ; Slovakia)
• Języki publikacji: EN

Abstrakty

EN

In this paper, Trefftz polynomials are used for the development of FEM based on the reciprocity relations. Such reciprocity principles are known from the Boundary Element formulations, however, using the Trefftz polynomials in the reciprocity relations instead of the fundamental solutions yields the non-singular integral equations for the evaluation of corresponding sub-domain (element) relations. A weak form satisfaction of the equilibrium is used for the inter-domain connectivity relations. For linear problems, the element stiffness matrices are defined in the boundary integral equation form. In non-linear problems the total Lagrangian formulation leads to the evaluation of the boundary integrals over the original (related) domain evaluated only once during the solution and to the volume integrals containing the non-linear terms. Also, Trefftz polynomials can be used in the post-processing phase of the FEM computations for small strain problems. By using the Trefftz polynomials as local interpolators, smooth fields of the secondary variables (strains, stresses, etc.) can be found in the whole domain (if it is homogeneous). This approach considerably increases the accuracy of the evaluated fields while maintaining the same rate of convergence as that of the primary fields. Stress smoothing for large displacements will be the aim of further research. Considering the examples of simple tension, pure bending and tension of fully clamped rectangular plate (2D stress/strain problems) for large strain-large rotation problems, the use of the initial stiffness, the Newton-Raphson procedure, and the incremental Newton-Raphson procedure will be discussed.

Słowa kluczowe

EN

finite element method; displacement; Trefftz polynomial

PL

metoda elementów skończonych; przemieszczenie; polynomial Trefftz'a

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2002
• Tom: Vol. 9, No. 4
• Strony: 469--480
• Opis fizyczny: Bibliogr. 27 poz., tab., wykr.

Twórcy

autor

Kompiš V.

• Faculty of Mechanical Engineering, University of Žilina, Vel'ky Diel, 010 26 Žilina, Slovakia

autor

Novák P.

• Faculty of Mechanical Engineering, University of Žilina, Vel'ky Diel, 010 26 Žilina, Slovakia

autor

Handrik M.

• Faculty of Mechanical Engineering, University of Žilina, Vel'ky Diel, 010 26 Žilina, Slovakia

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