ALGORITHM TO PERFORM GENERALIZED ASSEMBLY OF FINITE ELEMENT MATRICES

Resumo

Each type of computational system, with its dimension and degrees of freedom, makes the
implementation of the finite element (FE) matrices assembly developments very specific, sometimes
generating unnecessary redundancy in codes, which make them more difficult to understand,
implement, read and update. A generalization of the assembly numerical methodologies for any kind
of FE matrices can give us a unique algorithm that can be implemented once for all FEM
computational problems, without the necessity to create a new code for each different case. This work
presents an algorithm based on the general assembly strategy for finite-elements matrices for plane
frames, implemented in Paraski [2]. This one algorithm tries to extrapolate the previous idea, being
capable to perform the assembly of FE matrices for simple and multi connected systems, not only for
plane frames, with one-dimensional FE bar, having three degrees of freedom, but for other kinds of
finite element types, like FE triangular and quadrilateral in two dimensions, and FE hexahedron and
tetrahedron in three dimensions, all of them having their own variations on their quantity of degrees of
freedom. Some validation tests using MatLab codes for static analysis for plane frames with one
dimensional FE bar, and Helmholtz equations problems with two-dimensional FE quadrilateral, was
successfully made, showing the efficiency of this algorithm being used in different cases, for different
elements working in different dimensions, with specific degrees of freedom.