Topology Optimization
Topology optimization is concerned with material distribution and how the members within a structure are connected. It treats the “equivalent density” of each element as a design variable.
The solver calculates an equivalent density for each element, where 1 is equivalent to 100% material, while 0 is equivalent to no material in the element. The solver then seeks to assign elements that have a low stress value a lower equivalent density before analyzing the effect on the remaining structure. In this way extraneous elements tend towards a density of 0, with the optimum design tending towards 1. As a designer, you will need to exercise your judgment. For example, you may decide that you will omit material from all (finite) elements whose density is less than 0.3 (or 30%). Using an iso-plot of element densities helps to visualize the “remaining” structure as elements with a density below this threshold can be masked leaving behind the optimum design. Then you will need to take this geometry back to your CAD modeler, smooth it out (that is, use geometrically regular edges or surfaces, etc.) and re-evaluate the design for stresses, displacements, frequencies etc..
Mathematical Optimisation - Fundamentals and ApplicationsGokul Alex
My Session on Mathematical Optimisation Fundamentals and Industry applications for the Academic Knowledge Refresher Program organised by Kerala Technology University and College of Engineering Trivandrum, Department of Interdisciplinary Studies.
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This webinar will provide guidance to attendees on how to drive more engineering decisions using simulation tools.
Today, there are lots of different options. You can provide automation tools to simulation analysts to improve their productivity or you could provide CAD-embedded simulation tools to engineers for early simulation feedback on a daily basis. What is recommended can vary by company size. What works for a large company can and should be dramatically different than a small design shop.
Our panel of experts from Lifecycle Insights, Dassault Systems SIMULIA, Siemens PLM Software and Ansys will present their respective best practices.
Optimization Computing Platform for the Construction IndustryKostas Dimitriou
Optimization is now the disruptive driving force poised to address today's complex engineering challenges. Reducing Cost and Increasing Safety are two of the most important pillars in modern architectural, engineering and construction industries.
ACE OCP fills the gap for practical optimization tools to meet the massive challenges of the professional civil/architectural engineer in the construction industry.
For the first time a tool can add real engineering value in all three dimensions of the value proposition, increase revenues, decrease costs, and decrease risk.
Mathematical Optimisation - Fundamentals and ApplicationsGokul Alex
My Session on Mathematical Optimisation Fundamentals and Industry applications for the Academic Knowledge Refresher Program organised by Kerala Technology University and College of Engineering Trivandrum, Department of Interdisciplinary Studies.
Best Practices on Driving Design Decisions with SimulationDesign World
This webinar will provide guidance to attendees on how to drive more engineering decisions using simulation tools.
Today, there are lots of different options. You can provide automation tools to simulation analysts to improve their productivity or you could provide CAD-embedded simulation tools to engineers for early simulation feedback on a daily basis. What is recommended can vary by company size. What works for a large company can and should be dramatically different than a small design shop.
Our panel of experts from Lifecycle Insights, Dassault Systems SIMULIA, Siemens PLM Software and Ansys will present their respective best practices.
Optimization Computing Platform for the Construction IndustryKostas Dimitriou
Optimization is now the disruptive driving force poised to address today's complex engineering challenges. Reducing Cost and Increasing Safety are two of the most important pillars in modern architectural, engineering and construction industries.
ACE OCP fills the gap for practical optimization tools to meet the massive challenges of the professional civil/architectural engineer in the construction industry.
For the first time a tool can add real engineering value in all three dimensions of the value proposition, increase revenues, decrease costs, and decrease risk.
Model-Based User Interface Optimization: Part IV: ADVANCED TOPICS - At SICSA ...Aalto University
Tutorial on Model-Based User Interface Optimization. Part IV: ADVANCED TOPICS.
Presented by Antti Oulasvirta (Aalto University) at SICSA Summer School on Computational Interaction in 2015 in Glasgow. Note: This one-day lecture is divided into multiple parts.
