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Finite element method for linear micropolar elasticity and numerical study of some scale effects phenomena in MEMS. (English) Zbl 1098.74054
Summary: The finite element formulation for micropolar elasticity theory is derived from the potential energy functional of the discrete system. According to this formulation, three kinds of elements are designed and the effectiveness of these elements is investigated by a set of numerical tests. The scale effects in pure bending of ultra-thin beams and in the stress concentration problem for a plate with a hole are studied in detail. It is concluded that the beam bending stiffness will increase significantly when the beam thickness is close to a material characteristic length parameter, and that the stress concentration factor will decrease when the hole radius is close to the material characteristic length parameter. We also study the coupled parameter influence on the material mechanical behavior.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74A35 Polar materials
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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