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Structural Optimization in FEA

April 5th - May 10th, 2018
 07:00 PDT / 
10:00 EDT15:00 BST / 16:00 CEST

 Four-Session Online Training Course One 2.5 hour* session per week

Engineering Board PDH Credits: 10 hours**

Note: Once you register for the course using the "order" button (look right), you will receive a confirmation e-mail with your payment information. A few days before the course is due to start, you will receive all the details needed to attend. Please click here to view the FAQ section, or if you need to contact NAFEMS about this course.

Course Overview

Structural Optimization in Finite Element Analysis

Finite Element Analysis has emerged has a tool that can play a vital part in the drive towards the ultimate goal of any manufacturing process; to produce the most effective products in the most efficient manner. This simple statement embraces all of the ‘right first time’, ‘minimum design to test cycles’ and other practices that have evolved.

The introduction of a formal structural optimization strategy into this process has met with great success in many industries. It makes the creation of the most effective product that much more attainable.

Traditionally one might think of the Aerospace Industry as the classic example with the goal of keeping weight to a minimum.  Indeed the structural efficiencies of modern aircraft owe a lot to optimization methods. However, it would be wrong to think of this as always a strength and stiffness against weight minimization task. The interaction of Aerodynamics, Aeroelasticity, Structures, Performance, Operating Cost and many other disciplines all have to play a role in the overall vehicle design.

This gives the clue as to the broader nature of structural optimization across all industries. The objective does not need to be weight minimization. It could be, for example driving down the overall vibration amplitude of a hairdryer, whilst keeping away from unpleasant harmonic frequencies. Weight has still to be monitored, and we can place an upper limit on this – but the other factors are more important and will feature directly in the optimization analysis.

Similarly other disciplines can play a role in structural optimization. In the case of pump housing, we want this to be stiff and strong enough to do the job, with minimum weight. However the cost of manufacture is important so a parametric penalty function can be introduced which ‘steers’ the weight reduction to a compromise solution which is cheaper to machine.

How do we define the penalty function in the above case?  Well, that’s where the ingenuity of the analyst comes in! Knowing how to set up the optimization task and how to obtain innovative solutions with the tools provided is a key to success in Finite Element Analysis Structural Optimization.

The objective of this course is to show you a broad overview of the range of Finite Element Analysis-based tools available and what the methods and specializations of each encompass. Plentiful hints and tips will demonstrate powerful ways to use these methods. The goal is to achieve meaningful structural optimization in support of the most effective products.

Course Process and Details 

The course is completely code independent. No software is required.

Each topic in the class is treated as a building block and is presented using an overview of the physics and theory involved. The math is kept simple and the emphasis is on practical examples from real life to illustrate the topic. 

The mapping to Finite Element Analysis techniques is shown with numerous case studies. The tutor will be presenting methodology and results and involving the students in the process via Q and A periods during each session, follow up emails and a Course Bulletin Board

  • Interaction is encouraged throughout the course. Students are welcome to send in problems from Industry and these will be discussed as time permits.

  • Full notes are provided for the students, together with personal passwords for e-learning backup material, bulletin board access etc.

Students will join the audio portion of the meetings by utilizing the VoIP (i.e. headset connected to the computer via headphone and microphone jacks) or by calling into a standard toll line. If you are interested in additional pricing to call-in using a toll-free line, please send an email to:
e-learning @ .

Who Should Attend?

This course is aimed at practising engineers who wish to learn more about how to apply the various optimization methods available to Finite Element Analysis structural analysis in the most effective manner. Ideally, a student should have some experience of FEA analysis, but this is not essential. The material that is presented is independent of any particular software package, making it ideally suited to current and potential users of all commercial finite element software systems. This course is a must for all engineers who plan to apply optimization methods to their analysis projects with the goal of improving the efficiency of their designs.

Course Program

Notes: This is a four-week course. Each session represents one 2-hour session each week. (Note: Sessions may last for 2.5-3 hours, including the Q&A sessions.)  
Recordings of each session are made available to course attendees in the event they are unable to participate in one or more of the live meetings, or if they wish to review the material following each session.

