Finite Element Discretization
In this section, the finite element equations for the updated Lagrangian formulation are developed by means of the principle of virtual power. For this purpose the current domain Ω is subdivided into elements Ω e so that the union of the elements comprises the total domain, Ω = ∪ Ω e . The nodal coordinates in the current configuration are denoted by x iI , I= 1 to n N . Lower case subscripts are used for components, upper case subscripts for nodal values. In two dimensions, x iI = [x I ,y I ], in three dimensions x iI = [x I ,y I ,z I ]. The nodal coordinates in the undeformed configuration are X iI .
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