Theory And Application Of Bezier-Based Element Method

The purpose of this dissertation is to study a principle or method to describe and analyze the complex problems with high gradients arising from practical engineering. The main contents cover:1. The Bezier function was introduced to approximate high gradient functions, and a suitable coupled function was derived. Some detail numerical results show that the Bezier-based function is dominant over other combination function such as polynominal and trigonometric series, when to describe a high gradient function.2. As for the structural analysis and numerical simulation of a complex problem with high gradient, an idea was proposed, i.e. if the displacement field could be constructed by using both Bezier-based function and the mobile middle node? According to this strategy, a new coupling method, called as Bezier-Based Element Method (BBEM, for short), was proposed and studied in detail. The common types of coupling elements were derived, including Bezier Coupling Element(BCE) type and Bezier Iso-parametric Element(BIE) type. The new elements possess good performances in completeness and compatibility. Both BCE and BIE have a good compatibility with the conventional FEM.3. A reasonable criterion to control error of element was studied. Base upon this criterion, an indicator to drive the mobile node of BCE was presented. In order to improve the efficiency, an implementing scheme (according to the distribution of strain energy density) was suggested when to consider the fact that the high gradient usually appears only in a very local region, especially in the case of huge amount of computation. All programming has been finished on the platform of commercial codes Mathmatica and Fortran.4. A number of numerical examples and applications were presented to verify the proposed Bezier-Based Element Method. The engineering cases include: the belt die for diamond synthesize, the main frame of wire-rounded press, the hydraulic cylinder of open die forging press. The numerical results show that the BBEM has some good performances. With few elements, the BBEM can lead to a high accuracy. If using same DOFs, the computing precision of BBEM is remarkable higher than that of the conventional FEM.The research was supported by the National Natural Science Foundation (No.50175060) and the National Outstanding Youth Science Foundation (No.59825117).