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Mixed Petrov-Galerkin methods for the Timoshenko beam problem. (English) Zbl 0607.73076
A new mixed Petrov-Galerkin method is presented for the Timoschenko beam problem. The method has enhanced stability compared to the Galerkin formulation, allowing new combinations of interpolation, in particular, equal-order stress and displacement fields. The methodology is easily generalizable for multi-dimensional Hellinger-Reissner systems.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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