Using the principle of virtual displacement
, the equilibrium equation can be expressed for CLPT as:
According to Bathe (1996), the equation of virtual displacement
in the Total Lagrangian Formulation is given by Equation 1:
She pulls no punches in her attacks on "the most pernicious aspect of the second generation phenomenon: the virtual displacement
of the survivors by their own descendants through the appropriation of Holocaust narratives.
The principle of virtual work states that the equilibrium of the structure requires that for any virtual displacement
field imposed on the structure, the sum of the virtual work of the internal and the inertial forces is equal to the total virtual work of the external loads, which results in the following weak form integral equation:
In viewing the televised commentators these last several days, I have noticed that the demagogues, of two or three decades ago, have re-emerged from their political grottoes to advocate, among other things, the virtual displacement
of our civil liberties, the resumption of the assassination of heads of state and the granting of unfettered power or authority to certain governmental agencies, all in the name of ``protecting our way of life.
Performing the inner product between equation (1) and the virtual displacement field [delta][u.
Considering that the virtual displacement of nodes are arbitrary, equation (28) turns into the non-linear system of equation to be solved, i.
0] and [GAMMA] stand respectively for the volume of the undeformed membrane and the surface of the deformed membrane, t is the external surface force due to pressure and [delta]u is a virtual displacement vector compatible with displacement boundary conditions.
e] represent respectively the real displacements, the compatible virtual displacements, and positions.
The principle of virtual displacements
formulation for the dynamics equilibrium equation at t = t + [DELTA]t for the fiber can be written as
This yields the formulation of the d'Alembert principle, which states that a state of dynamic equilibrium exists if the virtual work for arbitrary virtual displacements
After a review of Newtonian dynamics, the basic concepts of analytical dynamics--classification of constraints, classification of forces, virtual displacements
, virtual work, and variational principles--are introduced and developed.