Slide_chpt01Introduction有限元课件.ppt

The Finite Element Method CONTENTS CONTENTS INTRODUCTION PHYSICAL PROBLEMS IN ENGINEERING COMPUTATIONAL MODELLING USING FEM Geometry modelling Meshing Material properties specification Boundary, initial and loading conditions specification SIMULATION Discrete system equations Equation solvers VISUALIZATION INTRODUCTION Design process for an engineering system Major steps include computational modelling, simulation and analysis of results. Process is iterative. Aided by good knowledge of computational modelling and simulation. FEM: an indispensable tool PHYSICAL PROBLEMS IN ENGINEERING Mechanics for solids and structures Heat transfer Acoustics Fluid mechanics Others COMPUTATIONAL MODELLING USING FEM Four major aspects: Modelling of geometry Meshing (discretization) Defining material properties Defining boundary, initial and loading conditions Modelling of geometry Points can be created simply by keying in the coordinates. Lines/curves can be created by connecting points/nodes. Surfaces can be created by connecting/rotating/ translating the existing lines/curves. Solids can be created by connecting/ rotating/translating the existing surfaces. Points, lines/curves, surfaces and solids can be translated/rotated/reflected to form new ones. Modelling of geometry Use of graphic software and preprocessors to aid the modelling of geometry Can be imported into software for discretization and analysis Simplification of complex geometry usually required Modelling of geometry Eventually represented by discretized elements Note that curved lines/surfaces may not be well represented if elements with linear edges are used. Meshing (Discretization) Why do we discretize? Solutions to most complex, real life problems are unsolvable analytically Dividing domain into small, regularly shaped elements/cells enables the solution within a single element to be approximated easily Solutions for all elements in the domain then approximate the solutions of the complex problem itse