Structural Optimization in FEA
Four-Session Online Training Course - 2.5/3 Hours per Session
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.
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 @ nafems.org .
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.
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.
- 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
- 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
- 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
- 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
- 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
|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|
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*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).
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 @ nafems.org ) 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 @ nafems.org in advance for group discounts.
For more information, please email e-learning @ nafems.org .
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