Software Architecture – Centric Methods and Agile Developmentsathish sak
Feedback – Not just for stereos anymore
Adaptable – Just in case you haven’t made up your mind
Simplicity – Let’s keep it that way
Small Groups – Because the boss is cheap
Today's fast paced product market has shorter lifecycles and tighter budgetary concerns. Tolerance analysis software provides an ideal solution to reduce the number of crucial steps needed to optimize a product at the design step itself. 3DCS Variation Analyst is the world's most used tolerance analysis software that is fully integrated into NX/ CATIA V5/ Creo and CAD Neutral Multi-CAD. 3DCS Variation Analyst is designed to use a consistent format and set of mathematical formulae that create reliable results, enabling engineers to gain a complete insight into their design. The software empowers design engineers to control variation and optimize their designs to account for inherent process and part variation, which in turn reduces non-conformance, scrap, rework and other associated costs.
3DCS Variation Analyst
Used by the world’s leading manufacturing OEM’s to reduce the cost of quality, 3DCS Variation Analyst comes in two flavours:
1) 3DCS Variation Analyst (NX / CAA V5 or Creo Based) is an integrated solution for NX / CATIA V5 or Creo. Since it is an integrated solution, users can not only activate 3DCS workbenches from within the modelling solution, they can use many of its inbuilt functionality to support their modelling.
3DCS Variation Analyst provides three analysis methods:
Monte Carlo Analysis
High-Low-Mean (Sensitivity Analysis) and
Geofactor Analysis (Relationship)
2_Analogy btw science math and engineering and ED.pptxaabhishekkushwaha9
An analogy between SMEs (Small and Medium Enterprises) and design could be drawn in various ways, highlighting similarities in their characteristics, processes, or importance. Here's one analogy:
Foundation and Flexibility:
SMEs are often likened to the building blocks of an economy, providing the foundation for growth and innovation. Similarly, design serves as the foundation for products, services, and experiences, shaping their functionality, usability, and aesthetics.
Just as SMEs need to be flexible and adaptable to changing market conditions, design also requires flexibility to meet evolving user needs, technological advancements, and design trends.
Problem-Solving Approach:
SMEs typically thrive by addressing niche markets, solving specific problems, or fulfilling unmet needs. Similarly, design is fundamentally about problem-solving, whether it's improving user experiences, optimizing efficiency, or enhancing aesthetics.
Both SMEs and design involve identifying challenges, brainstorming solutions, and implementing strategies to achieve desired outcomes.
Model-Based User Interface Optimization: Part I INTRODUCTION - At SICSA Summe...Aalto University
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Presented at SICSA Summer School on Computational Interaction 2015. Note: This one-day lecture is divided into multiple parts.
Model-Based User Interface Optimization: Part IV: ADVANCED TOPICS - At SICSA ...Aalto University
Tutorial on Model-Based User Interface Optimization. Part IV: ADVANCED TOPICS.
Presented by Antti Oulasvirta (Aalto University) at SICSA Summer School on Computational Interaction in 2015 in Glasgow. Note: This one-day lecture is divided into multiple parts.
Software Architecture – Centric Methods and Agile Developmentsathish sak
Feedback – Not just for stereos anymore
Adaptable – Just in case you haven’t made up your mind
Simplicity – Let’s keep it that way
Small Groups – Because the boss is cheap
Today's fast paced product market has shorter lifecycles and tighter budgetary concerns. Tolerance analysis software provides an ideal solution to reduce the number of crucial steps needed to optimize a product at the design step itself. 3DCS Variation Analyst is the world's most used tolerance analysis software that is fully integrated into NX/ CATIA V5/ Creo and CAD Neutral Multi-CAD. 3DCS Variation Analyst is designed to use a consistent format and set of mathematical formulae that create reliable results, enabling engineers to gain a complete insight into their design. The software empowers design engineers to control variation and optimize their designs to account for inherent process and part variation, which in turn reduces non-conformance, scrap, rework and other associated costs.
