L-System-Generated Mechanism Topology Optimization Using Graph-Based Interpretation

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Ergun Akleman ◽  
Gregory W. Reich ◽  
Philip S. Beran ◽  
Darren J. Hartl
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Level Set Methods ◽  
Optimization Techniques ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Multiple Case ◽  
Multiple Case Studies ◽  
Reconfigurable Structures

Traditional topology optimization techniques, such as density-based and level set methods, have proven successful in identifying potential design configurations for structures and mechanisms but suffer from rapidly increasing design space dimensionality and the possibility of converging to local minima. A heuristic alternative to these approaches couples a genetic algorithm with a Lindenmayer system (L-system), which encodes design variables and governs the development of the structure when coupled with an interpreter to translate genomic information into structural topologies. This work discusses the development of a graph-based interpretation scheme referred to as spatial interpretation for the development of reconfigurable structures (SPIDRS). This framework allows for the effective exploration of mechanism design spaces using a limited number of design variables. The theory and implementation of this method are detailed, and multiple case studies are presented to demonstrate the ability of SPIDRS to generate adaptive structures capable of achieving multiple design goals.

L-System-Generated Topology Optimization of Compliant Mechanisms Using Graph-Based Interpretation

2018 ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Darren J. Hartl ◽  
Ergun Akleman
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Level Set Methods ◽  
Optimization Techniques ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Reconfigurable Structures

Traditional topology optimization techniques, such as density-based and level set methods, have proven successful in identifying potential design configurations but suffer from rapidly increasing design space dimensionality and convergence to local minima. A heuristic alternative to these approaches couples a genetic algorithm with a Lindenmayer System (L-System), which encodes design variables and governs the development of the structure when coupled with some sort of interpreter. This work discusses the development of a graph-based interpretation scheme referred to as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS). This framework allows for the effective exploration of the design space using a limited number of design variables. The theory and implementation of this method are detailed, and a compliant mechanism case study is presented to demonstrate the ability of SPIDRS to generate structures capable of achieving multiple design goals.

Graph-Based Interpretation of L-System Encodings Toward Aeroelastic Topology Optimization of a Morphing Airfoil in Supersonic Flow

2019 ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Darren J. Hartl ◽  
Joshua D. Hodson ◽  
Gregory W. Reich ◽  
Philip S. Beran ◽  
...  
Keyword(s):  
Supersonic Flow ◽  
Performance Criteria ◽  
Preliminary Design ◽  
Structural Topology ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Interpretation Algorithm ◽  
Actuation Systems ◽  
Reconfigurable Structures

Abstract This work details the preliminary design of a morphing airfoil in supersonic flow using evolutionary design principles. The structural topology of the airfoil includes a fixed outer mold line, fixed spars, and designable internal stiffeners and actuators. The designable components are generated using a bio-inspired model known as a Lindenmayer System (L-System), which encodes design variables and governs the development of a structural topology when coupled with an interpretation algorithm. Here, we utilize a graph-based interpretation scheme known as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS), which has been shown to effectively explore the mechanism design space using a limited number of design variables. The optimization process behind this preliminary design problem is discussed, and optimal airfoil topologies capable of meeting specified aerodynamic performance criteria are presented in hopes of gaining a better understanding of how actuation systems could be integrated into the next generation of aircraft.

scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

Structural Analysis and Optimal Design of Lightweight Skate for Loading and Unloading

2013 ◽  
Vol 785-786 ◽  
pp. 1258-1261
Author(s):  
In Pyo Cha ◽  
Hee Jae Shin ◽  
Neung Gu Lee ◽  
Lee Ku Kwac ◽  
Hong Gun Kim
Keyword(s):  
Topology Optimization ◽  
Structural Analysis ◽  
Optimal Design ◽  
Optimization Techniques ◽  
Normal Operation ◽  
Stress And Strain ◽  
Initial Model ◽  
Design Variables ◽  
Model Set ◽  
Main Frame

Topology optimization and shape optimization of structural optimization techniques are applied to transport skate the lightweight. Skate properties by varying the design variables and minimize the maximum stress and strain in the normal operation, while reducing the volume of the objective function of optimal design and Skate the static strength of the constraints that should not degrade compared to the performance of the initial model. The skates were used in this study consists of the main frame, sub frame, roll, pin main frame only structural analysis and optimal design was performed using the finite element method. Simplified initial model set design area and it compared to SM45C, AA7075, CFRP, GFRP was using the topology optimization. Strength does not degrade compared to the initial model, decreased volume while minimizing the stress and strain results, the optimum design was achieved efficient lightweight.

