Theory Manual Version 3.4
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Subsection 3.7.2: BFSI Linearization Up Section 3.7: Weak Formulation for BFSI Subsection 3.7.4: BFSI Traction Interface

### 3.7.3 BFSI Spatial Discretization

The degrees of freedom , , are spatially interpolated over the domain using the same interpolation functions , with to , where is the number of nodes in an element, Here, , , and are the nodal values of the degrees of freedom that evolve over time. These relations may be used to evaluate , , , , , , etc. Similar interpolations are used for virtual increments , and , as well as real increments , and . In practice, interpolations are performed in the parametric space of each finite element, which is a material frame.
Now, the discretized form of , using Eq. (3.3.1.1-1), may be written as where The discretized form of becomes where whereas that of becomes where and finally, for the equations become where for external virtual work in Eq. (3.3.1.1-1), the discretized equations are where and the discretized forms of the linearized external virtual work are where
Combining these results, from the linearized virtual work equation of (3.5.2-2) we can represent the system of equations in a compact matrix form as
Subsection 3.7.2: BFSI Linearization Up Section 3.7: Weak Formulation for BFSI Subsection 3.7.4: BFSI Traction Interface