Plane isoparametric element based on Cosserat theory
QI Lei,ZHANG Ruojing(College of Aerospace Eng. & Mechanics,Tongji Univ.,Shanghai 200092,China)
To explain the scale effect of materials under the microscale,based on Cosserat theory and deduced from the stationary condition of potential energy functional,an eight-node Serendipity plane isoparametric element is proposed and a finite element method for plane is developed. There are three independent node freedoms at each node,including linear displacement in two directions and counterclockwise angular displacement. The stress concentration problem of a infinite flat plate with a central small hole is analyzed by the method in the case of uniaxial tension. The numerical calculation results are in good agreement with the analytical solution based on Cosserat theory,which indicate that the stress concentration factor k is strongly influenced by Poisson ratio μ,constant c and the value of a/l;the stress distribution around the little hole is significantly less than the prediction of classical elasticity theory due to the existence of couple stress. The method can be applied to the numerical analysis based on Mindlin couple stress theory by the regulation of constant c.