Principle of Virtual Displacements enforces equilibrium (in weak form) enforces traction(natural) boundary conditions does NoT enforce displacement(essential) boundary conditions will be satisfied for all equilibrated solutions, compatible or in- compatible Unit dummy displacement method Another application of the PVD: provides a way to compute reactions(or dis- placements) in structures directly from PVD. Consider the concentrated reaction force at point 0 of a structure in equilibrium under a set of loads and supports. We can prescribe an arbitrary admissible displacement field ii and the PVD will hold. The unit dummy displacement method consists of choosing the virtual displacement field such that )=l in the direction of the reaction Ro we are interested in. Then the virtual work of the reaction is to Ro=Ro. The PVD then reads(in the absence of body forces Ro·0=/o;;dV (10) ij∈ij 11) where Ei are the virtual strains produced by the virtual displacement field uo Example: 5¯ ¯ ¯ � � • Principle of Virtual Displacements: – enforces equilibrium (in weak form) – enforces traction (natural) boundary conditions – does NOT enforce displacement (essential) boundary conditions – will be satisfied for all equilibrated solutions, compatible or in￾compatible Unit dummy displacement method Another application of the PVD: provides a way to compute reactions (or dis￾placements) in structures directly from PVD. Consider the concentrated reaction force at point ��0�� of a structure in equilibrium under a set of loads and supports. We can prescribe an arbitrary admissible displacement field u¯i and the PVD will hold. The unit dummy displacement method consists of choosing the virtual displacement field such that u¯i(x0) = 1 in the direction of the reaction R0 we are interested in. Then the virtual work of the reaction is u¯0 · R0 = |R0. The PVD then reads (in the absence of body forces): R0 · u¯0 = σij �ijdV (10) V R0 = V σij �ijdV (11) where �ij are the virtual strains produced by the virtual displacement field u¯0. Example: 5