Finite Element Analysis. Barna Szabó
3rd Column c 43 Superscript left-parenthesis 3 right-parenthesis 4th Column c 44 Superscript left-parenthesis 3 right-parenthesis EndMatrix EndLayout EndLayout"/>
where the elements within the brackets are in the local numbering system whereas the coefficients aj and bi outside of the brackets are in the global system. The superscripts indicate the element numbers. The terms multiplied by
Assuming that the boundary conditions do not include Dirichlet conditions, the bilinear form can be written in terms of the
(1.76)
The treatment of Dirichlet conditions will be discussed separately in the next section.
The assembly of the right hand side vector from the element‐level right hand side vectors is analogous to the procedure just described. Referring to eq. (1.73) we write
where
1.3.6 Condensation
Each element has
Let us partition the coefficient matrix and right hand side vector of a finite element with
where the
we get
(1.78)
The condensed stiffness matrices and load vectors are assembled and the Dirichlet boundary conditions are enforced as described in the following section. Upon solving the assembled system of equations the coefficients of the internal basis functions are computed from eq. (1.77) for each element.
1.3.7 Enforcement of Dirichlet boundary conditions
When Dirichlet conditions are specified on either or both boundary points then