MENG 4326: The Finite Element Method in Mechanical Engineering

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MENG 4326 The Finite Element Method in
Mechanical Engineering
ENGR 5328 Finite Element Analysis
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MENG 4326/ENGR 5328

• 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 engineering related problems. (4326
  Catalog description)
• Prereqs MATH 3203, MENG 3306 Pre/Coreq MENG
  3316
• Text Fundamentals of Finite Element Analysis, by
  David V. Hutton, McGraw-Hill, 2004
• Class meeting times
• Three hours lecture with integral computer lab
• MW 500 - 615 pm

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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
• 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

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MENG 4326/ENGR 5328

• 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

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Course Grading
ENGR 5328 requires additional report topic to
be assigned
(Note Late homework and lab assignments will
receive a reduced grade no grade after one
week.)
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What is Finite Element Analysis?

• A computer-based numerical technique typically
  used to solve stress analysis, heat transfer,
  fluid flow and other types of engineering
  problems
• Based on solving a system of equations describing
  a parameter (e.g., displacement) over the domain
  of a continuous physical system (e.g., a parts
  surface)
• Jack Zecher, Finite Element Analysis, Schroff
  Development Corp., 2004

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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
• 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

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What is Finite Element Analysis?

• 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).
• Field problems 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

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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)

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What is a Boundary Value Problem?

• A boundary value problem 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.

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The Finite Element Method

• Involves the partitioning (discretizing) of a
  structure into a finite number of elements
• Bars, triangles, quadrilaterals, tetrahedrons,
  rectangular solids, etc.
• The elements have the material and behavioral
  properties of portion of the region they
  represent
• Elements are connected to one another at their
  corner points (nodes)
• Elements sharing nodes have the same behavior
  (displacement, force, etc.) at the common node

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2D Elements, Nodes, and Meshes
Nodes
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3D Elements, Nodes, and Meshes
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Typical Element Types
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The FEA Modeling Process
Physical Reality
Model of the Physical Reality
Good Predictor?
Mathematical (FEA) Model
Solution of the Mathematical (FEA) Model
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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.

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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.

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Some Example Applications
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Ski Resort Chairlift Grip Redesign
Source Algor Customer Application Stories,
Algor, Inc.
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Female Adhesive Anchor Analysis
Deflected Shape
Source Algor Customer Application Stories,
Algor, Inc.
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FEA in Different Industries

• Orbital Technologies Corporation
• The above illustration shows how engineers
  analyzed a Biomass Production System to conduct
  biotechnology plant research.

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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.

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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.

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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.

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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

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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
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ALGOR FEA Software
General FEA Process
Solve
Preprocess
Postprocess
Basic ALGOR FEA Software Modules
Solve
FEM Pro
Superview
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Additional ALGOR Modules
Solid Modeler
InCAD
FEM Pro
IGES
Solve
Report
Superdraw
Superview
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Summary
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MENG 4326/ENGR 5328

• 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 engineering related problems. (4326
  Catalog description)
• Prereqs MATH 3203, MENG 3306 Pre/Coreq MENG
  3316
• Text Fundamentals of Finite Element Analysis, by
  David V. Hutton, McGraw-Hill, 2004
• Class meeting times
• Three hours lecture with integral computer lab
• MW 500 - 615 pm

31
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
• 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

32
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
33
The FEA Modeling Process
Physical Reality
Model of the Physical Reality
Good Predictor?
Mathematical (FEA) Model
Solution of the Mathematical (FEA) Model
34
Additional ALGOR Modules
Solid Modeler
InCAD
FEM Pro
IGES
Solve
Report
Superdraw
Superview
35
The End