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The Finite Element Method in Mechanical Engineering

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Title: The Finite Element Method in Mechanical Engineering


1
The Finite Element Method in Mechanical
Engineering
  • MENG 4326

2
MENG 4326
  • An introduction to the finite element method in
    mechanical engineering. Emphasizes linear stress
    and strain analysis, but includes other field
    problems. Utilizes commercial computer codes to
    solve stress analysis, heat transfer, and other
    engineering related problems. (Catalog
    description)
  • Text Fundamentals of Finite Element Analysis, by
    David V. Hutton, McGraw-Hill, 2004
  • Class meeting times
  • Lecture MW 100 - 150 pm
  • Computer Lab F 900 am - 1145 am

3
Course Objectives
  • Demonstrate an understanding of the fundamental
    concepts of the finite element method form basic
    matrix equations
  • (stiffness) x (displacement) (load)
  • Select appropriate FE element for the physical
    model
  • Know how to apply loads and boundary conditions
  • Preprocess, solve, and postprocess 2- and
    3-dimensional, linear problems using ALGOR
    software
  • Understand importance of checking solutions with
    back-of-envelope calculations/engineering
    judgment

4
MENG 4326
  • Topics covered
  • Basic concepts of the Finite Element Method (FEM)
  • Stiffness matrices, spring and bar elements
  • Truss structures the direct stiffness method
  • Flexure elements
  • Method of weighted residuals
  • Interpolation functions for general element
    formulation
  • Applications in solid mechanics
  • Applications in heat transfer
  • Structural dynamics

5
Course Grading
(Note Late homework and lab assignments will
receive a reduced grade no grade after one
week.)
6
What is Finite Element Analysis?
  • The finite element method is a general technique
    for constructing approximate solutions to
    boundary-value problems. The method involves
    dividing the domain of the solution into a finite
    number of simple sub domains, the finite
    elements, and using variational concepts to
    construct an approximation of the solution over
    the collection of finite elements.
  • Becker, Carey, and Oden, Finite Elements, vol. 1
    An Introduction, Prentice-Hall, 1981

7
What is Finite Element Analysis?
  • Finite element analysis is a method for
    numerical solution of field problems. A field
    problem requires that we determine the spatial
    distribution of one or more dependent variables
    (e.g., temperature, displacement, stress).
    Mathematically, a field problem is described by
    differential equations or by an integral
    expression. Either description may be used to
    formulate finite elements.
  • Cook, Malkus, Plesha, and Witt, Concepts and
    Applications of Finite Element Analysis, 4th ed.,
    John Wiley, 2001

8
What is Finite Element Analysis?
  • The finite element method (FEM), sometimes
    referred to as finite element analysis (FEA), is
    a computational technique used to approximate
    solutions of boundary value problems in
    engineering.
  • Hutton, Fundamentals of Finite Element Analysis,
    McGraw-Hill, 2004 (Our text)

9
What is a Boundary Value Problem?
  • A boundary value problem is a mathematical
    problem in which one or more dependent variables
    must satisfy a differential equation everywhere
    within a known domain of independent variables
    AND satisfy specific conditions on the boundary
    of the domain.

10
The Finite Element Method
  • The FE method works by breaking a real object
    down into a large number of elements, such as
    little cubes
  • The behavior of each little element is readily
    predicted by set mathematical equations.
  • The "finite" in finite element analysis comes
    from the idea that there are a finite number of
    elements in a finite element model (as opposed to
    the infinite number of infinitesimal elements of
    integral calculus).
  • The computer adds up all the individual behaviors
    to predict the behavior of the actual object.

11
2D Elements, Nodes, and Meshes
Nodes
12
3D Elements, Nodes, and Meshes
13
The FEA Modeling Process
Physical Reality
Model of the Physical Reality
Good Predictor?
Mathematical (FEA) Model
Solution of the Mathematical (FEA) Model
14
Best Practices
  • FEA requires engineering judgment. In the best
    case, you should know the approximate answer
    before you begin.
  • Proper selection of elements, materials, loads,
    constraints and analysis parameters comes from
    experience.

