Abstract
Abstract This chapter discusses a variational formulation of boundary value problems in small deformation solid mechanics. It begins by introducing the important principle of virtual power, and shows that it encapsulates Cauchy’s traction law, and the local form of the basic balance of forces (equation of equilibrium), and the local from of the balance of moments (symmetry of the stress). Since the principle of virtual power encapsulates both the equation of equilibrium and the Cauchy relation for tractions, it can be used to formulate and solve boundary-value problems in solid mechanics in a variational or weak sense. Specifically, it is shown how the displacement problem of linear elastostatics may be formulated variationally using the principle of virtual power.
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