The Finite Element Method for the Analysis of Non-Linear and ...
The Finite Element Method for the Analysis of Non-Linear and ...
The Finite Element Method for the Analysis of Non-Linear and ...
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Setting up <strong>the</strong> governing equations<br />
<strong>The</strong> incremental strain in eq (2) can be fur<strong>the</strong>r decomposed to<br />
0ɛ ij = 0 e ij + 0 η ij (3)<br />
where <strong>the</strong> linear incremental strains are:<br />
(<br />
)<br />
0e ij = 1 3∑<br />
t<br />
t<br />
0u i,j + 0 u j,i +<br />
2<br />
0u k,i 0 u k,j + 0 u k,i 0u k,j<br />
k=1<br />
where <strong>the</strong> nonlinear incremental strains are:<br />
0η ij = 1 3∑<br />
0u k,i 0 u k,j<br />
2<br />
k=1<br />
Fur<strong>the</strong>rmore, stresses can be written incrementally as:<br />
δ t+∆t<br />
0 S ij = δ t 0S ij + 0 S ij (4)<br />
Institute <strong>of</strong> Structural Engineering <strong>Method</strong> <strong>of</strong> <strong>Finite</strong> <strong>Element</strong>s II 3