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Virtual work is the total work done by the applied forces and the inertial forces of a mechanical system as it moves through a set of virtual displacements. When considering forces applied to a body in static equilibrium, the principle of least action requires the virtual work of these forces to be zero.
D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing forces of inertia which, when added to the applied forces in a system, result in dynamic equilibrium. [1] [2] D'Alembert's principle can be applied in cases of kinematic constraints that depend on velocities.
The static equilibrium of a mechanical system rigid bodies is defined by the condition that the virtual work of the applied forces is zero for any virtual displacement of the system. This is known as the principle of virtual work. [5] This is equivalent to the requirement that the generalized forces for any virtual displacement are zero, that ...
The principle asserts for N particles the virtual work, i.e. the work along a virtual displacement, δr k, is zero: [9] = (+) = The virtual displacements , δ r k , are by definition infinitesimal changes in the configuration of the system consistent with the constraint forces acting on the system at an instant of time , [ 22 ] i.e. in such a ...
The principle of virtual work states that if a system is in static equilibrium, the virtual work of the applied forces is zero for all virtual movements of the system from this state, that is, δW = 0 for any variation δr. [15]
The equilibrium equations for the plate can be derived from the principle of virtual work. For the situation where the strains and rotations of the plate are small ...
The Föppl–von Kármán equations are typically derived with an energy approach by considering variations of internal energy and the virtual work done by external forces. The resulting static governing equations (Equations of Equilibrium) are
In other words, the summation of the work done on the system by the set of external forces is equal to the work stored as strain energy in the elements that make up the system. The virtual internal work in the right-hand-side of the above equation may be found by summing the virtual work done on the individual elements.