where [delta]x is a
virtual displacement between two neighboring trajectories of system (1).
According to the
virtual displacement principle of elastic mechanics, the momentum equation of coal-rock mass skeleton under quasi-static condition is [11]
In the finite element method, the coordinates, velocity, acceleration, and
virtual displacement are interpolated from their values at the nodes using shape functions, [N.sub.A], where A is the node number.
According to the principle of
virtual displacement, it can be obtained:
Using the principle of
virtual displacement, the equilibrium equation can be expressed for CLPT as:
The development of corrosion-induced rebar expansion is simulated based on the increase in the
virtual displacement resulting from corrosion-induced rebar expansion to understand the effect of the increase in rebar corrosion on the stress field in the surrounding concrete.
The cohesive virtual work [delta][W.sup.coh] is produced by traction vector [t.sub.d] between the faces of the discontinuity rd and the
virtual displacement jump vector [[[delta]u]]; thus
According to the principle of
virtual displacement, the virtual potential energy [delta]U should vanish at the equilibrium state of the system.
According to Bathe (1996), the equation of
virtual displacement in the Total Lagrangian Formulation is given by Equation 1:
where [delta]u is the
virtual displacement and [P.sup.*] is the generalized force.
The governing equations of the third-order nonlocal plate theory can be derived, using the dynamic version of the principle of
virtual displacement (Hamilton's principle), as