טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentJacobovitz Ido
SubjectNon-Uniform Rational B-Spline (NURBS) Finite Element Method-
A Natural Unified Approach to Geometrical Design
and Mechanical Analysis
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Pinhas Bar-Yoseph
Full Thesis textFull thesis text - English Version


Abstract

A typical product development process consists of two major stages: geometrical design and mechanical analysis. In the first stage, the geometrical shape of the object is created in a Computer-Aided Geometrical Design (CAGD) system. The second analysis stage includes finite element mechanical analysis of the object in order to verify design specifications. These stages encompass the general structure of a typical commercial CAGD-CAE system consisting of a geometrical design module and a finite element analysis module which, due to the iterative nature of a typical product development process, should interact intensively, but yet the existing modules are operated as completely separate modules. Efficient communication between CAGD and CAE modules is crucial for fast, low cost design process. However, while CAGD software uses advanced representations for geometric entities (e.g. B-spline functions), FE analysis software remains still with polynomial approximations for both the physical and geometrical descriptions. Therefore, transformations between the two representations is frequently required, and it is highly time and resources consuming.

The main goal of this research is to formulate an advanced finite element analysis using the same geometric representations as used by the CAGD model. Isoparametric finite element basis functions generated from NURBS are naturally employed to precisely construct the original CAGD geometric model. According to this isogeometric approach, the first coarse mesh is designed to accurately represent the desired geometry, and therefore subsequent finite element h-, p-, and k- refinements are obtained without further communication with the CAGD module. Unique scheme attributes based on intrinsic properties of NURBS functions are investigated in detail. Method adequacy and superiority are demonstrated by comparing convergence characteristics, complexity and computational cost to the B-spline and spectral element methods for heat transfer and linear elasticity problems.