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1

Numerical investigation of the effect of topology optimisation methods parameters in the topology quality, the strength, and the computational cost

Ait Ouchaoui A., Nassraoui M., Radi B.

Archives of Materials Science and Engineering

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2023

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Vol. 123, nr 2

55--71

EN

Purpose: The literature abounds with many distinct topology optimisation methods, many of which share common parameter configurations. This study demonstrates that alternative parameter configurations may produce better results than common parameters. Additionally, we try to answer two fundamental questions: identifying the most effective topology optimisation method and determining the optimal parameter selection within this optimisation method. In order to respond to these questions, we conducted a comparative and objective analysis of topology optimisation methods. Design/methodology/approach: This paper evaluates four prominent topology optimisation methodologies, SIMP, RAMP, BESO, and LSM, based on three essential criteria: structural strength, topology quality, and computational cost. We conducted an in-depth examination of 12,500 topology optimisation results spanning a broad range of critical parameter values. These outcomes were generated using MATLAB codes. In the meantime, we comprehensively compared our findings with the existing literature on this subject. Findings: As predicted, our chosen parameters had a substantial effect on the topology quality, structural strength, and computational cost of the topology optimisation outcomes. Across the 12,500 results, many parameter combinations appeared to produce favourable results compared to conventional parameters commonly found in the existing literature. Research limitations/implications: This study focuses exclusively on four specific topology optimisation methods; however, its findings may be extrapolated to apply to other methodologies. Additionally, while it extensively examines the effects of parameters on topology quality, strength, and computational cost, it does not encompass an exploration of these parameters' impacts on other performance criteria. Originality/value: Novel parameter configurations for topology optimisation have been identified, yielding enhanced outcomes in terms of topology quality, structural strength, and computational efficiency.

2

Reinforcement layout design of three-dimensional members under a state of complex stress

Cui Hao, Xia Junjie, Wu Lang, Xiao Min

Archives of Civil Engineering

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2023

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Vol. 69, nr 1

421--436

EN

This paper proposes a method to optimize reinforcement layout of three-dimensional members under a state of complex stress and multiple load cases (MLCs). To simulate three-dimensional members, the spatial truss-like material model is adopted. Three families of truss-like members along orthotropic directions are embedded continuously in concrete. The optimal reinforcement layout design is obtained by optimizing the member densities and orientations. The optimal design of three-dimensional member is carried out by solving the problem of minimum volume of reinforcing bars with stress constraints. Firstly, the optimized reinforcement layout under each single load case (SLC) is obtained as per the fully stressed criterion. Second, on the basis of the previous results, an equivalent multi-case optimization is proposed by introducing the idea of stiffness envelope. Finally, according to the characteristics of the truss-like material, a closed and symmetrical surface is adopted to fit the maximum directional stiffness under all SLCs. It can be proved that the densities and orientations of truss-like members are the eigenvalues and eigenvectors of the surface coefficient matrix, respectively. Several three-dimensional members are used as examples to demonstrate the capability of the proposed method in finding the best reinforcement layout design of each reinforced concrete (RC) member and to verify its efficiency in application to real design problems.

3

Topology optimization of a 3D part virtually printed by FDM

Antar I., Othmani M., Zarbane K., El Oumami M., Beidouri Z.

Journal of Achievements in Materials and Manufacturing Engineering

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2022

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Vol. 112, nr 1

25--32

EN

Purpose: This research work aims to exhibit the possibility to topologically optimize a mesostructured part printed virtually by FDM taking into account the manufacturing parameters. Design/methodology/approach: The topology optimization of a 3D part printed by FDM was carried out using the software ABAQUS. On the other hand, a numerical approach using a script based on G-code file has been achieved to create a virtual model. Then, it was optimized according to the Solid Isotropic Material with Penalization (SIMP) method, which minimizing the strain energy was the objective function and the volume fraction of 30% was the constraint. Findings: The final topological optimization design of the virtual model is approximately similar to the homogeneous part. Furthermore, the strain energy of the virtual model is less than the homogeneous part. However, the virtually 3D optimized part volume is higher than the homogeneous one. Research limitations/implications: In this study, we have limited our study on one layer owing to reduce the simulation time. Moreover, the time required to optimize the virtual model is inordinate. The ensuing study, we will optimize a multiple layer of the mesostructure. Practical implications: Our study provides a powerful method to optimize with accurately a mesostructure taken into consideration the manufacturing setting. Originality/value: In this paper, we have studied through an original approach the potential of topology optimization of a 3D part virtually printed by FDM. By means of our approach, we were able to optimize topologically the 3D parts printed by FDM taking into account the manufacturing parameters.

