Another Look at the Application of the Principle of Virtual Work with Particular Reference to Finite Plate and Shell Elements

Summary

In the finite element model each element may be looked upon as a deformable body, however with a limited number of deformation modes, determined by the number of nodal displacement and rotation components on its boundary. In terms of a corresponding number of suitably defined strain parameters finite element properties are derived for plate and shell elements, valid for arbitrarily large displacements and rotations. The membrane properties are derived from a strain– or a elastic potential distribution in the domain of the element. The bending properties follow from an equilibrium field of internal moments and are restricted to small deformations of the element. It is shown that for triangular elements all properties can be given in closed form, but for large rotations the equations of equilibrium can only be solved as rate equations if bending is taken into account.