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5.5
The Duality of the Force and Displacement Methods
The similarity of the formulations of the displacement and force methods of Sections 5.3
and 5.4 illustrates the dual nature of the two techniques. This is the same duality that ex-
ists with the principle of virtual work and the principle of complementary virtual work.
The displacement method and the principle of virtual work require kinematically admis-
sible displacements, i.e.,
a
must be formed, and provide equilibrium equations. On the
other hand, the force method and the principle of complementary virtual work begin with
equilibrium conditions, i.e.,
b
must be formed, and lead to kinematic equations. These
relationships are illustrated in Fig. 5.34.
The dominant method in use today is the displacement method because it can be im-
plemented in a systematic fashion with the global stiffness matrix being assembled by a
summation process. This is strikingly different from the force method for which the forma-
tion of
b
is difficult to systematize.
FIGURE 5.34
Element and system matrices.
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