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Conservative semidiscrete difference schemes for Timoshenko systems. (English) Zbl 1442.74220

Summary: We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. Our method of proof relies on discrete multiplier techniques.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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