An Assessment of Displacement Finite Elements for Couple Stress Elasticity

摘要

The conventional displacement finite element method is extended to the solution of two-dimensional boundary-value problems in linear couple stress theory of elasticity. The correct application of the principle of minimum potential energy in couple stress theory dictates the assumed displacement fields as well as their first derivatives be continuous inside each element and across the element boundary. Therefore, cubic interpolation polynomials are employed for the approximation of the displacement fields within one element and the formulation of the basic 3-node, 18-degree of freedom triangular element is discussed; all stiffness matrices and load vectors are derived explicitly. The performance of the present element is assessed and a comparison is made with an alternative displacement based 3-node, 9-degree of freedom triangle.