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# Structural Optimization in FE Analysis - NAFEMS e-Learning Training Course

## Four-Week Training Course

(one 2.5 hour session per week)

# 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 FEA Structural Optimization.

The objective of this course is show you a broad overview of the range of FEA 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

In the current climate travel and training budgets are tight. To help you still meet your training needs the following e-learning course has been developed to complement the live class. The e-learning course runs over a four week period with a single two hour session per week.

E-learning classes are ideal for companies with a group of engineers requiring training. E-learning classes can be provided to suit your needs and timescale. Contact us to discuss your requirements.

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 practicing engineers who wish to learn more about how to apply the various optimization methods available to FEA 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.

E-learning classes are ideal for companies with a group of engineers requiring training. E-learning classes can be provided to suit your needs and timescale. Contact us to discuss your requirements.

# Course Program

Note: 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
• Overview of Optimization Strategies
• Optimality Criteria
• 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
• 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
• 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.

# 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 @ 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 (5+), please send an email to e-learning @ nafems.org in advance for group discounts.

# Course Instructor

Tony Abbey has created and taught a wide range of FEA based training classes over the past 15 years. He has developed a reputation for providing the student with an experience that is full of insight gained from his extensive experience, but which also challenges and motivates. Tony has been working with FEA for over 30 years, both in Industry and for FEA software providers in the UK and the US.

His informal and interactive presentation style allows the key concepts to be taught in a manner which involves participants fully in the course material. Tony presents papers at NAFEMS and other conferences on a regular basis and has been involved with NAFEMS since its formation.

Why an e-Learning Class?

In the current climate travel and training budgets are tight. To help you still meet your training needs the following e-learning course has been developed to complement the live class. The e-learning course runs over a four week period with a single two hour session per week.

E-learning classes are ideal for companies with a group of engineers requiring training. E-learning classes can be provided to suit your needs and timescale. Contact us to discuss your requirements.