Page 93 - Finite Element Analysis with ANSYS Workbench

84 Chapter 5 Plate Bending analysis

5.2 Finite Element Method

5.2.1 Finite Element Equations
Finite element equations can be derived by applying the
method of weighted residuals to the governing differential
equation. Detailed derivation can be found in many finite element
textbooks including the one written by the same author. The
application leads to the finite element equations in matrix form as,
K 

      F F Q M   
F
p

where  is the element stiffness matrix;   is the element
K
vector containing nodal deflections in the z-direction and rotations
F
about the x- and y-coordinates;   is the element vector of the
Q
nodal shearing forces; F M  is the element vector of the nodal
bending moments; and   is the element vector containing nodal
F
p
loads from the applied pressure (, )p xy .

5.2.2 Element Types

Size of the matrices in the finite element equations
above depends on the element type selected. Element types could
be in triangular or quadrilateral shapes as shown in the figures.
These elements may consist of only corner nodes as well as
additional nodes on their edges.

3 7 3
4
4 6
5 8
2
2
6
1 1 5