An Approximation Method of Bézier Curve

It is proved that the linear space constructed by power base is a banach space under 2-norm by using approximation method. For the Bézier curve--the elements in banach space, the linear combination of the low-order S power base is used to approximate optimal the high-order Bernstein base function. The original Bézier curve is instituted by the linear combination of low-order S power base and the optimal approximation element of the original Bézier curve is obtained.

An Application of Multiresolution Analysis and Lifting Scheme in FEM

Based on multiresolution analysis and lifting scheme, and an adaptive finite element method（FEM） is developed. The coarse solution can be obtained in the approximation element. The coarse solution can be refined via adding details hierarchically and locally, then sharp transitions may be captured. The numerical example has verified the effectiveness of the proposed method.

Hybrid Journal Bearings: Theoretical and Experimental Results

The analysis of actual lubrication problems needs to take into account particularities in the flow coming from kinematic conditions and contact geometry. For hybrid journal bearings lubricated by low dynamic viscosity fluid, turbulence and pressure drops due to inertia forces in the recess outlets are phenomena which must be taken into account to compute their working characteristics. A global method of study of lubricated contacts in isothermal laminar or not laminar flow by finite element method is presented. It can solve a great number of lubrication problems. A new type of approximation element for lubrication (Hermitian type) is used because it offers the following advantages: The nonlinearities in lubrication which come from turbulence phenomena, geometrical discontinuities (pressure drops) or boundary conditions (recess pressure) require the derivation of unknown functions. Added interpolations are not necessary to determine these values because the nodal unknowns are the values of the function and its derivatives in the two directions. As the modified Reynolds equation is in Cartesian coordinates, in the case of closed geometries such as journal bearings, joining is done just by nodal identification which guarantees continuity of the pressure and of its derivatives. The validity of this numerical model is realized with an experimental study done with a three recess hybrid journal bearing for different kinematic and geometric configurations. In a general way, experimental and theoretical results are in good agreement.