2020 Volume 2020 Pages 20200001
A new discrete analysis method of solid mechanical problems is proposed in this paper. In this method, we use isolated elements which are completely cut off a solid to be analyzed. A set of displacement functions is provided for each isolated element so that be able to express the translation and the rotation of a rigid body. The principle of minimum potential energy that is expanded in order to satisfy the continuity of the displacement of isolated elements adjoining to each other is applied. Therefore, node or spring, Lagrange’s multiplier and penalty functions don’t exist in this method. The displacement functions of power series are used to describe the mechanical state of an isolated element and finally, the coefficients of series are determined by the variational principle. When analysis is executed, the apart isolated elements are returned to one deformed continuum by the action of natural boundary conditions of the variational principle. Two numerical examples of the plane stress problem are shown at the end of this paper.