4

Optimal design of Wire-and-Arc Additively Manufactured I-beams for prescribed deflection

Bruggi Matteo, Laghi Vittoria, Trombetti Tomaso

Computer Assisted Methods in Engineering and Science

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2022

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Vol. 29, no. 4

357--378

EN

Alloys fabricated by wire-and-arc additive manufacturing (WAAM) exhibit a peculiar anisotropy in their elastic response. As shown by recent numerical investigations concerning the optimal design of WAAM-produced structural components, the printing direction remarkably affects the stiffness of the optimal layouts, as well as their shape. So far, single-plate specimens have been investigated. In this contribution, the optimal design of WAAM-produced I-beams is addressed assuming that a web plate and two flat flanges are printed and subsequently welded to assemble the structural component. A formulation of displacement-constrained topology optimization is implemented to design minimum weight specimens resorting to a simplified two-dimensional model of the I-beam. Comparisons are provided addressing solutions achieved by performing topology optimization with (i) conventional isotropic stainless steel and with (ii) WAAM-produced orthotropic stainless steel at prescribed printing orientations. Lightweight solutions arise whose specific shape depends on the selected material and the adopted printing direction.

5

Topology optimization without volume constraint – the new paradigm for lightweight design

Nowak Michał, Boguszewski Aron

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 4

art. no. e137732

EN

In the paper the new paradigm for structural optimization without volume constraint is presented. Since the problem of stiffest design (compliance minimization) has no solution without additional assumptions, usually the volume of the material in the design domain is limited. The biomimetic approach, based on trabecular bone remodeling phenomenon is used to eliminate the volume constraint from the topology optimization procedure. Instead of the volume constraint, the Lagrange multiplier is assumed to have a constant value during the whole optimization procedure. Well known MATLAB topology based optimization code, developed by Ole Sigmund, was used as a tool for the new approach testing. The code was modified and the comparison of the original and the modified optimization algorithm is also presented. With the use of the new optimization paradigm, it is possible to minimize the compliance by obtaining different topologies for different materials. It is also possible to obtain different topologies for different load magnitudes. Both features of the presented approach are crucial for the design of lightweight structures, allowing the actual weight of the structure to be minimized. The final volume is not assumed at the beginning of the optimization process (no material volume constraint), but depends on the material’s properties and the forces acting upon the structure. The cantilever beam example, the classical problem in topology optimization is used to illustrate the presented approach.

6

Topology algorithm built as an automaton with flexible rules

Tajs-Zielińska Katarzyna, Bochenek Bogdan

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 5

art. no. e138813

EN

Developing novel methods, approaches and computational techniques is essential for solving efficiently more and more demanding up-to-date engineering problems. Designing durable, light and eco-friendly structures starts at the conceptual stage, where new efficient design and optimization tools need to be implemented. Nowadays, apart from the traditional gradient-based methods applied to optimal structural and material design, innovative techniques based on versatile heuristic concepts, like for example Cellular Automata, are implemented. Cellular Automata are built to represent mechanical systems where the special local update rules are implemented to mimic the performance of complex systems. This paper presents a novel concept of flexible Cellular Automata rules and their implementation into topology optimization process. Despite a few decades of development, topology optimization still remains one of the most important research fields within the area of structural and material design. One can notice novel ideas and formulations as well as new fields of their implementation. What stimulates that progress is that the researcher community continuously works on innovative and efficient topology optimization methods and algorithms. The proposed algorithm combined with an efficient analysis system ANSYS offers a fast convergence of the topology generation process and allows obtaining well-defined final topologies.

7

Design optimization for the weight reduction of 2-cylinder reciprocating compressor crankshaft

Arshad Ali, Cong Pengbo, Elsayed Elmenshawy Adham Ahmed Awad, Blumbergs Ilmārs

Archive of Mechanical Engineering

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2021

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LXVIII, nr 4

449--471

EN

This study aims to optimize the 2-cylinder in-line reciprocating compressor crankshaft. As the crankshaft is considered the "bulkiest" component of the reciprocating compressor, its weight reduction is the focus of current research for improved performance and lower cost. Therefore, achieving a lightweight crankshaft without compromising the mechanical properties is the core objective of this study. Computational analysis for the crankshaft design optimization was performed in the following steps: kinematic analysis, static analysis, fatigue analysis, topology analysis, and dynamic modal analysis. Material retention by employing topology optimization resulted in a significant amount of weight reduction. A weight reduction of approximately 13% of the original crankshaft was achieved. At the same time, design optimization results demonstrate improvement in the mechanical properties due to better stress concentration and distribution on the crankshaft. In addition, material retention would also contribute to the material cost reduction of the crankshaft. The exact 3D model of the optimized crankshaft with complete design features is the main outcome of this research. The optimization and stress analysis methodology developed in this study can be used in broader fields such as reciprocating compressors/engines, structures, piping, and aerospace industries.