3DCS Variation Analyst
Used by the world’s leading manufacturing OEM’s to reduce the cost of quality, 3DCS Variation Analyst comes in two flavours:
1) 3DCS Variation Analyst (NX / CAA V5 or Creo Based) is an integrated solution for NX / CATIA V5 or Creo. Since it is an integrated solution, users can not only activate 3DCS workbenches from within the modelling solution, they can use many of its inbuilt functionality to support their modelling.
3DCS Variation Analyst provides three analysis methods:
Monte Carlo Analysis
High-Low-Mean (Sensitivity Analysis) and
Geofactor Analysis (Relationship)
2_Analogy btw science math and engineering and ED.pptxaabhishekkushwaha9
An analogy between SMEs (Small and Medium Enterprises) and design could be drawn in various ways, highlighting similarities in their characteristics, processes, or importance. Here's one analogy:
Foundation and Flexibility:
SMEs are often likened to the building blocks of an economy, providing the foundation for growth and innovation. Similarly, design serves as the foundation for products, services, and experiences, shaping their functionality, usability, and aesthetics.
Just as SMEs need to be flexible and adaptable to changing market conditions, design also requires flexibility to meet evolving user needs, technological advancements, and design trends.
Problem-Solving Approach:
SMEs typically thrive by addressing niche markets, solving specific problems, or fulfilling unmet needs. Similarly, design is fundamentally about problem-solving, whether it's improving user experiences, optimizing efficiency, or enhancing aesthetics.
Both SMEs and design involve identifying challenges, brainstorming solutions, and implementing strategies to achieve desired outcomes.
Model-Based User Interface Optimization: Part I INTRODUCTION - At SICSA Summe...Aalto University
Tutorial on Model-Based User Interface Optimization. Part I: INTRODUCTION.
Presented at SICSA Summer School on Computational Interaction 2015. Note: This one-day lecture is divided into multiple parts.
You could be a professional graphic designer and still make mistakes. There is always the possibility of human error. On the other hand if you’re not a designer, the chances of making some common graphic design mistakes are even higher. Because you don’t know what you don’t know. That’s where this blog comes in. To make your job easier and help you create better designs, we have put together a list of common graphic design mistakes that you need to avoid.
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5. Optimization
Definitions
• World English Dictionary
• “To find the best compromise among several often-conflicting requirements, as in engineering design.”
• Webster-Merriam Dictionary
• “A mathematical technique for finding a maximum or minimum value of a function of several variables subject to a
set of constraints, as linear programming or systems analysis.”
• The Wikipedia definition for mathematical optimization
• “It is the selection of a best element (with regard to some criteria) from some set of available alternatives.
• In the simplest case, an optimization problem consists of maximizing or minimizing a real function by
systematically choosing input values from within an allowed set and computing the value of the function.”
5
6. Design Process
Overview
• Classical Design Process Integrating Manual Optimization
• Creation of design
• Analysis of design(s)
• Evaluation of analysis results
• Summation of limiting factors (cost, requirements, time)
• Definition of updates for a new design
• Return to analysis
• Design Process withOptiStruct
• Creation of FE model
• Definition of design variables, objective and constraints
• Automated computational evaluation of the design space
• Evaluation of analysisresults
• Definition of updates for a new improved design
• Return to analysis
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7. Structural Optimization
Development Time
• Fact
• Most of the product cost is determined at
the concept design stage.
• Problem
• Concept design offers minimum knowledge,
but maximum design freedom.
• Need
• OptiStruct provides effective concept design
tools to minimize downstream “re-design”
costs and time-to-market.
