Prev Subsubsection 188.8.131.52: External Work Up Section 6.2: Elastodynamics Subsection 6.2.6: Energy-Momentum Conservation Scheme Next
We use the following interpolations: where are shape functions of the element parametric coordinates . Note that the operator should be evaluated at , using . For example, in the case of a scalar function , where the contravariant basis vectors may be evaluated from the covariant basis vectors using .
The discretization of the internal work produces where The discretization of the stress and elasticity terms in the internal work is where The discretization of the mass term in the internal work is where
For the external work of body forces, where and where For prescribed tractions, where and where where is the skew-symmetric tensor whose dual vector is .