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Zbl 1224.74011
Sysala, Stanislav
Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type. (English)
[J] Appl. Math., Praha 55, No. 2, 151-187 (2010). ISSN 0862-7940; ISSN 1572-9109/e

Summary: A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is also investigated. The effectiveness of the algorithms is illustrated on numerical examples.

MSC 2000:: *74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
90C20 Quadratic programming
90C31 Sensitivity, etc.

Keywords: non-linear subsoil of Winkler's type; semi-coercive beam problem; approximation; iterative method; convergence; projection; load stability

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