15
Best Practices
  • Understand that the computer model never matches
    reality (its only an approximation).
  • The surest route to failure in FEA is to
    underestimate the complexity of the technology.

16

Some Example Applications
17
Ski Resort Chairlift Grip Redesign
Source Algor Customer Application Stories,
Algor, Inc.
18
Female Adhesive Anchor Analysis
Deflected Shape
Source Algor Customer Application Stories,
Algor, Inc.
19
FEA in Different Industries
  • Orbital Technologies Corporation
  • The above illustration shows how engineers
    analyzed a Biomass Production System to conduct
    biotechnology plant research.

20
FEA in Different Industries
Automotive Industry
  • Danly Engineering Services, Division of Enprotech
    Mechanical Services, Inc.
  • The above illustration shows how engineers
    analyzed a power press with additional cutouts.

21
FEA in Different Industries
Biomedical Industry
  • Ophthalmic Consultants of Boston and the Tufts
    University School of Medicine
  • The above illustration shows stresses on an eye
    as it underwent a 30 saccadic eye movement.
    This was modeled to help understand why retinal
    detachments occur.

22
FEA in Different Industries
Power/Utility Industry
  • Cronulla Sewage Treatment Plant
  • The above illustration shows how engineers
    modeled a piping system to verify that the number
    of bellows could safely be reduced by using
    lightweight, spiral-wound stainless steel. This
    allowed them to keep a 90 million sewage
    treatment plant upgrade on budget.

23
Application of the FEM
  • FEM is employed to predict the behavior of
    virtually all physical phenomena in engineering
  • Mechanical stress (stress analysis)
  • Mechanical vibration
  • Heat transfer - conduction, convection, radiation
  • Fluid Flow - both liquid and gaseous fluids
  • Many other field phenomena

24
Finite Element Analysis (FEA)
  • Typical Steps in FEA
  • Create a mesh (a grid of nodes and elements) that
    represents the model
  • Apply the loads
  • Define the boundary conditions which prevent the
    model from moving
  • Define the element properties
  • Assemble the element stiffness matrices
  • Solve the system of linear algebraic equations
  • Calculate the stresses
  • Review deflections and stresses results

Solve
Preprocess
Postprocess
25
ALGOR FEA Software
General FEA Process
Solve
Preprocess
Postprocess
Basic ALGOR FEA Software Modules
Solve
Superdraw
Superview
26
Additional ALGOR Modules
Solid Modeler
InCAD
FEM Pro
Solve
Report
Superdraw
Superview
IGES
27

Summary
28
MENG 4326
  • An introduction to the finite element method in
    mechanical engineering. Emphasizes linear stress
    and strain analysis, but includes other field
    problems. Utilizes commercial computer codes to
    solve stress analysis, heat transfer, and other
    engineering related problems.
  • Class meeting times
  • Lecture MW 100 - 150 pm
  • Computer Lab F 900 am - 1145 am

29
What is Finite Element Analysis?
  • Finite element analysis is a method for numerical
    solution of boundary value problems.
  • The method involves dividing the domain of the
    solution into a finite number of simple sub
    domains, the finite elements, and using
    variational concepts to construct an
    approximation of the solution over the collection
    of finite elements.

30
Finite Element Analysis (FEA)
  • Typical Steps in FEA
  • Create a mesh (a grid of nodes and elements) that
    represents the model
  • Apply the loads
  • Define the boundary conditions which prevent the
    model from moving
  • Define the element properties
  • Assemble the element stiffness matrices
  • Solve the system of linear algebraic equations
  • Calculate the stresses
  • Review deflections and stresses results

Solve
Preprocess
Postprocess
31
The Modeling Process
Physical Reality
Model of the Physical Reality
Good Predictor?
Mathematical (FEA) Model
Solution of the Mathematical (FEA) Model
32
ALGOR FEA Software
General FEA Process
ALGOR FEA Software Modules
33
The End
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