8

Milestones in the 150-year history of topology optimization: a review

Lógó János, Ismail Hussein

Computer Assisted Methods in Engineering and Science

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2020

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Vol. 27, no. 2-3

97--132

EN

Structural optimization is one of the most intensively investigated research areas in engineering. Recently, topology optimization has become the most popular engineering subfield. The starting date of structural optimization cannot be precisely determined. Michell’s optimization paper, published in 1904, is considered as the first publication in this subfield. However, his paper starts with a statement that his work is a generalization of Maxwell’s idea presented in the paper published in 1870. The authors of this review paper consider that this date can be accepted as the starting date of topology optimization. This paper is an overview of subjectively selected state-of-art achievements in topology optimization during its history of 150 years. The selection of the achievements is a rather difficult task because, in the early period of the history of topology optimization, a lot of meetings were classified and the results were not available for the public. The optimization community has almost no knowledge about the publications in topology optimization in the 1950s. Around that time, one can find some information on workshops and meetings connected to the Cambridge University or Oxford University with researchers such as Foulkes, Cox, Hemp, and Shield, who published significant results and these communications are generally not known for the reason mentioned above. After the 1970s, this situation has changed and there were more possibilities to find publications due to the changes and thanks to digitalization. As indicated earlier here subjectively selected works are overviewed from the 150-year history focusing on the first hundred twenty years.

9

Applications of Michell’s theory in designof high-rise buildings, large-scale roofs and long-span bridges

Graczykowski Cezary, Lewiński Tomasz

Computer Assisted Methods in Engineering and Science

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2020

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Vol. 27, no. 2-3

133--154

EN

This paper analyzes the relations between the theory of Michell structures, which is one ofthe most important theories in structural optimization, and some remarkable engineeringstructures, including selected high-rise buildings, large-scale roof coverings and long-span bridges. The first part of this study briefly presents the development of Michell’s theory, its basic concepts, assumptions, and examples and fundamental features of Michellstructures. Then, several untypical engineering structures that make use of said conceptsare presented, including skyscrapers proposed by the Polish structural designer W. Zalewski and the international architectural office of Skidmore, Owings and Merill (SOM). Next, large-scale roof coverings of “Spodek” arena in Poland as well as selected bridgesare thoroughly analyzed in the context of similarity to Michell structures. The conductedstudy reveals that considered structural forms of the analyzed structures follow some ofthe concepts known from Michell’s theory and thus possess many features of the optimalstructural designs.

10

Application of topology optimization to thighbone and thighbone/implant structure modelling

Kutylowski Ryszard, Szwechlowicz Marek

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 4

1006--1019

EN

This paper presents an application of topology optimization in bioengineering. The varia- tional approach to the topology optimization is applied. Using an original numerical algorithm and a programme developed in Matlab, the structure of the thighbone was modelled by FEM. The numerical results of the mass distribution in modelled bone are provided. Obtained topologies are similar to the density distribution in real bone tissue including the case when the implant is imposed into the human body.

11

Finite element analysis of dynamic properties of thermally optimal two-phase composite structure

Nienartowicz M., Stręk T.

Vibrations in Physical Systems

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2014

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Vol. 26

203--210

EN

This paper presents modelling and a FEM analysis of dynamic properties of a thermally optimal two-phase composite structure. Simulations were provided for 2D models. At the first step, topology optimization was performed, where an internal energy was minimized. At the second step, analysis of dynamic properties was executed. Calculations allowed to determine eigenfrequencies and the mode shape of the structure. Solid isotropic material with penalization (SIMP) model was used to find the optimal solution. The optimization algorithm was based on SNOPT method and Finite Element Method.

12

Material Selection of Compliant Mechanism for Vibration Isolation

Vijayan V., Karthikeyan T.

Mechanics and Mechanical Engineering

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2014

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Vol. 18, nr 2

121--134

EN

The flexible material is always absorbing some energy and reflects it. This concept was adopted from complaint mechanism principle and it was developed with the help of topology optimization technique. An innovative idea is used these principles to create a new design to absorb the vibration in the machine shop, through an innovative design model and analysis ware discussed. This paper gives a different material selection for design of compliant mechanism and also outline about the complaint mechanisms principle and shows how it is useful in mechanical field. Recently this technique is developed with the help of advanced design and also combination of some other technique. A study has been made in this for different materials.

13

Design of the optimal fiber reinforcement for masonry structures via topology optimization

Bruggi M., Milani G., Taliercio A.

