Civil Engineering Reference
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(10.10)
Equations (10.10) can also be expressed in a more compact matrix form:
(10.11)
where [K] is known as the stiffness matrix and {
δ
} and {F} are the vectors of nodal
displacements and nodal forces, respectively.
The unknowns in (10.10) and (10.11) are, respectively, the nodal displacements and the
nodal forces. This equation system of six equations with twelve unknowns can be solved
after introducing the boundary conditions as shown by the following example.
Nodes 1 and 2 of the triangle are located on a fi xed and a sliding support, respectively,
leading to the boundary conditions u
1
= v
1
= v
2
= 0 and F
x2
= 0. Node 3 is loaded by
a vertical force F, leading to F
x3
= 0 and F
y3
= F. Thus, the number of unknowns is re-
duced from twelve to six and the linear equation system of six equations can be solved
uniquely (Fig. 10.2).
Figure 10.2
Example,
system of linear equations
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