Evolutionary truss topology optimization using a graph-based parameterization concept

A novel parameterization concept for the optimization of truss structures by means of evolutionary algorithms is presented. The main idea is to represent truss structures as mathematical graphs and directly apply genetic operators, i.e., mutation and crossover, on them. For this purpose, new genetic graph operators are introduced, which are combined with graph algorithms, e.g., Cuthill-McKee reordering, to raise their efficiency. This parameterization concept allows for the concurrent optimization of topology, geometry, and sizing of the truss structures. Furthermore, it is absolutely independent from any kind of ground structure normally reducing the number of possible topologies and sometimes preventing innovative design solutions. A further advantage of this parameterization concept compared to traditional encoding of evolutionary algorithms is the possibility of handling individuals of variable size. Finally, the effectiveness of the concept is demonstrated by examining three numerical example

A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA

Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algorithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical examples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications

Simultaneous Topology, Shape, and Sizing Optimisation of Plane Trusses with Adaptive Ground Finite Elements Using MOEAs

This paper proposes a novel integrated design strategy to accomplish simultaneous topology shape and sizing optimisation of a two-dimensional (2D) truss. An optimisation problem is posed to find a structural topology, shape, and element sizes of the truss such that two objective functions, mass and compliance, are minimised. Design constraints include stress, buckling, and compliance. The procedure for an adaptive ground elements approach is proposed and its encoding/decoding process is detailed. Two sets of design variables defining truss layout, shape, and element sizes at the same time are applied. A number of multiobjective evolutionary algorithms (MOEAs) are implemented to solve the design problem. Comparative performance based on a hypervolume indicator shows that multiobjective population-based incremental learning (PBIL) is the best performer. Optimising three design variable types simultaneously is more efficient and effective

ON AN EVOLUTIONARY DEVELOPMENTAL METHODOLOGY FOR PIN-JOINT FRAMEWORK OPTIMIZATION

M.S.M.S. Thesis. University of Hawaiʻi at Mānoa 201

Multiobjective Topology Optimization for Preliminary Design Using Graph Theory and L-System Languages

Topology optimization is a powerful tool that, when employed at the preliminary stage of the design process, can determine potential structural configurations that best satisfy specified performance objectives. However, the use of conventional topology optimization approaches such as density-based and level set methods requires a fair amount of user knowledge of or intuition for both the design problem being considered and the desired result. While straightforward for simple structural problems with a relatively small design space, advancements in the area of smart materials and a growing interest in developing structures with increased multifunctionality may begin to render these methods as ineffective. Thus, there is a growing need for an inherently multiobjective preliminary design tool capable of exploring a vast design space to identify well-performing solutions to problems with which users have little/no intuition or experience. This work proposes the use of a heuristic alternative to conventional topology optimization approaches which couples a genetic algorithm with a parallel rewriting system known as a Lindenmayer System (L-System). The L-System encodes design variables into a string of characters that, when interpreted by a deterministic algorithm, governs the development of the topology. In particular, this work explores two distinct L-System interpretation approaches. The first is a geometry-based approach known as turtle graphics, which tracks its spatial position and orientation at all times and constructs line segments between specified coordinates. The second is a newly-developed graph-based approach referred to as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS). This algorithm is based on the nodes, edges, and faces of a planar graph, allowing for an edge- and face-constructing agent to move more freely around the design space and introduce deliberate and natural topological modifications. This graph-based approach can also be extended to consider a three-dimensional structural design domain, the first known demonstration of 3-D L-System topology optimization. It will be demonstrated that the proposed L-System topology optimization framework effectively explores the physical design space and results in configurations comparable to both known optimal or ideal solutions as well as those found using conventional topology optimization methods, but with the advantage of straightforward multiobjective/multiphysical extension. The implementation of a sizing optimization scheme to determine optimal structural member thicknesses for SPIDRS-generated topologies will also be discussed, and several potential multiphysical design applications will be introduced

New approaches to optimization in aerospace conceptual design

Aerospace design can be viewed as an optimization process, but conceptual studies are rarely performed using formal search algorithms. Three issues that restrict the success of automatic search are identified in this work. New approaches are introduced to address the integration of analyses and optimizers, to avoid the need for accurate gradient information and a smooth search space (required for calculus-based optimization), and to remove the restrictions imposed by fixed complexity problem formulations. (1) Optimization should be performed in a flexible environment. A quasi-procedural architecture is used to conveniently link analysis modules and automatically coordinate their execution. It efficiently controls a large-scale design tasks. (2) Genetic algorithms provide a search method for discontinuous or noisy domains. The utility of genetic optimization is demonstrated here, but parameter encodings and constraint-handling schemes must be carefully chosen to avoid premature convergence to suboptimal designs. The relationship between genetic and calculus-based methods is explored. (3) A variable-complexity genetic algorithm is created to permit flexible parameterization, so that the level of description can change during optimization. This new optimizer automatically discovers novel designs in structural and aerodynamic tasks

APPLICATIONS OF PARAMETERIZED L-SYSTEMS FOR PRELIMINARY STRUCTURAL DESIGN AND OPTIMIZATION

Preliminary design is a complicated problem that is often solved using topology optimization. In this work, a heuristic approach to topology optimization is considered. This approach involves the coupling of a genetic optimization with a parallel rewriting system, known as an L-System. This approach encodes design variables into a string of characters that are then coupled with an interpreter to develop a structure in a given domain. By considering a heuristic bio-inspired approach over more traditional density and level set topology approaches, we are able to avoid numerical issues and rapid increasing design space dimensionality associated with complicated multi objective problems. In this work a new interpreter for L-Systems, called the Spatial Interpretation for the Design of Reconfigurable Structures (SPIDRS), is applied to several design problems. This work seeks to show SPIDRS as a powerful preliminary design tool for difficult problems that lack traditional engineering intuition. First, a morphing airfoil inspired by the rotor blade of the UH-60 is considered. SPIDRS is utilized to determine the internal structural layout as well as the placement of actuators to facilitate morphing to meet a shape objective while minimizing mass. A coupled fluid structure interaction (FSI) evaluation is performed using the finite element method (Abaqus) and vortex lattice method (XFOIL). The resulting final shape of the airfoil, as determined by the FSI evaluation, and the mass are used as objectives in a genetic optimization Second, a set of origami fold design problems are considered. SPIDRS is first validated using the well established square twist pattern and the results are compared to previous work in the literature. SPIDRS is then used with an arbitrary continuous kinematic objective to determine its ability to evolve towards an unknown solution pattern. The standard square twist pattern is also utilized to evaluate the efficacy of altering the original SPIDRS production rules for use specifically in origami

Speciation, clustering and other genetic algorithm improvements for structural topology optimization

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1996.Includes bibliographical references (p. 103-106).by James Wallace Duda.M.S

Analysis, Design, and Optimization of Structures with Integral Compliant Mechanisms for Mid-Frequency Response

An analysis, design, and optimization methodology for structures that vibrate in the 1 kHz to 10 kHz frequency range has been developed. This methodology is the synthesis of several established research fields including structural dynamics, compliant mechanism design, finite element computational analysis, and structural optimization via an evolutionary algorithm.Ph.D.Mechanical EngineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/60284/1/Dede_Dissertation.pd