Surface Modeling Theories And Methods Based On Elastic-plastic Deformation

Curve and surface modeling method has been widely used in the design. But traditional methods are generally defined on Cartesian coordinate system and which can not be representation of conic. To solve this problem we proposed new modeling based on cylindrical coordinates.Analysised the traditional curve and surface modeling methods based on the latest research progress. And with depth research of surface modeling in elastic-plastic theory, the researches include:Rotated the curves on Cartesian coordinate system can obtain the rotating surface, and then give them relevant properties and rotating basis if they have.Improvements the rotating surface to, we can get tensor Bézier surface, B-spline surface and spline with smooth cofactor. These methods conquer the rotated surface so symmetry which make it difficult to apply in surface modeling.Introduce the trigonometric functions to constitute a mixed tensor basis on cylindrical coordinates, this tensor type modeling is well smoothly spliced during the end and begin. And it provides a new method on surface modeling.In studing the elastoplastic theory we found when given a ring plates applied to a particular load on annular plate boundary and split line the thin plate deflection to ring spline.When given a plate and subdivided by arcs and rays and applied an appropriate load on subdivision line and the boundary, the surfaces can be pure and non-pure spline with smoothing cofactor.