7
8. Optimization
Problem Statement
• Design Variables – What should I operate on to achieve my target?
xi
L ≤ xi ≤ xi
U i = 1, 2, 3,…, N
• Responses – What characteristics are relevant to my problem?
j j = 1, 2, 3, …, M
• Constraints – What performance targets must be met?
gj(x) ≤ 0 j = 1, 2, 3, …, M
• Objective – If all constraints are satisfied, what should OptiStruct minimize/maximize?
min f(x) also min [max f(x)]
• Example: explicit y(x) = x² – 2x or implicit y³ – y²x + yx = 0
Note: The functions f(x), gi(x), can be linear, non-linear, implicit or explicit and are continuous.
9
9. Optimization
Algorithms
• This optimization problem has to be solved, i.e. the optimum solution has to be found.
• Two major optimization algorithm groups exist to solve optimization problems
• Mathematical Programming Methods (OptiStruct uses only these methods)
• Usually require sensitivity information as they rely on gradients
• Solve the optimization problem in a “steepest descent” fashion using mathematical logic
• Few function evaluations – good if function evaluation is time consuming, such as a FE simulation
• Convergence to a localminimum
• Example: Sequential Quadratic Programming or Method of feasible directions
• Evolutionary algorithms
• Do not require sensitivity information
• Often mimic natural behavior to improvedesign
• Require many function evaluations – good if function evaluation is fast
• More likely to find the global optimum
• Example: Genetic Algorithm or Particle Swarm optimization
9
10. Introduction to OptiStruct & Theoretical Background
Sessions
• Optimization
• Design Process
• Structural Optimization
• Sensitivities
• Gradient-Based
Methodology
• Example
• Terminology
• Interpreting the results
• Techniques
• Workflow
• Design interpretation
Sensitivities &
Gradient-Based
Methodology
Terminology
and
Interpreting
the Results
Techniques,
workflow and
design
interpretation
Optimization
Basics
00‘ 10‘ 15‘ 20‘ 30‘
10
11. Optimization
Sensitivities
Sensitivities are calculated if the optimization algorithm requires gradient information
• It is the derivative of a response with respect to a design variable.
They are calculated for each defined response and each design variable
• The simplest way to calculate them is global finite difference
• Each Design Variable is perturbed and the function is evaluated
• This is very slow, as a FE model has to be solved each time
• In OptiStruct, analytical sensitivities are calculated, which is muchfaster.
11
12. Gradient-Based Optimization
Workflow
1. Start from ax0 point
2. Evaluate the function f(xi) and the gradient of the
function f(xi) at thexi
3. Determine the next point using the negative gradient
direction
xi+1 = xi - f(xi)
4. Repeat the step 2 to 3 until the function converged
to the minimum
x0
x1
x3
x2
12
13. Simple Beam
Example
• A cantilever beam is modeled with 1D beam elements and loaded with force F = 2400 N
• The width and height of cross-section are optimized to minimize weight
• Ensure that normal and shear stresses do not exceed yield
• The height h should not be larger than twice the width b
13
14. Simple Beam
Example
• Design Variables – cross-section of the beam
width bL < b < bU 20 < b < 40
height hL < h < hU 30 < h < 90
• Responses
normal stress , shear stress , mass
• Constraints
(b, h) max, where max = 160
(b, h) max, where max = 60
h 2 b
• Objective
weight min mass (b, h)
14
15. beam width b
15
beam
height
h
max = 160
max = 60
h 2 b
30 ≤ h ≤90
20 ≤ b ≤40
Feasible
Domain
Infeasible
Domain
m=11
m=9
m=7
Simple Beam
Example
Mathematical Design Space
16. Introduction to OptiStruct & Theoretical Background
Sessions
• Optimization
• Design Process
• Structural Optimization
• Sensitivities
• Gradient-Based
Methodology
• Example
• Terminology
• Interpreting the results
• Techniques
• Workflow
• Design interpretation
Sensitivities &
Gradient-Based
Methodology
Terminology
and
Interpreting
the Results
Techniques,
workflow and
design
interpretation
Optimization
Basics
00‘ 10‘ 15‘ 20‘ 30‘
16
17. Optimization
Terminology
• Design Variables
• System parameters that are varied to optimize system
performance.
