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Structural Optimization in FEA

Structural Optimization in FEA

Course Overview

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 

IDCompetence Statement
OPTpr4Familiarity with at least two of the traditional problem definition methods such as Simplex methods, Linear Programming, Geometric Programming, Quadratic Programming
OPTpr5Familiarity with gradient search methods such as steepest descent
OPTpr6Understanding of unconstrained and constrained strategies
OPTpr7Understanding of at least one of the -modern-methods of search strategy such as Neural Networks, Genetic Algorithms, etc.
OPTpr8Ability to carry out Linear Static Analysis or similar level of analyses in other core disciplines and produce validated results
OPTpr9Thorough awareness of effects of bad modelling practice and need for adequate checking
OPTpr10Awareness of difference between global and local minima
OPTpr11Awareness of parametric controls such as CAD geometry dimensions.
OPTkn1List the various steps in a general optimisation study.
OPTkn2List the various types of optimisation search algorithms available in the system(s) you use.
OPTkn3State whether the optimisation system(s) you use are controlling CAD geometry or finite element parameters (or both).
OPTkn4State the maximum problem size recommended for your optimization tool in terms of design variables and constraints
OPTkn5Define the convergence criteria used in your optimization tool for establishing an optimum
OPTkn6List some direct and indirect methods used for the optimum solution of a constrained nonlinear programming problem.
OPTkn7State whether your system can handle multiobjective functions
OPTkn8Outline 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.
OPTkn9State if linearization of local design space can be used during an optimization with your system
OPTkn10List which Artificial Intelligence based approaches that your system uses
OPTkn11State whether your system can deal with discrete variables as well as continuous variables
OPTkn12State whether your system can define objective functions of more than one term, such as weight AND cost
OPTkn13List the various methods of establishing feasible search directions
OPTkn14List methods which transform constrained problems to unconstrained problems
OPTkn15Define a discrete design variable
OPTco1Explain the terms goal (objective function), variable and constraint.
OPTco2Explain why an optimum solution is not always a robust solution.
OPTco3Describe the basic methodology used to achieve shape modification in any system(s) you use.
OPTco4Describe the basic methodology used to create structural holes in any system(s) you use.
OPTco5Explain the concept and usage of a Pareto Set.
OPTco6Explain the concept of Objective Space and Design Space.
OPTco7Explain the terms local minima, global minima and saddle point.
OPTco8Describe the advantages and disadvantages of the search algorithms available in the software tools you use.
OPTco9Describe Basis Vector methods to reduce the number of design variables
OPTco10Describe Design Variable Linking
OPTco11Describe the Kuhn Tucker conditions
OPTco12Explain how you would investigate the design evaluation trends shown by your software using GUI based graphs, tables tec.
OPTco13Describe how you would confirm that the optima found is not a local minima
OPTco14Explain the importance of the definition of the applied loading case set to be used in the optimization
OPTco15Describe the process to take the optimum solution found and map it into a practical CAD design
OPTco16Describe how you would review the final design to understand what the main driving parameters are
OPTco17Describe what steps you may take to understand why an optimization problem will not converge to a solution and how to improve the strategy
OPTco18Discuss how important it is to find the absolute minima relative to practical limits on design, manufacturing etc.
OPTco19Define the difference between sizing, shape and topology optimization
OPTco20Describe how linearization of design space is used, with pros and cons
OPTco21Explain the difference between parameter based and non-parameter based optimization and where each is most effective
OPTco22Discuss why mutation in a gene pool is important in a Genetic Algorithm
OPTco23Describe the difference in approach to an objective function between topology optimization and sizing optimization
OPTco24Describe what is meant by a stochastic approach to optimization
OPTco25Describe what is meant by an optimality criterion based method and give an example
OPTco26Describe typical ways of dealing with discrete variables and their pros and cons
OPTco27Describe a typical multi-term objective function and mention any drawbacks with this approach
OPTco27bDiscuss the importance of an accurate baseline FE Analysis with validated results as the starting point for optimization
