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1

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

Fassi Hicham Fihri, Aniyou Hadji

Management and Production Engineering Review

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2023

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Vol. 14, No. 4

109--116

EN

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.

2

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

Xia Meng, Li Jing

Archives of Electrical Engineering

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2023

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Vol. 72, nr 4

1121--1133

EN

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.

3

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.

4

Force mechanism and conceptual design of reinforced concrete short beam without web reinforcement

Chen Yi-Jun, Zhang Hu-Zhi, Lu Bei-Rong, Huang Yao-Sen

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 4

659--671

EN

Topology Optimization and Finite Element Analysis were carried out for reinforced concrete short beams to reveal the force mechanism. The results show that load-transfer paths for the beams can evolve from Bi-directional Evolutionary Structural Optimization and be mechanically supported by the Michell criterion. In the beams, the distribution of a high- -stress compression area appears as a truss under a concentrated load and a tie-arch under a uniform load. The beams do not have much higher bearing capacity but can consume many more materials. Consequently, new design ideas were recommended based on the load transfer paths obtained by Topology Optimization.

5

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.

6

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.

7

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

Cui Hao, Xie Longfa, Xiao Min, Deng Manfang

Archives of Civil Engineering

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2022

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Vol. 68, nr 3

523--537

EN

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 the MLC is 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.

8

The Method of Transferring Topology Optimization Results Directly to the CAD System Database

Łyduch Konrad, Łukaszyk Jacek, Nowak Michał

Advances in Science and Technology. Research Journal

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2022

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Vol. 16, no 1

243--252

EN

The article presents a method of transferring topological optimization results directly to CAD system. The devel- oped method is based on sequential removal and addition of material, ignoring lesser fragments of the model. The input data includes coordinates of nodes imported from the model of finite element method optimized object. The algorithm is able to recognize geometry patterns during material addition and subtraction. Based on the results of the recognition process, individual 3D features are placed in CAD design tree (like „Feature Manager” design tree in Solidworks, used in the procedure described in the article below). Thus, the described algorithm allows for convenient and quick editing of transferred geometry of the optimized object directly in the CAD environment. The algorithm was tested on various examples of 2D and 3D models. The execution code of the presented method was written in Python programming language, and the macro for the CAD program was written in VB.NET. The proposed solution is independent of the optimizer used.

9

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.

10

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.

11

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.

12

Topology optimization of structures with stress and additive manufacturing constraints

Fiuk Grzegorz, Mrzygłód Mirosław

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 2

459--468

EN

The paper presents a new methodology dedicated to design for additive manufacturing. Based on a hybrid algorithm of topological optimization, the method enables application of advanced constraints and validates solutions “on the fly” using virtual prototyping. Advanced constraints consider the influence of directions of additive manufacturing as well as the equivalent stress. In the optimization framework, real material properties related to three manufacturing directions were considered. The new design methodology is illustrated by benchmark tests and examples of wrist-hand orthosis topology optimization in which stress and manufacturing constraints were taken into account. As demonstrated by the conducted comparison tests with available commercial tools, the solutions obtained with the new method were characterized by lower mass and shorter computation time.

13

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.

14

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.

15

A mathematical programming method for the topology optimization of a truss-like continuum

Cui Hao, Zhou Kemin

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 3

751--763

EN

A mathematical programming method to optimize the distribution field of a truss-like material is presented. The densities and angles of members are optimized in two separate procedures in each iteration. An explicit sub-problem in a variable separation form is established at every iteration procedure. At each sub-problem, the stress constraint function is expanded into a trigonometric series of the member angles. According to the extreme condition, the optimal orientations of members are determined. The member densities are optimized using the method of moving asymptotes (MMA). Two examples demonstrate that the optimal truss-like structures are very close to analytic solutions.

16

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.

17

Efektywne rozwiązania w optymalizacji topologicznej konstrukcji z ograniczeniami naprężeniowymi i zmęczeniowymi

Mrzygłód M.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2018

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z. 109

115--122

PL

W artykule zaprezentowano nową metodę optymalizacji konstrukcji przy zastosowaniu optymalizacji topologicznej. Metoda pozwala uzyskać rozwiązania spełniające przyjęte ograniczenia technologiczne i wytrzymałościowe w pierwszym kroku bez konieczności żmudnego dostosowywania kształtu do postaci nadającej się do wytwarzania. Jak potwierdzają wyniki z przeprowadzonych testów, nowa metodyka umożliwia uzyskanie rozwiązań efektywnych, czyli lekkich i zwartych konstrukcji spełniających przyjęte ograniczenia i nadających do bezpośredniego wytwarzania technologia przyrostową.