• Beam width b and beam height h
• Design Space
• Selected parts which are designable during optimization
process.
• For example, material in the design space of a topology
optimization.
20 < b < 40 and 30 < h < 90
17
18. Optimization
Terminology
• Response
• Measurement of system performance: (b, h), (b, h), mass (b, h)
• Constraint Functions
• Bounds on response functions of the system that need to be satisfied for the design to be acceptable
(b, h) 160
(b, h) 60
h 2 b
• Objective Function
• Any response function of the system to be optimized.
• The response is a function of the design variables.
• Examples are Mass, Stress, Displacement, Moment of Inertia, Frequency, Center of Gravity, Buckling factor, etc.
min mass (b, h)
18
19. Optimization
Terminology
• Feasible Design
• One that satisfies all the constraints.
• Infeasible Design
• One that violates one or more
constraint functions.
• Optimum Design
• Set of design variables along with the
minimized (or maximized) objective
function and satisfy all the constraints.
19
20. Interpreting the Results
Process Concerns
• Objective
• Did we reach our objective?
• How much did the objective improve?
• Design Variables
• Values of variables for the improved design
• Constraints
• Did we violate any constraints?
• Two ways of determining each of these in OptiStruct
• .out file from optimization run
• .mvw and _hist.mvwfiles from optimization run
20
21. Interpreting the Results
Common Issues
• Local vs. global extreme (minimum/maximum)
• Problem may be over constrained
• Review the objective, constraints and design variables to allow more design
freedom
• Efficiency of Optimization
• Relation between constraints and design variables with respect to their numbers
• Unconstrained OptimizationProblem
• Optimization problem setup is not appropriate
• Issues related to FEAmodeling
• Stress constraints on nodes connected to rigids
21
22. Introduction to OptiStruct & Theoretical Background
Sessions
• Optimization
• Design Process
• Structural Optimization
• Sensitivities
• Gradient-Based
Methodology
• Example
• Terminology
• Interpreting the results
• Techniques
• Workflow
• Design interpretation
Sensitivities &
Gradient-Based
Methodology
Terminology
and
Interpreting
the Results
Techniques,
workflow and
design
interpretation
Optimization
Basics
00‘ 10‘ 15‘ 20‘ 30‘
22
23. Optimization
Concept LevelTechniques
• Topology
• Given a design envelope, topology optimization finds the optimum
material placement within that space according to the constraints and
objective.
• Free Size
• Given a shell structure, free size optimization finds the optimum
thickness on an element-by-element basis that meets the constraints
and objective.
• Topography
• Given a shell structure, topography optimization creates a bead
pattern from the elements that meets the constraints and objective.
Topology
Free Size
Topography
23
24. Optimization
Fine Tuning-LevelTechniques
• Parameter/Size
• Given a structure, size optimization finds the optimum component
thickness that meets the constraints and objective.
• Shape
• Given a structure and a number of user-defined shapes, shape
optimization finds the optimum fractional summation of those
shapes that meets the constraints and objective.
• Free Shape
• Given a structure with features on its boundaries, free shape
modifies the boundary nodes to find a more optimal structure that
meets the constraints andobjectives.
Parameter/
Size
Shape
Free Shape
24
26. Design Interpretation
OSSmooth
OSSmooth is a semi-automated design interpretation software, facilitating the recovery of a modified
geometry resulting from a structural optimization, for further use in the design process and FEA
reanalysis.
• OSSmooth can be used in three different ways:
• OSSmooth for geometry
• FEA topology reanalysis
• FEA topography reanalysis
• The tool has two incarnations:
• Standalone version that comes with the OptiStruct installation.
• Dependent version that is embedded in HyperWorks.
Only this version can handle the reanalysis as it is using HyperWorks features.
• OSSmooth will be covered in detail in the followingchapters.
26