Geometry cells and surface definition by finite elements

The approximation of the geometry is important for computer-aided design. Due to the different requirements on the representation of the geometry of technical objects in various fields of applications a certain variety of curve, surface and body representation should be permitted [Boehm et al. ‘841. This paper presents an element-wise representation of geometrical objects. Basis of this technique is the approximation of the geometry by curve, surface and body elements. In order to avoid conflicts with the expression element we call this small geometric unit a cell. Advantages of this geometry cells are: (a) the representation is general (it exists no limitation to simple bodies), (b) the representation is computer-oriented (complex geometrical objects can be generated from simple cells in the computer and interactively modified), (c) the representation is geometry-oriented (several geometrical operations can be easily performed). For various applications a set of cells with different qualities is needed. This cell-wise approximation of the geometry is particularly well-suited if the designed object should later be analysed with the finite element method [Grieger ‘781 and, if the finite element idealisation should automatically created by mesh generation program. The second part of the paper deals with a special application of the finite element method to the surface definition problem [Grieger ‘731. A thin elastic plate is moved from the initial plane position to the final position in space. This procedure can be performed with a finite element program if plate elements of the fifth order are incorporated. An extension of this technique is the use of a shell element based on shape functions of complete fifth order.