The times and dates listed for each session are tentative; we try to schedule these sessions at times convenient for the majority of course attendees.

Session 1

  • Finite Element Analysis Overview
  • Background  and History of Structural Optimization
  • Putting Optimization in perspective
  • The Goals of Optimization
  • Terminology, Definition and Classification
  • The upside and the downside of Optimization
  • Overview of Optimization Categories applied to FEA
  • Sizing
  • Shape
  • Topology
  • Discussion of internal FEA optimizers and external optimizers
  • Difference in Approach
  • Advantages and Disadvantages
  • Overview of Optimization Strategies
  • Optimality Criteria
  • Gradient-based methods
  • Design Sensitivity and approximate solutions
  • Homogeneous Stress or Energy solutions
  • Design Of Experiments, Genetic Algorithm and similar methods
  • Some simple Case Studies to illustrate the concepts
  • Homework – simple Optimization examples

Session 2

  • Homework review
  • Theoretical background to Optimization
  • Implications for Practical FEA implementation
  • A closer look at Sizing Optimization
  • Background theory
  • Case Studies in Sizing optimization
  • A more sophisticated approach to objectives, variables  and constraints
  • Linking Design Variables
  • Practical Gauge Constraints
  • Complex Responses
  • Response functions as Objectives
  • Compound Objectives
  • Practical Hints and Tips
  • Case Studies of the methods
  • Homework – sizing of a  shell and beam model

Session 3

  • Homework Review
  • Shape optimization in detail
  • Parametric and Nonparametric issues
  • Traditional gradient based approaches
  • Homogeneous methods
  • DOE, GA and similar methods
  • Improving practicality of results
  • Practical hints and tips
  • Case studies in shape optimization
  • Topology Optimization in detail
  • Parametric and Nonparametric issues
  • Interface with CAD and production – concept study or practical design?
  • Review of methods available
  • Practical hints and tips
  • Case studies in topology optimization
  • Homework – topology optimization of a 2D planar structure

Session 4

  • Homework Review
  • Multi Objective Methods
  • Background Theory
  • Multi-Disciplinary Optimization (MDO)
  • Case Studies in MDO
  • Optimization of Nonlinear and Dynamic Response systems
  • Case Studies in Nonlinear and Dynamic Response
  • Robust Optimization – moving away from the one point solution
  • Background theory and case studies for Robust Optimization
  • Homework – a multi-objective problem

*Note: While we will make every attempt to follow the course outline, the schedule may be shifted at some point. However, ample notice will be given prior to the start of the course date with regards to the course schedule.