Exploring a Multiscale Topology Optimization Design Space Using a Parametric L-system Approach

2022 ◽  
Author(s):  
Brent Bielefeldt ◽  
Richard Beblo ◽  
Joshua D. Deaton ◽  
Kevin Lawson ◽  
Robert Lowe
Keyword(s):  
Topology Optimization ◽  
System Approach ◽  
Optimization Design ◽  
Design Space ◽  
L System

scholarly journals An explicit topology optimization method using moving polygonal morphable voids (MPMVs)

2020 ◽  
Vol 23 (2) ◽  
pp. 536-540 ◽  
Author(s):  
Hoang Van-Nam
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Density Field ◽  
Optimization Approach ◽  
Design Variables ◽  
Mesh Independence ◽  
Gradient Based ◽  
Element Density ◽  
Optimization Solvers

Introduction: Conventional topology optimization approaches are implemented in an implicit manner with a very large number of design variables, requiring large storage and computation costs. In this study, an explicit topology optimization approach is proposed by movonal morphable voids whose geometry parameters are considered as design variables. Methods: Each polygonal void plays as an empty-material zone that can move, change its shapes, and overlap with its neighbors in a design space. The geometry eters of MPMVs consisting of the coordinates of polygonal vertices are utilized to render the structure in the design domain in an element density field. The density function of the elements located inside polygonal voids is described by a smooth exponential function that allows utilizing gradient-based optimization solvers. Results & Conclusion: Compared with conventional topology optimization approaches, the MPMV approach uses fewer design variables, ensure mesh-independence solution without filtering techniques or perimeter constraints. Several numerical examples are solved to validate the efficiency of the MPMV approach.

Generative Design and Topology Optimization of Disk Brake Floating Carrier

2020 ◽  
Author(s):  
Filippo Colombo Zefinetti ◽  
Daniele Regazzoni ◽  
Marco Rossoni
Keyword(s):  
Topology Optimization ◽  
Laser Scanning ◽  
Design Space ◽  
Initial Conditions ◽  
Optimization Techniques ◽  
Operating Conditions ◽  
Generative Design ◽  
Common Solution ◽  
Disk Brake ◽  
And Topology

Abstract In the last past years, computer-aided technologies to improve existing products by widening the design space have been largely investigated. Topology optimization and generative design are two of the most representative technologies of such kind. This paper aims at investigating the use of generative design and topology optimization techniques to improve products whose design has not changed radically over the years. The product under investigation is a disk brake floating caliper that is the most common solution for commercial vehicles. In general, increasing the stiffness of the floating caliper while keeping its weight under control is desirable both from performance and fuel consumption point of view. The solution here proposed aims at exploiting two new ways to approach the engineering design process and evaluate which one is more suitable for problems of this kind. Starting from the original carrier shape, acquired with laser scanning, the two technologies have been applied on the same initial conditions. The initial design space volume corresponds to the acquired shape, the loads and the constraints for the simulation have been drawn reasonably to resemble the actual operating conditions. Keeping the input parameters constants, two different off-the-shelf software packages have been used to perform the computation and with the objective of maximizing the stiffness of the carrier while reducing its mass. The comparison and the improvements on the final designs have been drawn taken as reference to the original caliper.

