Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler’s type. (English) Zbl 1224.74011

Sysala, Stanislav

Appl. Math., Praha 55, No. 2, 151-187 (2010).

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:

74B20	Nonlinear elasticity
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
90C20	Quadratic programming
90C31	Sensitivity, stability, parametric optimization

Keywords:

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

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