PSE Competencies addressed by this training course 

ID Competence Statement
OPTpr4 Familiarity with at least two of the traditional problem definition methods such as Simplex methods, Linear Programming, Geometric Programming, Quadratic Programming
OPTpr5 Familiarity with gradient search methods such as steepest descent
OPTpr6 Understanding of unconstrained and constrained strategies
OPTpr7 Understanding of at least one of the -modern-methods of search strategy such as Neural Networks, Genetic Algorithms, etc.
OPTpr8 Ability to carry out Linear Static Analysis or similar level of analyses in other core disciplines and produce validated results
OPTpr9 Thorough awareness of effects of bad modelling practice and need for adequate checking
OPTpr10 Awareness of difference between global and local minima
OPTpr11 Awareness of parametric controls such as CAD geometry dimensions.
OPTkn1 List the various steps in a general optimisation study.
OPTkn2 List the various types of optimisation search algorithms available in the system(s) you use.
OPTkn3 State whether the optimisation system(s) you use are controlling CAD geometry or finite element parameters (or both).
OPTkn4 State the maximum problem size recommended for your optimization tool in terms of design variables and constraints
OPTkn5 Define the convergence criteria used in your optimization tool for establishing an optimum
OPTkn6 List some direct and indirect methods used for the optimum solution of a constrained nonlinear programming problem.
OPTkn7 State whether your system can handle multiobjective functions
OPTkn8 Outline via a sketch a typical 2 variable optimization problem using variables as x and y axes and show objective function and constraints on the sketch.
OPTkn9 State if linearization of local design space can be used during an optimization with your system
OPTkn10 List which Artificial Intelligence based approaches that your system uses
OPTkn11 State whether your system can deal with discrete variables as well as continuous variables
OPTkn12 State whether your system can define objective functions of more than one term, such as weight AND cost
OPTkn13 List the various methods of establishing feasible search directions
OPTkn14 List methods which transform constrained problems to unconstrained problems
OPTkn15 Define a discrete design variable
OPTco1 Explain the terms goal (objective function), variable and constraint.
OPTco2 Explain why an optimum solution is not always a robust solution.
OPTco3 Describe the basic methodology used to achieve shape modification in any system(s) you use.
OPTco4 Describe the basic methodology used to create structural holes in any system(s) you use.
OPTco5 Explain the concept and usage of a Pareto Set.
OPTco6 Explain the concept of Objective Space and Design Space.
OPTco7 Explain the terms local minima, global minima and saddle point.
OPTco8 Describe the advantages and disadvantages of the search algorithms available in the software tools you use.
OPTco9 Describe Basis Vector methods to reduce the number of design variables
OPTco10 Describe Design Variable Linking
OPTco11 Describe the Kuhn Tucker conditions
OPTco12 Explain how you would investigate the design evaluation trends shown by your software using GUI based graphs, tables tec.
OPTco13 Describe how you would confirm that the optima found is not a local minima
OPTco14 Explain the importance of the definition of the applied loading case set to be used in the optimization
OPTco15 Describe the process to take the optimum solution found and map it into a practical CAD design
OPTco16 Describe how you would review the final design to understand what the main driving parameters are
OPTco17 Describe what steps you may take to understand why an optimization problem will not converge to a solution and how to improve the strategy
OPTco18 Discuss how important it is to find the absolute minima relative to practical limits on design, manufacturing etc.
OPTco19 Define the difference between sizing, shape and topology optimization
OPTco20 Describe how linearization of design space is used, with pros and cons
OPTco21 Explain the difference between parameter based and non-parameter based optimization and where each is most effective
OPTco22 Discuss why mutation in a gene pool is important in a Genetic Algorithm
OPTco23 Describe the difference in approach to an objective function between topology optimization and sizing optimization
OPTco24 Describe what is meant by a stochastic approach to optimization
OPTco25 Describe what is meant by an optimality criterion based method and give an example
OPTco26 Describe typical ways of dealing with discrete variables and their pros and cons
OPTco27 Describe a typical multi-term objective function and mention any drawbacks with this approach
OPTco27b Discuss the importance of an accurate baseline FE Analysis with validated results as the starting point for optimization
OPTco28 Describe parameter linking in a design variable with pros and cons
OPTco29 Describe synthetic type constraints created from multiple responses with pros and cons
OPTco30 Explain why an optimum solution may actually violate one or more constraints
OPTco31 Discuss and sketch what is implied by a "best infeasible" solution
OPTco32 Describe the terms mean and standard deviation
OPTco33 Describe the Normal Probability distribution
OPTco34 Describe the method of Genetic Algorithms
OPTco35 Explain the process of Neural Network based optimization
OPTco36 Describe the training phase of a Neural Network
OPTco37 Describe the Quasi-Newton root finding method
OPTco38 Describe the Secant root finding method
OPTco38b Describe Convex and Non-Convex sets
OPTco39 Explain the difference between a gradient based and non-gradient based search method
OPTco40 Describe how various optimization strategies such as Shape, Sizing, Topology may be combined in a single project
OPTco41 Describe DOE usage in optimization and how the resulting surface model may be used
OPTco42 Describe the various DOE search strategies
OPTco43 Describe Topometry optimization and its relationship to shape optimization
OPTco44 Describe Topography optimization and how it is used in the overall optimization process
OPTco45 Describe the implications of non-linear Optimization
OPTco46 Explain the design variable and Objective function options available to Composite Structural Analysis as opposed to Isotropic Structural Analysis
OPTco47 What special care is needed when carrying out optimization of Composite Structures
OPTap1 Employ available software tools to carry out parameter, shape and topology optimisation studies.
OPTap2 Use appropriate software tools to carry out multidisciplinary optimisation studies, if relevant.
OPTap3 Conduct sensitivity studies to inform optimisation studies.
OPTap4 Utilise appropriate and efficient optimisation algorithms, where a choice is given.
OPTap5 Demonstrate the definition and execution of an optimization task, starting with a baseline FE Analysis
OPTap6 Conduct an optimization analysis of a composite based structure
OPTan1 Analyse the results from sensitivity studies and draw  conclusions from trends.
OPTan2 Determine whether the results from an optimisation study represent a robust solution.
OPTan3 Determine whether an optimization study should use discrete variables and the practical benefits gained from this approach
OPTan4 Determine the best design variables and optimization technique to use for composite structures
OPTsy1 Plan effective analysis strategies for optimisation studies.
OPTsy2 Formulate a series of simple benchmarks in support of a complex optimisation study.
OPTsy3 Plan an evaluation study for a new optimization tool to brought into your operation
OPTsy4 Create a process to take an FE based optimum design and evolve into a practical CAD design
OPTsy5 Formulate a check list of do's and dont's for setting up a realistic optimization problem, include practical, logistic and FE solver and optimizer specific issues
OPTsy6 Prepare an overview of your complete optimization process from concept to product
OPTsy7 Describe how your company uses optimization and recommend areas for improvement
OPTsy8 Describe a range of ideas for objective functions, other than weight minimization, with practical examples
OPTsy9 Describe the technical and resource management issues associated with Multidisciplinary Optimization
OPTsy10 Create a presentation to give at Management Level to justify a major purchase and implementation of Optimization in the design and manufacturing process
OPTev1 Justify the appropriateness of goals, constraints and variables used in an optimisation study.
OPTev2 Select suitable idealisations for optimisation studies.
OPTev3 Provide effective specialist advice on optimisation to colleagues.
OPTev4 Assess appropriate hardware and software solutions to meet the needs of planned optimisation studies.
OPTev5 Justify an optimum design configuration by comparing with initial solution and simple variations or information from the optimization tool.
OPTev6 Justify an optimum design based on its applicability to manufacture and assembly
OPTev7 Assess the application and effectiveness of using EXCEL Solver, MATLAB, open source or programmatic in-house solutions to an optimization problem as an alternative to COTS

