Duality method in limit analysis problem of non-linear elasticity
Keywords:
non-linear elastic solid, limit analysis problem, duality methodAbstract
The limit analysis problem (LAP) for estimation of mechanical durability for non-linear elastic solids is examined. The appropriate dual problem is formulated. After the standard piecewise linear continuous finite-element approximation, the dual LAP is transformed into the problem of mathematical programming with linear limitations as equalities. This finite dimensional problem is solved by the standard method of gradient projection.
References
[1] G. M. Bartenev and Yu. V. Zelenev. A course in the physics of polimers (in Russian) . Chemistry, Leningrad, 1976.
[2] I. A. Brigadnov. On the existence of a limiting load in some problems of hyperelasticity. Mech . of Solids, 5: 46-51, 1993.
[3] I. A. Brigadnov. Existence theorems for boundary value problems of hyperelasticity. Sbomik: Mathematics, 187(1): 1-14, 1996.
[4] I. A. Brigadnov. On mathematical correctness of static boundary value problems for hyperelastic materials. Mech. of Solids, 6: 37-46, 1996.
[5] I. A. Brigadnov. Numerical methods in non-linear elasticity. In J.-A. Desideri, P. Le Tallec, E. Onate, J. Periaux, and E. Stein, eds., Numerical Methods in Engineering'96, pages 158-163, Chichester, 1996. John Wiley & Sons Ltd.
[2] I. A. Brigadnov. On the existence of a limiting load in some problems of hyperelasticity. Mech . of Solids, 5: 46-51, 1993.
[3] I. A. Brigadnov. Existence theorems for boundary value problems of hyperelasticity. Sbomik: Mathematics, 187(1): 1-14, 1996.
[4] I. A. Brigadnov. On mathematical correctness of static boundary value problems for hyperelastic materials. Mech. of Solids, 6: 37-46, 1996.
[5] I. A. Brigadnov. Numerical methods in non-linear elasticity. In J.-A. Desideri, P. Le Tallec, E. Onate, J. Periaux, and E. Stein, eds., Numerical Methods in Engineering'96, pages 158-163, Chichester, 1996. John Wiley & Sons Ltd.
Published
2023-01-26
Issue
pp. 385-390
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Brigadnov, I. A. (2023). Duality method in limit analysis problem of non-linear elasticity. Computer Assisted Methods in Engineering and Science, 10(4), 385-390. https://cames3.ippt.pan.pl/index.php/cames/article/view/1052
