MECH3300 Finite Element Methods

Apr 18, 2013

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Concepts. Node - a generalised joint - connection point at which equations are written - there are at most 6 unknowns (degrees of freedom) at a node (3 displacements, 3 rotations)Element - connection between a group of nodes representing stiffness or other properties approximately- interpolation of displacement between the nodal values is used - this becomes more accurate as element size is reducedReference node - an extra point used to orient the cross-section of a beam.

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MECH3300 Finite Element Methods

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MECH3300 Finite element methods

MECH3300 Finite element methods. Lecture 10 Issues in modelling Solving the equations. Use of symmetry.

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MECH3300 Finite element Methods

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MECH3300 Finite Element Methods Lecture 3

MECH3300 Finite Element Methods Lecture 3 . Practical aspects of implementing a direct stiffness solution for a structure made of beams. Exploiting the sparseness of [K].

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MECH3300 Finite Element Methods

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MECH3300 Finite Element Methods

Estimation of stress intensity. For well-known crack geometries, K or G can be found from formulae or charts. For more general cases, a finite element model can be used, both to estimate K and to predict growth of a crack.Several methods can be used to make FE estimates of KI. (1) Use the stres

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MECH3300 Finite Element Methods

Orthotropic materials. Most packages accept data for orthotropic materials those for which 3 perpendicular axes the principal material axes exist. These can have 3 Young's modulii and 3 Poisson ratios. Often both directions transverse to a fibre are the same, so that we can specify just a lo

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2.29 Numerical Fluid Mechanics Fall 2009 – Special Lecture 2. Discontinuous Galerkin Finite Element Methods. Mattheus P. Ueckermann MSEAS Group Department of Mechanical Engineering Massachusetts Institute of Technology. Presentation Outline. Background/Motivation Scalar Advection

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Introduction to Finite Element Methods. MCE 565 Wave Motion & Vibration in Continuous Media Spring 2005 Professor M. H. Sadd. Need for Computational Methods.

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MESF593 Finite Element Methods. HW #4 11:00pm, 10 May, 2010. Prob. #1 (10%). T 1. a 1 , CTE 1 , E 1. a 3 , CTE 3 , E 3. a 2 , CTE 2 , E 2. z. z. z. z. T 2. x. y. y. x. (a) Front View. (b) Edge View. T 1. a 1 , CTE 1 , E 1. a 3 , CTE 3 , E 3. a 2 , CTE 2 , E 2. T 2.

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Introduction to Finite Element Methods

Introduction to Finite Element Methods. ME6442, Dr. A.A. Ferri. Consider the flexural vibration of a non-uniform beam. x. w 1. w 2. q 1. q 2. Within each element, we have a particular E, I, r , A, L. w 1. w 2. q 1. q 2. x.

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Introduction to Finite Element Methods

Introduction to Finite Element Methods. (MCE 305) THEORY OF ELASTICITY BY DR. OLOKODE O.S MECHANICAL ENGINEERING DEPARTMENT UNIVERSITY OF AGRICULTURE, ABEOKUTA. Need for Computational Methods.

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MECH593 Finite Element Methods

MECH593 Finite Element Methods. Introduction Dr. Wenjing Ye. Introduction. Problem solving procedure:. Identify problem Generate models Solve equations Interpret results. Numerical methods - methods that seek quantitative approximations

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Finite element methods. L ászló Szirmay-Kalos. Representation of functions by finite data. Finite function series: L ( p )   L j b j ( p ). 1. box. 1. tent. b 1. b 1. b 2. b 2. b 3. b 3. Piece-wise constant. Piece-wise linear. Representation of the radiance.

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Generalized Finite Element Methods

Generalized Finite Element Methods. Other approximation methods. Suvranu De. Last class. Approximation properties of the Galerkin method. Galerkin method. Last class. Properties. Property 1: The discretization error is orthogonal to the approximation space X h in the energy norm.

790 views • 76 slides

Introduction to Finite Element Methods

Introduction to Finite Element Methods. MCE 565 Wave Motion & Vibration in Continuous Media Spring 2005 Professor M. H. Sadd. Need for Computational Methods.

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Generalized Finite Element Methods

Generalized Finite Element Methods. Mathematical Preliminaries. Suvranu De. Sets Linear (Vector) Spaces Inner product spaces and Cauchy Schwartz inequality Normed spaces Hilbert and Banach spaces Some Function Spaces Continuity spaces Lebesgue spaces Sobolev (Hilbert) spaces

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Generalized Finite Element Methods

Generalized Finite Element Methods. Approximation (Partition of Unity). Suvranu De. Discussion on MLS type approximations. Advantages Provides “ local ” shape functions (banded matrices) without having to use a “mesh” ( meshfree approximation )

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Generalized Finite Element Methods

Generalized Finite Element Methods. Discontinuous Approximations. Suvranu De. This class. Discontinuous approximations Modification of weight functions Visibility Criterion Diffraction Method Surface Mesh Enrichment using PUM X-FEM. Why ?.

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Generalized Finite Element Methods

Generalized Finite Element Methods. Integral Equation Methods. Discretization Convergence Theory. Suvranu De. Outline. Integral Equation Methods Reminder about Galerkin and Collocation Example of convergence issues in 1-D First and second kind integral Equations

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Generalized Finite Element Methods

Generalized Finite Element Methods. Polynomial interpolation. Suvranu De. In this class. Interpolation Polynomial interpolation Lagrange form Newton form Interpolation error estimate Piecewise polynomial interpolation (the finite element idea) in 1 and 2D Hermite interpolation.

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Generalized Finite Element Methods

Generalized Finite Element Methods. Approximate solution techniques: Rayleigh-Ritz and Galerkin Methods. Suvranu De. Last class. Strong formulation (BVP) Minimization statement Weak formulation (VBVP). This class. Approximate solution techniques: Rayleigh Ritz Method Galerkin Method

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Generalized Finite Element Methods

Generalized Finite Element Methods. Strong formulation, minimization principles, and weak formulation. Suvranu De. Last 5 classes. Polynomial interpolation Approximation Least squares Moving least squares Partition of unity paradigm Wavelets. This class. Differential equations:

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