Purchasing Details

Members Price
£259 | $320 | €295

Non-Members Price
£385 | $475 | €437
Order Ref: el-232
Event Type: Course
Location: e-Learning Online
Date: April 5, 2018

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Course Tutor:

Read Tony's bio on the NAFEMS tutors page

Session 1
Thursday, April 5th

no sessions on April 12th or 19th

Session 2
Thursday, April 26th

Session 3
Thursday, May 3rd

Session 4
Thursday, May 10th

*The length of each session can vary, depending on Q&A, homework responses, and other contributing factors.

Engineering Board PDH Credits

**It is your individual responsibility to check whether these e-learning courses satisfy the criteria set-out by your state engineering board. NAFEMS does not guarantee that your individual board will accept these courses for PDH credit, but we believe that the courses comply with regulations in most US states (except Florida, North Carolina, Louisiana, and New York, where providors are required to be pre-approved).

Special Note(s):

Telephony surcharges may apply for attendees who are located outside of North America, South America and Europe. These surcharges are related to individuals who join the audio portion of the web-meeting by calling in to the provided toll/toll-free teleconferencing lines. We have made a VoIP option available so anyone attending the class can join using a headset (headphones w/ microphone) connected to the computer. There is no associated surcharge to utilize the VoIP option, and is actually encouraged to ensure NAFEMS is able to keep the e-Learning course fees as low as possible. Please send an email to the e-Learning coordinator (e-learning @ ) to determine if these surcharges may apply to your specific case. 

Just as with a live face-to-face training course, each registration only covers one person. If you plan to register a large group (10+), please send an email to e-learning @ in advance for group discounts.  

For more information, please email e-learning @ .

For NAFEMS cancellation and transfer policy, click here