Minimum length-scale constraints for parameterized implicit function based topology optimization

Open access via Springer Compact Agreement The author would like to thank the Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/). The author also would like to acknowledge the support of the Maxwell compute cluster funded by the University of Aberdeen. Finally, the author thanks the anonymous reviewers for their helpful comments and suggestions that improved this paper.Peer reviewedPublisher PD

Topology Optimization Applications on Engineering Structures

Over the years, several optimization techniques were widely used to find the optimum shape and size of engineering structures (trusses, frames, etc.) under different constraints (stress, displacement, buckling instability, kinematic stability, and natural frequency). But, most of them require continuous data set where, on the other hand, topology optimization (TO) can handle also discrete ones. Topology optimization has also allowed radical changes in geometry which concludes better designs. So, many researchers have studied on topology optimization by developing/using different methodologies. This study aims to classify these studies considering used methods and present new emerging application areas. It is believed that researchers will easily find the related studies with their work

Topology optimization for additive manufacture

Additive manufacturing (AM) offers a way to manufacture highly complex designs with potentially enhanced performance as it is free from many of the constraints associated with traditional manufacturing. However, current design and optimisation tools, which were developed much earlier than AM, do not allow efficient exploration of AM's design space. Among these tools are a set of numerical methods/algorithms often used in the field of structural optimisation called topology optimisation (TO). These powerful techniques emerged in the 1980s and have since been used to achieve structural solutions with superior performance to those of other types of structural optimisation. However, such solutions are often constrained during optimisation to minimise structural complexities, thereby, ensuring that solutions can be manufactured via traditional manufacturing methods. With the advent of AM, it is necessary to restructure these techniques to maximise AM's capabilities. Such restructuring should involve identification and relaxation of the optimisation constraints within the TO algorithms that restrict design for AM. These constraints include the initial design, optimisation parameters and mesh characteristics of the optimisation problem being solved. A typical TO with certain mesh characteristics would involve the movement of an assumed initial design to another with improved structural performance. It was anticipated that the complexity and performance of a solution would be affected by the optimisation constraints. This work restructured a TO algorithm called the bidirectional evolutionary structural optimisation (BESO) for AM. MATLAB and MSC Nastran were coupled to study and investigate BESO for both two and three dimensional problems. It was observed that certain parametric values promote the realization of complex structures and this could be further enhanced by including an adaptive meshing strategy (AMS) in the TO. Such a strategy reduced the degrees of freedom initially required for this solution quality without the AMS

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

Robust topology optimization for cellular composites with hybrid uncertainties

Copyright © 2018 John Wiley & Sons, Ltd. This paper will develop a new robust topology optimization method for the concurrent design of cellular composites with an array of identical microstructures subject to random-interval hybrid uncertainties. A concurrent topology optimization framework is formulated to optimize both the composite macrostructure and the material microstructure. The robust objective function is defined based on the interval mean and interval variance of the corresponding objective function. A new uncertain propagation approach, termed as a hybrid univariate dimension reduction method, is proposed to estimate the interval mean and variance. The sensitivity information of the robust objective function can be obtained after the uncertainty analysis. Several numerical examples are used to validate the effectiveness of the proposed robust topology optimization method

Topology Optimization via Machine Learning and Deep Learning: A Review

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs. At the same time, machine learning (ML) methodology including deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies: (1) TO and (2) ML perspectives. The TO perspective addresses "why" to use ML for TO, while the ML perspective addresses "how" to apply ML to TO. In addition, the limitations of current MLTO research and future research directions are examined

Design and optimization of self-deployable damage tolerant composite structures: A review

Composite deployable structures are becoming increasingly important for the space industry, emerging as an alternative to conventional metallic mechanical systems in space applications. In most cases, the life-cycle of these structures includes a single deployment sequence, once the spacecraft is in orbit. So long as reliability is ensured, this fact opens the possibility of using the materials past their elastic regime and, possibly, beyond the initiation of damage, increasing the efficiency and applicability of the developed designs. This review explores this possibility, surveying the design of deployable structures, as well as the state of the art on the design and damage tolerance in composites. An overview of the developments performed on the topology optimization of composite structures is included for its novelty and potential application in the design of deployable structures. Finally, the possibility of combining these topics into a single efficient design approach is discussed

Mixed Approaches to Handle Limitations and Execute Mutation in the Genetic Algorithm for Truss Size, Shape and Topology Optimization

A high-performance genetic algorithm for the optimal synthesis of trusses in discrete search spaces is developed. The main feature of the proposed computational procedure is the possibility of obtaining effective solutions without the violation of any constraint. In general, a varying of cross-sectional areas of bars, coordinates of nodes and topology system is provided. A group of individuals in the population can be accepted for further consideration only if all specified limitations have been fulfilled. Penalties that significantly change an objective function are introduced for other individuals. This mechanism of handling limitations provides for correction of inaccuracies that can introduce penalty functions for satisfying the problem conditions. Both a random change to the entire set of admissible values and a random choice of values among adjacent elements in this set can be performed during the mutation stage. Standard test examples for benchmark mathematical functions and trusses show high efficiency of the considered iterative procedure in terms of solution accuracy

Design framework for multifunctional additive manufacturing: coupled optimization strategy for structures with embedded functional systems

The driver for this research is the development of multi-material additive manufacturing processes that provide the potential for multi-functional parts to be manufactured in a single operation. In order to exploit the potential benefits of this emergent technology, new design, analysis and optimization methods are needed. This paper presents a method that enables in the optimization of a multifunctional part by coupling both the system and structural design aspects. This is achieved by incorporating the effects of a system, comprised of a number of connected functional components, on the structural response of a part within a structural topology optimization procedure. The potential of the proposed method is demonstrated by performing a coupled optimization on a cantilever plate with integrated components and circuitry. The results demonstrate that the method is capable of designing an optimized multifunctional part in which both the structural and system requirements are considered