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

Michał Nowak Aron Boguszewski
Bulletin of the Polish Academy of Sciences Technical Sciences | 2021 | 69 | 4 | e137732 | DOI: 10.24425/bpasts.2021.137732
Keywords topology optimization lightweight design biomimetic structural optimization
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Abstract

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.
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Authors and Affiliations

Michał Nowak
1
ORCID: ORCID
Aron Boguszewski
1
  1. Poznan University of Technology, Division of Virtual Engineering, ul. Jana Pawła II 24, 60-965 Poznań, Poland

Topology algorithm built as an automaton with flexible rules

Katarzyna Tajs-Zielińska Bogdan Bochenek
Bulletin of the Polish Academy of Sciences Technical Sciences | 2021 | 69 | 5 | e138813 | DOI: 10.24425/bpasts.2021.138813
Keywords topology optimization cellular automaton flexible update rules
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Abstract

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.
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Authors and Affiliations

Katarzyna Tajs-Zielińska
1
Bogdan Bochenek
1
  1. Faculty of Mechanical Engineering, Cracow University of Technology, Al. Jana Pawła II 37, 31-864 Kraków, Poland

A discrete variable based methodology for topology optimization considering spatially uneven manufacturing errors

Meng Xia Jing Li
Archives of Electrical Engineering | 2023 | vol. 72 | No 4 | 1121-1133 | DOI: 10.24425/aee.2023.147430
Keywords interval field manufacturing errors morphological operation topology optimization
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Abstract

Manufacturing errors (MEs) are unavoidable in product fabrication. The omnipresence of manufacturing errors (MEs) in product engineering necessitates the development of robust optimization methodologies. In this research, a novel approach based on the morphological operations and interval field (MOIF) theory is proposed to address MEs in the discrete-variable-based topology optimization procedures. On the basis of a methodology for deterministic topology optimization (TO) based on the Min-Cut, MOIF introduces morphological operations to generate geometrical variations, while the dimension of the structuring element is dynamically set by the interval field function’s output. The effectiveness of the proposed approach as a powerful tool for accounting for spatially uneven ME in the TOs has been demonstrated.
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Authors and Affiliations

Meng Xia
1
Jing Li
1
  1. School of Information and Electrical Engineering, Hangzhou City University, Hangzhou, 310027, China

Numerical benchmarks for topology optimization of structures with stress constraints

Grzegorz Fiuk Mirosław W. Mrzygłód
Bulletin of the Polish Academy of Sciences Technical Sciences | 2021 | 69 | 6 | e139317 | DOI: 10.24425/bpasts.2021.139317
Keywords topology benchmarks stress constraints topology optimization additive manufacturing
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Abstract

Modern industry requires an increasing level of efficiency in a lightweight design. To achieve these objectives, easy-to-apply numerical tests can help in finding the best method of topological optimization for practical industrial applications. In this paper, several numerical benchmarks are proposed. The numerical benchmarks facilitate qualitative comparison with analytical examples and quantitative comparison with the presented numerical solutions. Moreover, an example of a comparison of two optimization algorithms was performed. That was a commonly used SIMP algorithm and a new version of the CCSA hybrid algorithm of topology optimization. The numerical benchmarks were done for stress constraints and a few material models used in additive manufacturing.
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Authors and Affiliations

Grzegorz Fiuk
1
ORCID: ORCID
Mirosław W. Mrzygłód
1
ORCID: ORCID
  1. Opole University of Technology, Faculty of Mechanical Engineering, ul. Mikołajczyka 5, 45-271 Opole, Poland

Conceptual design of reinforced concrete structures using truss-like topology optimization

Hao Cui Longfa Xie Min Xiao Manfang Deng
Archives of Civil Engineering | 2022 | vol. 68 | No 3 | 523-537 | DOI: 10.24425/ace.2022.141900
Keywords conceptual design reinforced concrete topology optimization truss-like material
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Abstract

The paper proposes a procedure for the conceptual design of reinforced concrete (RC) structures under a multiple load case (MLC), based on the truss-like topology optimization method. It is assumed that planar truss-like members are densely embedded in concrete to simulate RC structures. The densities and orientations of the reinforcing bars at nodes are regarded as optimization variables. The optimal reinforcement layout is obtained by solving the problem of minimizing the total volume of reinforcing bars with stress constraints. By solving a least squares problem, the optimized reinforcement layout under theMLCis obtained.According to the actual needs of the project, the zones to be reinforced are determined by reserving a certain percentage of elements. Lastly, a recommended reinforcement design is determined based on the densities and orientations of truss-like members. The reinforcement design tends to be more perfect by adding necessary structural reinforcements that meet specification requirements. No concrete cover is considered. Several examples are used to demonstrate the capability of the proposed method in finding the best reinforcement layout design.
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Authors and Affiliations