Morphing Airfoil Design via L-System Generated Topology Optimization

2019 ◽  
Author(s):  
Madalyn Mikkelsen ◽  
Michayal Mathew ◽  
Patrick Walgren ◽  
Brent Bielefeldt ◽  
Pedro B. C. Leal ◽  
...  
Keyword(s):  
Structural Integrity ◽  
Aerodynamic Performance ◽  
Operating Conditions ◽  
Structural Topology ◽  
High Lift ◽  
L System ◽  
Design Variables ◽  
Weakly Coupled ◽  
System L ◽  
Internal Configuration

Abstract Morphing airfoils present an effective approach to managing the different requirements in each segment of a mission profile (e.g., takeoff/landing, cruise, and active maneuvering). In this work, an approach to morphing airfoil design that couples aerodynamic performance and internal structural configuration is detailed. The internal structural topology is formulated using a Lindenmayer System (L-System) coupled with a graph-based interpreter known as Spatial Interpretation for Development of Reconfigurable Structures (SPIDRS). The L-System encodes design variables that are interpreted via SPIDRS graphical operations and governs the development of the internal configuration (composed of elastic structural members and actuators). The global optimization uses a weakly coupled fluid-structure interaction (FSI) scheme for a first-order estimation of the aeroelastic loads that are critical for airfoil aerodynamic performance and structural integrity. Each airfoil is evaluated in two states: a standard non-actuated state to determine performance in standard operating conditions (e.g., cruise) and a high lift state, where internal shape memory alloy actuators are deformed to create a high lift configuration for the airfoil (e.g., takeoff/landing). Evaluating the aerodynamic performance of airfoils in these two states results in a series of potential solutions that best manage the tradeoff between aerodynamic metrics for both evaluated cases.

Image Matching Assessment of Attainable Topology via Kriging-Interpolated Level-Sets

2014 ◽  
Author(s):  
David Guirguis ◽  
Mohamed Aly ◽  
Karim Hamza ◽  
Hesham Hegazi
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Image Matching ◽  
Level Sets ◽  
Optimization Techniques ◽  
Design Domain ◽  
Structural Topology ◽  
Level Set Function ◽  
Design Variables ◽  
Gradient Optimization

Level-set methods are domain classification techniques that are gaining popularity in the recent years for structural topology optimization. Level sets classify a domain into two or more categories (such as material and void) by examining the value of a scalar level-set function (LSF) defined in the entire design domain. In most level-set formulations, a large number of design variables, or degrees of freedom is used to define the LSF, which implicitly defines the structure. The large number of design variables makes non-gradient optimization techniques all but ineffective. Kriging-interpolated level sets (KLS) on the other hand are formulated with an objective to enable non-gradient optimization by defining the design variables as the LSF values at few select locations (knot points) and using a Kriging model to interpolate the LSF in the rest of the design domain. A downside of concern when adopting KLS, is that using too few knot points may limit the capability to represent complex shapes, while using too many knot points may cause difficulty for non-gradient optimization. This paper presents a study of the effect of number and layout of the knot points in KLS on the capability to represent complex topologies in single and multi-component structures. Image matching error metrics are employed to assess the degree of mismatch between target topologies and those best-attainable via KLS. Results are presented in a catalogue-style in order to facilitate appropriate selection of knot-points by designers wishing to apply KLS for topology optimization.

Mixed Integer Optimization With NURBs HyPerModels

2007 ◽  
Author(s):  
Cameron J. Turner ◽  
Richard H. Crawford ◽  
Matthew I. Campbell
Keyword(s):  
Design Space ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Underlying Structure ◽  
Optimization Strategy ◽  
Integer Optimization ◽  
Design Variables ◽  
Complementary Approach ◽  
Integer Programming Problems ◽  
Optimum Solution

The challenge of determining the best design in a multimodal design space with multiple local optimal solutions often challenges the best available optimization techniques. By casting the objective function of the optimization problem in the form of a Non-Uniform Rational B-spline (NURBs) metamodel, known as a HyPerModel, significant optimization advantages can be achieved, including the ability to efficiently find the global metamodel optimum solution with less computational expense than traditional approaches. This optimization strategy, defined by the HyPerOp algorithm, uses the underlying structure of a HyPerModel to intelligently select starting points for optimization runs and to identify regions of the design space that do not contain locations for the global metamodel optimum location. This paper describes the application of the HyPerOp algorithm to mixed integer programming problems and demonstrates its use with two example applications. The algorithm works with design spaces composed of continuous and integer design variables and provides a complementary approach for improved optimization capabilities.

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