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Finite element analysis of plane couple-stress problems using first order stress functions. (English) Zbl 0629.73054
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 \(C^ 0\) 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.

74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques
74S30 Other numerical methods in solid mechanics (MSC2010)
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