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| A Modified Couple Stress Linear Elasticity and Finite Element Method for Generalized Elastic Bodies |
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Abstract Upon on the theory of elasticity with couple-stress, a modified constitutive equation between couple stress and curvature tensor is developed in this paper, taking account of the deformation as a result of translation and rotation in generalized elasticity bodies under infinitesimal deformation. The penalty function method is used to construct the constrained variational form for generalized elasticity, with the rotational angle as independent degree of freedom to relax the C1 continuity in finite element. The finite element equation of motion is given for the generalized elastic body, discretized by elements with 8-nodes and 48 degree of freedom. Static and dynamical analysis of a cantilever beam are presented showing the advantage in structural analysis fields for the generalized elasticity with couple stress effects, comparing to the classic elasticity and structural mechanics. In contrast to the classical elasticity and structural mechanics, the generalized elasticity for deformation body can capture the size dependent effects in material, which have a great influence on the dynamical characteristic of micro-structure.
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Received: 06 April 2011
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2012, Vol. 33 
