Untitled

138 Antonio J. Gil
Total Potential Energy
1
0
−1
−2
−3
x 104
2
−4
1 2 3 4 5 6
Iterations
Infinite Norm on Residual Forces
10 2
10 0
10 −2
10 −4
10 −6
10 −8
10 −10
10
1 2 3 4 5 6
−12
Iterations
Fig. 11. Numerical example: Convergence curves.
Fig. 12. Numerical example: Displacements OX & OZ.
Levy & Spillers Present work
Node u v w u v w
1 0.015 -0.015 -1.431 0.014 -0.014 -1.423
2 0.000 -0.017 -2.605 0.000 -0.017 -2.600
5 0.000 0.000 -6.642 0.000 0.000 -6.626
Table 2. Numerical example: Displacements (in).
6Concluding Remarks
This chapter has offered a complete consistent numerical formulation for the structural
analysis of prestressed hyperelastic Saint Venant-Kirchoff membranes. Two
structural loading steps can be considered successively: in the first, the prestressing
loads are transferred to the structure whereas in the second, in service loads such
as live loads or wind load arise. By taking into account this approach, an initial