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Training Class Description
Optimization Analysis using
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

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.

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.

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
Who Should Attend?
Class Program
Session 1
•        Finite Element Analysis Overview
•        Background  and History of Structural Optimization
•        Putting Optimization in perspective
    o        The Goals of Optimization
    o        Terminology, Definition and Classification
    o        The upside and the downside of Optimization
•        Overview of Optimization Categories applied to FEA
    o        Sizing
    o        Shape
    o        Topology
•        Discussion of internal FEA optimizers and external optimizers
    o        Difference in Approach
    o        Advantages and Disadvantages

•        Overview of Optimization Strategies
    o        Optimality Criteria
    o        Gradient based methods
    o        Design Sensitivity and approximate solutions
    o        Homogeneous Stress or Energy solutions
    o        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
    o        Background theory
    o        Case Studies in Sizing optimization
•        A more sophisticated approach to objectives, variables  and constraints
    o        Linking Design Variables
    o        Practical Gauge Constraints
    o        Complex Responses
    o        Response functions as Objectives
    o        Compound Objectives
    o        Practical Hints and Tips
    o        Case Studies of the methods
•        Homework – sizing of a  shell and beam model

Session 3
•        Homework Review
•        Shape optimization in detail
    o        Parametric and Nonparametric issues
    o        Traditional gradient based approaches
    o        Homogeneous methods
    o        DOE, GA and similar methods
    o        Improving practicality of results
    o        Practical hints and tips
    o        Case studies in shape optimization
•        Topology Optimization in detail
    o        Parametric and Nonparametric issues
    o        Interface with CAD and production – concept study or practical design?
    o        Review of methods available
    o        Practical hints and tips
    o        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
In Partnership with
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.