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Bending analysis of micropolar elastic beam using a 3-D finite element method. (English) Zbl 1210.74166
Summary: Based on Eringen’s micropolar elasticity theory (MET) and variation principle, a 3-D Wilson’s non-compatibility finite element formulation (FEM) with eight nodes is derived and a corresponding computer program is developed for solving the micropolar elastic beam problems. First, we developed an analytical solution for straight beam problems, based on the theory of material strength. Then the new 3-D FEM is applied to solve both straight and curve beam problems. Our numerical results are found to be in excellent agreement with the exact analytical solution obtained by MET developed in this paper for the straight beam case and the results from Gauthier for the curved beam case.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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