Wiadomości Konserwatorskie

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2013

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Nr 34

23--27

EN

The optimal layout of the fiber reinforcement to be placed on existing masonry structures is determined using topology optimization [1]. The problem can be conveniently formulated as the minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. Strength criteria for masonry elements are provided by means of a recently presented lower bound limit analysis homogenization model [2], relying into a discretization of one-fourth of the unit cell by six CST elements. The macroscopic strength domain of masonry can be obtained in closed form, thanks to the limited number of variables involved. A multi-constrained discrete formulation that locally controls the stress field over the whole design domain [3] is adopted. The contribution presents some preliminary numerical results addressing the fiber-reinforcement of a benchmark masonry wall.

PL

Optymalny układ zbrojenia z włókna do umieszczenia na istniejących konstrukcjach murowych jest określany za pomocą optymalizacji topologii.

14

Effects of Local Volume Constraints on Optimal Topologies of Continuums

Cai K., Gao Z.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 9b

133-136

EN

Optimal stiffness design of a structure with local volume constraints on its subdomains is investigated. In practical engineering, a structure may have many subdomains with local volume constraints to meet the multi-function of structure. A new heuristic approach simulating the bone remodelling process is presented to solve such problem. The essentials of the present approach are summarized as follows. Firstly, the topology optimization of structure is equivalent to bone remodelling process. Corresponding to the dead zone in bone remodelling theory, a floating interval of reference strain energy density (SED) is proposed. Secondly, the update of the design variable, i.e. the relative density of a material point, is determined by comparison between the local SED and the current interval of reference SED. Thirdly, to satisfy the global constraints in an optimization problem, the global reference interval changes in simulation. Finally, to satisfy the local volume constraints of subdomains in structure, the same amount of local reference intervals are adopted to modify the update rule of local materials. Numerical examples are employed to demonstrate the effects of the local volume constraints on the optimal topologies of structures.

PL

Zbadano metody optymalnego projektowania system z ograniczeniami lokalnych rozmiarów w subdomenach. Przedstawiono nową metodę heurystyczną symulującą szkielet procesu modelowania w celu rozwiązania tego problemu.

15

Optymalizacja topologii konstrukcji belkowych przy użyciu metody wzrostu struktury bazowej

Król R.

Mechanik

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2012

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R. 85, nr 1CD

PL

W artykule przedstawione zostały algorytmy optymalizacji topologii konstrukcji belkowych dwu- i trójwymiarowych w oparciu o wzrost struktury wyjściowej. Opracowane zostały odrębne elementarne strategie takie, jak dodawanie nowej belki, usuwanie belki z konstrukcji oraz dodawanie lub usuwanie węzłów. Strategie te mogą być kombinowane oraz wykonywane wielokrotnie. W przedstawionej metodzie nie ma potrzeby budowania złożonej wyjściowej struktury bazowej (ang. ground structure), której przygotowanie dla dużych konstrukcji może być pracochłonne. Zadaniem użytkownika jest jedynie określenie prostopadłościanu podzielonego równomiernie na węzły, każdy z których jest kandydatem na dołączenie do konstrukcji. Jako kryterium wyboru węzłów-kandydatów lub nowych elementów belkowych przyjęto maksymalne naprężenia zredukowane spośród uśrednionych dla każdego wariantu konstrukcji. W stosunku do klasycznych metod optymalizacji topologii, przedstawiona metoda jest bardzo wymagająca obliczeniowo. Może być jednak z powodzeniem użyta do modyfikacji konstrukcji przeznaczonej do dalszej optymalizacji np. pod względem rozkładu materiału na elementy w celu minimalizacji podatności.

EN

This article presents topology optimization algorithms of 2D and 3D beam structures. Developed methods doesn’t use ground structure, which can be very complex for large constructions. Four kinds of elementary strategies has been developed: addition of a beam, removal of a beam, addition of a node and removal of a node. These strategies can be combined and can be used repeatedly. User has to define cuboidal grid of candidate-nodes. It can be dense, sparse, large or limit only small region of the initial structure. As a selection criterion, these beams are being added to the structure, which increases average stress in all finite elements the most. Methods presented in this article are computationally expensive in comparison to the other classical ground structure methods. It can be used to correct topology of beam structures before further compliance and volume optimization.

16

Evolutionary algorithms in selected optimization and identification problems of mechanical systems

Burczyński T., Beluch W., Kuś W., Nowakowski M., Orantek P.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2002

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z. 139

87--121

EN

This chapter deals with applications of evolutionary algorithms to the topology optimization of elastic structures, shape optimization of elasto-plastic structures, the identification of voids and cracks in structures under dynamical loading and the identification and optimization of boundary conditions in cracked structures.