Pre-assembly for FEM 2D non-curvilinear quadrilateral Lagrangian elements

• Autorzy: Sowa M. , Typańska D.
• Języki publikacji: EN

Abstrakty

EN

The paper concerns an idea of preparing auxiliary equations and data for the finite element method assembly. This is made for a specific element type and element order and is referred to as the pre-assembly. Most importantly the prepared auxiliary equations require that only the element’s placement (coordinates) needs to be known, while the remaining coefficients that are required are stored in data sheets. The pre-assembly allows programmers who implement the FEM to significantly reduce the effort put into the assembly algorithm through its replacement by a few simple equations and the application of the prepared data. These data sheets can be prepared and can be utilized by FEM programmers. The construction of these data sheets for non-curvilinear quadrilateral Lagrangian elements (of any selected order) is explained in this paper.

Słowa kluczowe

EN

pre-assembly; finite element method; higher order elements; quadrilateral Lagrangian elements

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Computer Applications in Electrical Engineering
• Rocznik: 2014
• Tom: Vol. 12
• Strony: 106--119
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Sowa M.

• Silesian University of Technology 44-100 Gliwice, ul. Bolesława Krzywoustego 2

autor

Typańska D.

• Poznań University of Technology 60-965 Poznań, ul. Piotrowo 3a

Bibliografia

• [1] Barański M., Demenko A., Łyskawiński W., Szeląg W.: Finite element analysis of transient electromagnetic-thermal phenomena in a squirrel cage motor. COMPEL, Vol. 30 No. 3 (2011).
• [2] Karban P., Mach F., Kůs P., Pánek D., Doležel I.: Numerical solution of coupled problems using code Agros2D. Computing Volume 95, Issue 1 Supplement, pp. 381-408 May (2013).
• [3] Sowa M., Typańska D.: Pre-assembly of FEM n-th order triangular elements. Pozn. Univ. Technol. Acad. J., Electr. Eng. No. 77, 133-140 (2014).
• [4] Bolkowski S., Stabrowski M., Skoczylas J., Sroka J., Sikora J., Wincenciak S., Computer methods for the analysis of the electromagnetic field (in Polish). WNT, Warsaw (1993).
• [5] Sikora J., Numerical methods of solving boundary value problems. Basics of the finite element method and the boundary element method (in Polish). Lublin University of Technology Publishing House (2012).
• [6] www.wolfram.com/mathematica/
• [7] www. maplesoft. com/products/maple/
• [8] Freitag L.A., Plassmann P.E.: Local optimization-based untangling algorithms for quadrilateral meshes. Proceedings of the 10th International Meshing Roundtable, Newport Beach, CA, 397-406 (2001).
• [9] Danalia I., Joly P., Kaber S.M., Postel M.: An Introduction to Scientific Computing. Twelve Computational Projects Solved with MATLAB. Springer Science+Business Media, LLC, New York (2007).