Theory Manual Version 3.4
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Subsection 6.2.3: Generalized Method for Elastodynamics Up Section 6.2: Elastodynamics Subsubsection 6.2.4.1: Internal Work

6.2.4 Linearization

The solution of the nonlinear equation is obtained by linearizing this relation as where the operator represents the directional derivative of at along an increment of [23]. According to the generalized method [42], the virtual work is evaluated using intermediate time step values, at for all parameters except , which is evaluated at . It follows from these definitions that the linearizations of critical variables are given by To linearize the virtual work, we need to express the integrals appearing in and over the material frame of the finite element solid domain.
Subsection 6.2.3: Generalized Method for Elastodynamics Up Section 6.2: Elastodynamics Subsubsection 6.2.4.1: Internal Work