Abstract
Abstract This chapter introduces the calculus of variations and associated mathematical operators on functionals, which are used to formulate boundary value problems in structural mechanics. Weak forms of equilibrium are derived in terms of the principle of virtual work and the theorem of minimum potential energy. These are used to establish the governing field equations (Euler–Lagrange differential equations) and associated geometric, natural, or mixed boundary conditions. Weak forms of kinematic compatibility are derived in terms of the principle of complementary virtual Work and the theorem of minimum complementary potential energy. Examples are provided for each.
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