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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<strong>Element</strong> Matrices<br />
where <strong>the</strong> following notation has been used<br />
H S , H = <strong>the</strong> shape function matrices (usually denoted by N)<br />
0<br />
f S , 0 f B = vector <strong>of</strong> surface <strong>and</strong> body <strong>for</strong>ces at time 0<br />
B L , t 0B L , t tB L =<br />
linear strain displacement trans<strong>for</strong>mation matrices<br />
t<br />
0B NL , t tB NL = nonlinear strain displacement trans<strong>for</strong>mation matrices<br />
0C, t C = incremental stress strain material property matrices<br />
t<br />
τ , t ˆτ = matrix <strong>and</strong> vector <strong>of</strong> Cauchy stresses<br />
t<br />
0S, t Ŝ = matrix <strong>and</strong> vector <strong>of</strong> 2nd Piola-Kirchh<strong>of</strong>f stresses<br />
<strong>The</strong>se matrices depend on <strong>the</strong> type <strong>of</strong> <strong>Finite</strong> <strong>Element</strong> considered<br />
Institute <strong>of</strong> Structural Engineering <strong>Method</strong> <strong>of</strong> <strong>Finite</strong> <strong>Element</strong>s II 13
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