OPTco28Describe parameter linking in a design variable with pros and cons
OPTco29Describe synthetic type constraints created from multiple responses with pros and cons
OPTco30Explain why an optimum solution may actually violate one or more constraints
OPTco31Discuss and sketch what is implied by a "best infeasible" solution
OPTco32Describe the terms mean and standard deviation
OPTco33Describe the Normal Probability distribution
OPTco34Describe the method of Genetic Algorithms
OPTco35Explain the process of Neural Network based optimization
OPTco36Describe the training phase of a Neural Network
OPTco37Describe the Quasi-Newton root finding method
OPTco38Describe the Secant root finding method
OPTco38bDescribe Convex and Non-Convex sets
OPTco39Explain the difference between a gradient based and non-gradient based search method
OPTco40Describe how various optimization strategies such as Shape, Sizing, Topology may be combined in a single project
OPTco41Describe DOE usage in optimization and how the resulting surface model may be used
OPTco42Describe the various DOE search strategies
OPTco43Describe Topometry optimization and its relationship to shape optimization
OPTco44Describe Topography optimization and how it is used in the overall optimization process
OPTco45Describe the implications of non-linear Optimization
OPTco46Explain the design variable and Objective function options available to Composite Structural Analysis as opposed to Isotropic Structural Analysis
OPTco47What special care is needed when carrying out optimization of Composite Structures
OPTap1Employ available software tools to carry out parameter, shape and topology optimisation studies.
OPTap2Use appropriate software tools to carry out multidisciplinary optimisation studies, if relevant.
OPTap3Conduct sensitivity studies to inform optimisation studies.
OPTap4Utilise appropriate and efficient optimisation algorithms, where a choice is given.
OPTap5Demonstrate the definition and execution of an optimization task, starting with a baseline FE Analysis
OPTap6Conduct an optimization analysis of a composite based structure
OPTan1Analyse the results from sensitivity studies and draw  conclusions from trends.
OPTan2Determine whether the results from an optimisation study represent a robust solution.
OPTan3Determine whether an optimization study should use discrete variables and the practical benefits gained from this approach
OPTan4Determine the best design variables and optimization technique to use for composite structures
OPTsy1Plan effective analysis strategies for optimisation studies.
OPTsy2Formulate a series of simple benchmarks in support of a complex optimisation study.
OPTsy3Plan an evaluation study for a new optimization tool to brought into your operation
OPTsy4Create a process to take an FE based optimum design and evolve into a practical CAD design
OPTsy5Formulate 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
OPTsy6Prepare an overview of your complete optimization process from concept to product
OPTsy7Describe how your company uses optimization and recommend areas for improvement
OPTsy8Describe a range of ideas for objective functions, other than weight minimization, with practical examples
OPTsy9Describe the technical and resource management issues associated with Multidisciplinary Optimization
OPTsy10Create a presentation to give at Management Level to justify a major purchase and implementation of Optimization in the design and manufacturing process
OPTev1Justify the appropriateness of goals, constraints and variables used in an optimisation study.
OPTev2Select suitable idealisations for optimisation studies.
OPTev3Provide effective specialist advice on optimisation to colleagues.
OPTev4Assess appropriate hardware and software solutions to meet the needs of planned optimisation studies.
OPTev5Justify an optimum design configuration by comparing with initial solution and simple variations or information from the optimization tool.
OPTev6Justify an optimum design based on its applicability to manufacture and assembly
OPTev7Assess 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
Structural Optimization in FEA

Class of 2024 - dates coming soon.

I​f you'd like us to let you know when this class is scheduled, let us know using the e-learning waitlist, and we'll be in touch to help you book your place.

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Four-Session Online Training Course

2.5/3 hours per session
PDH Credits - 10

Attend the live sessions, or view the recordings at your convenience.

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Please click here to view the FAQ section, or if you need to contact NAFEMS about this course.

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) 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 NAFEMS cancellation and transfer policy, click here.