...Introduction to Finite Element Method Mathematic Model Finite Element Method Historical Background Analytical Process of FEM Applications of FEM Computer Programs for FEM 1. Mathematical Model (1) Modeling Physical Problems Mathematica l Model Solution Identify control variables Assumptions (empirical law) (2) Types of solution Sol. Eq. Exact Sol. Approx. Sol. Exact Eq. Approx. Eq. ◎ ◎ ◎ ◎ (3) Methods of Solution (3) Method of Solution A. Classical methods They offer a high degree of insight, but the problems are difficult or impossible to solve for anything but simple geometries and loadings. B. Numerical methods (I) Energy: Minimize an expression for the potential energy of the structure over the whole domain. (II) Boundary element: Approximates functions satisfying the governing differential equations not the boundary conditions. (III) Finite difference: Replaces governing differential equations and boundary conditions with algebraic finite difference equations. (IV) Finite element: Approximates the behavior of an irregular, continuous structure under general loadings and constraints with an assembly of discrete elements. 2. Finite Element Method (1) Definition FEM is a numerical method for solving a system of governing equations over the domain of a continuous physical system, which is discretized into simple geometric shapes called finite element. Continuous system Time-independent PDE Time-dependent...
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