Lecture 10 and 11 ENGR3030U Zeid Ch 17

Lecture 10 and 11 ENGR3030U Zeid Ch 17 - ENGR3030U George...

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Unformatted text preview: ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Finite Element Method Ch. 17 Objectives: Why the finite element method? Procedure of the finite element method. FEA and FEM. Preprocessors: mesh generation. Postprocessors: results display. Understanding the results. How CAD systems facilitate both FEA and FEM. ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Finite element modelling (FEM) and analysis (FEA) popular tools in CAD/CAM systems. Solves engineering problems involving complex shape or geometry, material properties, boundary conditions, and loading conditions. Useful where closed-form solutions not available to governing equilibrium equations. Finite element method (also FEA) consists of dividing shape into small elements and solving equilibrium equation for each element, then adding up results. Introduction ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 1. Create finite elements divide continuum into quasidisjoint nonoverlapping elements. Key points connecting elements called nodes . Finite Element Procedure Figure 17.1 Finite element mesh of a beam. ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 1. Approximate the solution within an element polynomial approximates variation of unknown within each element and may be scalar (ex., temperature), or vector (ex., horizontal and vertical displacements). Polynomials easy to differentiate and integrate. 2. Develop element matrices and equations properties defined for element (stiffness matrix, mass matrix, etc.). Equations for elements derived by direct method, variational method, weighted residual method, and energy method. 3. Generate global system matrix equation combining element equations into matrix, forming system of algebraic equations. Boundary conditions must then be applied. Finite Element Procedure ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 1. Solve for unknowns at nodes use Gauss elimination methods to obtain values for field variables at nodes. Obtaining values within elements can be obtained, but not normally done. 2. Interpret results Analyze solution for use in design decisions. Requires sound background in engineering and FEA. Dangerous to treat FEM/FEA as blackbox. Finite Element Procedure ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 Premise method solves integral form of governing equations. Solution is approximate. Differential operator stays intact and finite element method uses interpolation functions to approximate solution space. Finite difference method uses finite-difference approximation of differential operator while keeping solution space intact. Finite Element Analysis ENGR3030U George Platanitis, Ph.D, P.Eng. Fall 2009 CAD system have FEA/FEM built into them....
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Lecture 10 and 11 ENGR3030U Zeid Ch 17 - ENGR3030U George...

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