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2 2014

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Pre-assembly of FEM n-th order triangular elements

Sowa M., Typańska D.

Poznan University of Technology Academic Journals. Electrical Engineering

2014

No. 77

133--139

The paper presents a method of preparing data, which can be used to simplify the procedure of formulating local stiffness matrices in the finite element method (the part of preparing this data is hence referred to as the pre-assembly). For the presentation of the methodology non-curvilinear triangular elements have been chosen, where it has been taken into account that any order can be selected for the elements. The paper presents a mathematical basis of how the auxiliary data is prepared. The appropriate relations to the final FEM equations are also given.

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

Sowa M., Typańska D.

Computer Applications in Electrical Engineering

2014

Vol. 12

106--119

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.