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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Truss <strong>and</strong> Cable <strong>Element</strong>s<br />
Matrix Equivalent Formulation<br />
Strain Displacement Matrices<br />
t<br />
0B L = ( 0 J −1 ) 2 ( 0 x T N Ț rN ,r + t u T N Ț rN ,r )<br />
t<br />
0B NL = ( 0 J −1 )N ,r :independent <strong>of</strong> orientation<br />
where 0 J −1 = dr<br />
d 0 s <strong>and</strong> 0 s(r) is <strong>the</strong> arc length (coordinate) at point<br />
(x 1(r), x 2(r), x 3(r)) given by<br />
n∑<br />
0<br />
s(r) = N k0 s k<br />
k=1<br />
<strong>The</strong> only non zero stress component is t 0˜S 11<br />
<strong>and</strong> <strong>the</strong> tangent Stress<br />
Strain relationship <strong>the</strong>re<strong>for</strong>e is:<br />
0C 1111 = ∂t 0˜S 11<br />
∂ t 0˜ɛ 11<br />
Institute <strong>of</strong> Structural Engineering <strong>Method</strong> <strong>of</strong> <strong>Finite</strong> <strong>Element</strong>s II 17