Finite element analysis of plane couple‐stress problems using first order stress functions

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Abstract
A complementary energy based variational principle, using first order stress functions, is developed for plane linear elastic couple‐stress problems. The principle is analogous to that used in a total potential energy based Mindlin/Reissner thick plate bending analysis and as such is a generalization of the classical analogy between plate stretching and plate bending. Traction boundary conditions are enforced using a Lagrange multiplier technique. The resulting C0 finite element ‘equilibrium stress model’ is validated by investigating the reduction of the stress concentration factor associated with a small hole in a field of uniform tension.

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