Abstract:
The present paper is dedicated to the development of the foundations of the application of the finite element method to calculate the boundary value problems of statics of micropolar bending deformation of thin elastic plates. On the basis of application of laws of displacements, free rotations and functional of the total potential energy of the system, effective quadrangular finite elements are developed. With the help of the corresponding Lagrange variation principle of the applied theory of micropolar plates stiffness characteristics of finite element are determined and on the basis of the constructed stiffness matrix procedure of forming the resolving system of linear algebraic equations is performed. Concrete problem of bending of square micropolar elastic plate under a uniformly distributed power load is considered, when the edges of the plate are hinged-supported. The numerical results are compared with the results obtained on the basis of the theoretical study of the problem. The analysis of numerical results sets effective properties of the micropolar material from the point of view of stiffness and strength of the plate compared with the classic material.
Keywords:micropolar, elastic, plate, bend, potential energy functional of the system, finite element method.
