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Altair OptiStruct®
Concept Design with Topology and Topography
Optimization
Altair Engineering
April, 2009
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Tipologia: Notas de estudo
2014
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Altair OptiStruct
® Concept Design with Topology and Topography Optimization Altair Engineering April, 2009
Chapter 1 - Introduction
HyperWorks Overview OptiStruct Overview
OptiStruct in HyperWorks
OptiStruct Optimization Overview
Topology Shape Free-shape Size Free-size Topography Optimization Design Process Solver Neutral Integrated FEA Solver Concept Level Design Design Fine Tuning Gauge9 & 10 Gauge1, 2 & 3 Gauge Gauge Gauge Gauge Gauge11, 12 & 13 Gauge14 & DOE Approximations Stochastic Studies
Chapter 2 – Theoretical Background
Optimization Optimization Concepts and Definitions
Structural Optimization Concepts
The Optimization Problem Statement:
- (^) Objective (What do I want?) min f(x) also min [max f(x)]
- (^) Design Variables (What can I change?) XiL^ ≤ Xi ≤ XiU^ i =1,2,3,…N
- (^) Design Constraints (What performance targets must be met?) gj(x) ≤ 0 j = 1, 2, 3, …, M Note: The functions f(x), gi(x), can be linear, non-linear, implicit or explicit, and are continuous Example: Explicit y(x) = x^2 – 2x Implicit y^3 – y^2 x + yx - √ x = 0
Optimization Definitions
- (^) Shape: is an automated way to modify the structure shape based on predefined shape variables to find the o ptimal shape.
- (^) Size: is an automated way to modify the structure parameters (Thickness, 1D properties, material properties, etc…) to find the o ptimal design.
- (^) Gauge: is a particular case of size, where the DV are 2D props (Pshell or Pcomp)
- (^) Free Shape: is an automated way to modify the structure shape based on set of nodes that can move totally free on the boundary to find the o ptimal shape.
- (^) Composite shuffle: is an automated way to determine the optimum laminate stack sequence. DVs are the plies sequence of stacking. It is used for composite material only defined using PCOMP(G) or PCOMPP.
Optimization Terminology
- (^) Design Variables: System parameters that are varied to optimize system performance.
- (^) Design Space: selected parts which are designable during optimization process. For example, material in the design space of a topology optimization.
20 < b < 40
30 < h < 90
Optimization Terminology
- (^) Objective Function: Any response function of the system to be optimized. The response is a function of the design variables. Ex. Mass, Stress, Displacement, Moment of Inertia, Frequency, Center of Gravity, Buckling factor, and etc.
- (^) Constraint Functions: Bounds on response functions of the system that need to be satisfied for the design to be acceptable.
min Weight (b,h)
(b,h) 70 MPa (b,h) 15 MPa
h 2 * b
Optimization Problem Example
- (^) A cantilever beam is modeled with 1D beam elements and loaded with
force F=2400 N. Width and height of cross-section are optimized to
minimize weight such that stresses do not exceed yield. Further the
height h should not be larger than twice the width b.
Optimization Problem Example
Mathematical Design Space Beam width, b (mm) Beam height, h (mm)
Optimization Terminology
Gradient-based Optimization
- Start from a X0 point
- Evaluate the function F(Xi) and the gradient of the function F(Xi) at the Xi.
- Determine the next point using the negative gradient direction: Xi+1 = Xi - F(Xi).
- Repeat the step 2 to 3 until the function converged to the minimum. X 0 X 1 X 2 X 3
Optimization GUI
Optimization Panel
Optimization Menu
Model Browser
Optimization Setup module in HyperMesh
- (^) Definition of Design Variables