Civil Engineering Reference
In-Depth Information
The nodal displacements u
1
, u
2
, u
3
, v
1
, v
2
and v
3
can then be expressed by the six inter-
polation coeffi cients a
1
, a
2
, a
3
, b
1
, b
2
and b
3
as follows:
(10.2)
From these six linear equations a
1
, a
2
, a
3
, b
1
, b
2
and b
3
can be evaluated as functions of
the nodal coordinates and nodal displacements:
(10.3)
where A is the area of the triangular element.
Assuming elastic, isotropic stress--strain behavior strains and stresses within the ele-
ment can be derived from the two-dimensional formulation of the compatibility equa-
tions and Hooke's law:
(10.4)
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