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A numerical algorithm for a Kirchhoff-type nonlinear static beam. (English) Zbl 1417.74015

Summary: A boundary value problem is posed for an integro-differential beam equation. An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. A theorem on the algorithm error is proved.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
45J05 Integro-ordinary differential equations
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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