EN

In the article, a new method for structural design using topological optimization is proposed. The method allows obtaining solutions that meet the adopted manufacturing and endurance constraints in the first step without the need of shape adjusting process to form suitable for production. As it is illustrated in the carried out tests, the proposed methodology allows to obtain effective solutions: lightweight and compact structures that meet the assumed constraints and give the possibility to direct fabrication by additive manufacturing.

18

Optymalizacja topologiczna dźwigni pedału hamulca

Szmyt W.

Postępy w Inżynierii Mechanicznej

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2018

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nr 11(6)

79--90

PL

Przedstawiono sposób przeprowadzenia optymalizacji topologicznej dźwigni pedału hamulca w programie solidThinking Inspire. Pokazano geometrię przed optymalizacją, nadane warunki brzegowe optymalizacji oraz obliczeń wytrzymałościowych, a także geometrię po optymalizacji. Porównano wyniki obliczeń wytrzymałościowych oraz masy badanych obiektów przed i po optymalizacji. Zoptymalizowana geometria spełniła przyjęte kryteria przy jednoczesnym zmniejszeniu masy o 34,1%.

EN

The paper showcased topology optimization of the brake pedal lever performed in solidThinking Inspire software. Geometries before and after optimization were shown, as well as boundary conditions for optimization and strength assessment. The stresses and masses of geometries before and after optimization were compared. Optimized geometry met assumed strength criteria along with reduced mass by 34,1%.

19

Weight reduction of motorcycle frame by topology optimization

Bala Manikandan C., Balamurugan S., Balamurugan P., Lionel Beneston S.

Journal of Achievements in Materials and Manufacturing Engineering

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2018

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Vol. 91, nr 2

67--77

EN

Purpose: of this paper is to improve the fuel efficiency of electrical motorcycle by reducing the weight of its frame without affecting the basic functionalities, dimensions and performance. Design/methodology/approach: Weight reduction of the frame was achieved by topology optimization technique. Initially the load and stresses acting on the frame was studied. Material of the frame was chosen as Aluminium and the frame was geometrically modelled using Autodesk Fusion 360. With the help of ANSYS AIM 18.2, weight of the frame was optimized by the design modifications suggested by the concept of topology optimization, for the corresponding loads and stresses induced on it. It was observed that the stress induced on the modified design was lesser than that of respective permissible yield stress of the frame material. After optimization, the weight of the frame was reduced from 3.0695 kg to 2.215 kg with the weight reduction of 27.84%. The weight reduction shows that the topology optimization is an effective technique, without compensate the performance of the frame. Approach used in the paper for the weight reduction of the frame is the topology optimization. The modelled frame was topology optimized by using ANSYS 18.2. After the topology optimization, the regions where the metal removal is possible, for weight reduction was identified. Findings: In this paper, the motor cycle frame was optimized and weight of the frame was reduced from 3.065 kg to 2.215 kg. Weight reduction of 27.84% was achieved without compensating the performance. Research limitations/implications: All the components of the automobile may be topology optimized for the weight reduction, thereby improving the fuel efficiency. Innovative design/Improvement in design also possible. Practical implications: By reducing the weight of the frame, weight of the automobile also reduces. Reduction in weight of the automobile leads to improved fuel efficiency. Originality/value: Weight of the motorcycle frame reduced by topology optimization. The regions of material removal at the frame, without compensating the performance was identified.

20

Dynamic analysis of optimized two-phase auxetic structure

Idczak E., Stręk T.

Vibrations in Physical Systems

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2017

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Vol. 28

art. no. 2017003

EN

This paper presents a dynamic analysis of earlier optimized auxetic structure. This optimization based on the distribution of two materials in such way to obtain a minimal value of Poisson’s ratio (PR), which indicates the auxetic properties. The initial optimized shape was so-called star structure, which if is made from one material has the PR close to 0.188. After optimization with the goal function of PR-minimization, the obtained value was equal to -9.5043. Then the eigenfrequencies for the optimized structure were investigated. The calculations were carried out by means of Finite Element Method (FEM). For optimization of the value of Poisson’s ratio was used algorithm MMA (Method of Moving Asymptotes). The computing of single material properties (PR, Young’s modulus, density) for the whole shape was made by means of SIMP method (Solid Isotropic Method with Penalization).