Finite Element Approach to Plane Microelasticity

The object of the investigation reported herein was to explore the applicability of the finite element technique to the stress and deformation analysis of multidimensional bodies of microelastic materials. For simplicity, the presentation has been restricted to micropolar materials. No particular difficulty is, however, envisioned if the more general case of a micromorphic material is considered. The strain-energy density and the constitutive equations were calculated for both plane strain and plane stress. Subsequently, the stiffness matrix was developed for a simple triangular finite element. Results presented are applicable to a large class of practical problems, some of which will be covered in a subsequent paper. From this investigation, it is clear that the same process may be extended to elements of other shapes, higher-order elements for plane problems, flexural elements and elements of three-dimensional bodies.