Information Technology Reference
In-Depth Information
FIGURE 6.22
Displacement pattern and accuracy of the finite element solution of the structure of Fig. 6.14a as the number of
elements varies.
6.5
Trial Functions and Formulation of Some Elements
6.5.1
Trial Functions
Fundamental to the successful implementation of the finite element method is the estab-
lishment of the element stiffness matrix and loading vector. This entails the evaluation of
integrals, a task which, as discussed in the following section, must often be accomplished
numerically. Also essential to establishing a useful element is the selection of adequate
trial functions for each element [Wunderlich and Redanz, 1995]. For the displacement finite
element method, the trial functions are approximate patterns of displacements, rotations,
or other fundamental variables often expressed in terms of the same variables at the nodes,
i.e., u i
=
N i v i
or if the superscript indicating the i th element is dropped
u
=
Nv
(6.47)
where v is a vector of values of u , or derivatives of u , at nodal points, and N is appropri-
ately constructed to permit u to take the desired values at the nodes. Of course, to insure
Search WWH ::




Custom Search