Hao Cui
1
ORCID: ORCID
Longfa Xie
1
ORCID: ORCID
Min Xiao
1
ORCID: ORCID
Manfang Deng
1
ORCID: ORCID
  1. College of Civil Engineering and Architecture, Jiangxi Science and Technology Normal University, No.605 Fenglin Avenue, 330013, Nanchang, China

Towards an Optimal Motor Mounting Bracket Using Topology Optimization Combined with Sustainability and Manufacturing Cost Analysis

Hicham Fihri FASSI Hadji ANIYOU
Management and Production Engineering Review | 2023 | vol. 14 | No 4 | DOI: 10.24425/mper.2023.147208
Keywords Engine mount topology optimization Numerical simulation Sustainability manufacturing Costing analysis
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Abstract

The engine is the most important component of a vehicle. It attaches to the main frame via the engine mounting bracket which supports weight and operating loads. The engine mount therefore plays a crucial role in the durability and comfort of the vehicle. This article contributes to the search for the most optimal model from the point of view of resistance, environmental impact, and manufacturing cost. This involves, on the one hand, optimizing the support by reducing its initial mass by 30%, and on the other hand, seeking suitable material and manufacturing process with the least environmental impact. To this end, topology optimization will be combined with an environmental assessment and a manufacturing cost analysis. Four materials will be tested and evaluated. Finally, a cost analysis will present a comparison between a conventional process and 3D printing.
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Authors and Affiliations

Hicham Fihri FASSI
Hadji ANIYOU

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

Hao Cui Junjie Xia Lang Wu Min Xiao
Archives of Civil Engineering | 2023 | vol. 69 | No 1 | 421-436 | DOI: 10.24425/ace.2023.144181
Keywords topology optimization truss-like material reinforcement layout multiple load cases complex stress
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Abstract

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.
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Authors and Affiliations

Hao Cui
1
ORCID: ORCID
Junjie Xia
1
ORCID: ORCID
Lang Wu
1
ORCID: ORCID
Min Xiao
1
ORCID: ORCID
  1. College of Civil Engineering and Architecture, Jiangxi Science and Technology Norma lUniversity, No.605 Fenglin Avenue, 330013, Nanchang, China

Integrating a Complete Approach for Optimization and Sustainability in Brake Disc Rotors

Hicham Fihri FASSI Reda OURIHI Fatima Zohra EL HILALI
Management and Production Engineering Review | 2024
Keywords 3D printing Additive Manufacturing topology optimization FEA Sustainability Brake DiscRotor
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Abstract

This study employed two primary approaches to determine the optimum structure: the lightweight and sustainable models. The lightweight model considered various factors such as materials, geometry, and dimensions of the brake disc rotor and brake pads. On the other hand, the sustainable model considers the manufacturing process and aims to reduce the carbon footprint. To calculate the optimal lightweight structure, finite element analysis was conducted using two different materials to compare the resulting stresses and determine the most appropriate material. Subsequently, four different models were utilized in finite element analysis to evaluate the displacement and stress and establish the optimum structure. Regarding sustainability, two distinct processes were employed to assess the environmental impact and energy consumption to adopt an eco-friendly approach. This paper investigates the transition from the initial brake disc rotor to a lightweight model, employing finite element analysis, topology optimization, and sustainability considerations. The work is achieved by comparing the cost between conventional and 3D printing processes.
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Authors and Affiliations

Hicham Fihri FASSI
Reda OURIHI
Fatima Zohra EL HILALI

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

Ali Arshad Pengbo Cong Adham Awad Elsayed Elmenshawy Ilmārs Blumbergs
Archive of Mechanical Engineering | 2021 | vol. 68 | No 4 | 449-471 | DOI: 10.24425/ame.2021.139311
Keywords reciprocating compressor crankshaft optimization weight reduction topology optimization stress distribution crank web crankshaft lightweight design crack modeling modal analysis
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Abstract

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.
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Authors and Affiliations

Ali Arshad
1
ORCID: ORCID
Pengbo Cong
2
Adham Awad Elsayed Elmenshawy
1
Ilmārs Blumbergs
1
ORCID: ORCID
  1. Institute of Aeronautics, Faculty of Mechanical Engineering, Transport and Aeronautics, Riga Technical University, Latvia
  2. Institute of Mechanics and Mechanical Engineering, Faculty of Mechanical Engineering, Transport and Aeronautics, Riga Technical University, Latvia

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