Classification and Application of Element

Abstract

In chapter 2, the structure of FEM, i.e., the derivation process of stiffness equation and element stiffness matrix, was explained. It might be needlessly time consuming, if we had to follow these processes every time we solve a problem. Fortunately, there is no need for it. Because the stiffness equation is, as will be understood from the derivation process in chapter 2, basically invariable whether it belongs to two-dimensional problem or to three-dimensional problem. FEM is formulated and programmed so as to be applicable to a variety of problems. Several kinds of element shapes are prepared as a standard for the variety of modeling which requires different geometry. The element stiffness matrix for each element is also predetermined as a standard. Our effort is limited to select — according to the kind of the problem or the geometry of the object — the appropriate element from a pool of prepared elements. If we cannot find the appropriate element from the standard, new elements must be developed. In this case, the stiffness matrix of the new element will be gained by following derivation process in chapter 2. It is admittedly rare that we face a problem that needs element derivation, because a fairly abundant number of elements are usually prepared for the general purpose FEM software. The situation is quite similar in the case of spring calculation by FEM, and it is important to select appropriate elements corresponding to the type of spring.