Finite element method for linear micropolar elasticity and numerical study of some scale effects phenomena in MEMS

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 are investigated by a set of numerical tests. The scale effects in the pure bending of ultra-thin beam and in the stress concentration problem of the plate with a hole are studied in detail. It is concluded that the beamʹs bending stiffness will increase significantly when the beamʹs thickness is close to the material characteristic length parameter, and that the stress concentration factor will decrease when the hole radius is close to the material characteristic length parameter. The coupling parameterʹs influences on the material mechanical behaviors are also studied.