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An 88-48-88 line matlab code for asymptotic homogenisation of spatially varying multiscale configurations

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2025年第3期68卷

作者： Ma, Chuang Li, Shaoshuai Xue, Dingchuan Zhu, Yichao Guo, Xu Sch Dalian Univ Technol Dalian 116023 Peoples R China Penn State Univ Dept Engn Sci & Mech University Pk PA 16802 USA Dalian Univ Technol State Key Lab Struct Anal Optimizat & CAE Software Ind Equipment Dalian 116023 Peoples R China

Nowadays, partly thanks to the development of novel manufacturing techniques, more complex multiscale configurations whose microstructural building blocks can vary smoothly in space, have gained increasing research interest. Compared with periodic multiscale structures, the microstructural variance in spatially varying multiscale configuration (SVMSC) leads to innumerate cell problems to solve, if it is analysed with asymptotic homogenisation (AH). Algorithms and/or softwares for the compliance evaluation of SVMSCs are naturally needed. Zhu et al. proposed an improved asymptotic homogenisation method (AH plus) for evaluating the stiffness performance of SVMSC. Then to facilitate practical application, machine learning models are trained to summarise the macro-micro transition indicated by the cell problems. However, the implementation and application of this algorithm still present challenges due to these complex mathematical treatments behind the realisation of theory in computation. In order to offer a shortcut to readers doing spatially varying multiscale analysis on their owns, this article provides and explains a set of matlab codes based on the AH plus method for the performance evaluation of multiscale structures, especially when the structure exhibits spatial gradients. This code package is composed of three moduli: an 88-line script to compute the homogenised properties of a given irregular-shaped building block, a 48-line script to train a neural network expressing the homogenised properties, and an 88-line script to conduct online compliance computation. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the code presented in this article. The complete matlab codes are given in the Appendixes and can be downloaded from the web-site https://***/DLUTMARG/MLBAH88-48-88.

关键词： Asymptotic homogenisation Smoothly varying multiscale configuration (SVMSC) Generalised lattice configurations matlab code Machine learning

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matlab code for a level set-based topology optimization method using a reaction diffusion equation

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2015年第5期51卷 1159-1172页

作者： Otomori, Masaki Yamada, Takayuki Izui, Kazuhiro Nishiwaki, Shinji Kyoto Univ Dept Mech Engn & Sci Nishikyo Ku Kyoto 6158540 Japan

This paper presents a simple matlab implementation for a level set-based topology optimization method in which the level set function is updated using a reaction diffusion equation, which is different from conventional level set-based approaches (Allaire et al. 2002, 2004;Wang et al. 2003) that use the Hamilton-Jacobi equation to update the level set function. With this method, the geometrical complexity of optimized configurations can be easily controlled by appropriately setting a regularization parameter. We explain the code in detail, and also the derivation of the topological derivative that is used in the level set-based topology optimization. Numerical results for stiffness maximization problems are provided to facilitate the reader's understanding. The presented code is intended for educational purposes only. This paper was inspired by previously published papers presenting matlab code for a SIMP method (Sigmund 2001;Andreassen et al. 2011), a level set-based method (Challis 2010), and FreeFem ++ code for a structural optimization method (Allaire and Pantz 2006). Readers can investigate results provided by these different methods and discover the prominent aspects of each particular method. The code presented here can be downloaded from http://***/members/yamada/***.

关键词： Education matlab code Topology optimization Level set method Topological derivative Reaction diffusion equation

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matlab code for plotting ambiguity functions

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2002年第3期38卷 1064-1068页

作者： Mozeson, E Levanon, N Tel Aviv Univ Dept Elect Engn Syst IL-69978 Tel Aviv Israel

A matlab code capable of plotting ambiguity functions of many different radar signals is presented. The program makes use of matlab's sparse matrix operations, and avoids loops. The program could be useful as a pe... 详细信息

关键词： functions pulse compression radar computing radar signal processing sparse matrices Doppler-shifted signal version matlab code ambiguity functions plotting matched-filter response pedagogical tool radar courses radar signals sparse matr radar computing RADAR SIGNALS Radar signal processing Plotting Pulse compression Sparse matrix ambiguity function

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SoRoTop: a hitchhiker's guide to topology optimization matlab code for design-dependent pneumatic-driven soft robots

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OPTIMIZATION AND ENGINEERING 2024年第4期25卷 2473-2507页

作者： Kumar, Prabhat Indian Inst Technol Hyderabad Dept Mech & Aerosp Engn Hyderabad 502285 Telangana India

Demands for pneumatic-driven soft robots are constantly rising for various applications. However, they are often designed manually due to the lack of systematic methods. Moreover, design-dependent characteristics of pneumatic actuation pose distinctive challenges. This paper provides a compact matlab code, named SoRoTop, and its various extensions for designing pneumatic-driven soft robots using topology optimization. The code uses the method of moving asymptotes as the optimizer and builds upon the approach initially presented in Kumar et al. (Struct Multidiscip Optim 61(4):1637-1655, 2020). The pneumatic load is modeled using Darcy's law with a conceptualized drainage term. Consistent nodal loads are determined from the resultant pressure field using the conventional finite element approach. The robust formulation is employed, i.e., the eroded and blueprint design descriptions are used. A min-max optimization problem is formulated using the output displacements of the eroded and blueprint designs. A volume constraint is imposed on the blueprint design, while the eroded design is used to apply a conceptualized strain energy constraint. The latter constraint aids in attaining optimized designs that can endure the applied load without compromising their performance. Sensitivities required for optimization are computed using the adjoint-variable method. The code is explained in detail, and various extensions are also presented. It is structured into pre-optimization, MMA optimization, and post-optimization operations, each of which is comprehensively detailed. The paper also illustrates the impact of load sensitivities on the optimized designs. SoRoTop is provided in "Appendix A" and is available with extensions in the supplementary material and publicly at https://***/PrabhatIn/SoRoTop.

关键词： Pneumatically driven soft robots Design-dependent loads Topology optimization Robust formulation matlab code

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A filter-based level set topology optimization method using a 62-line matlab code

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2020年第2期62卷 1001-1018页

作者： Yaghmaei, Mohammad Ghoddosian, Ali Khatibi, Mohammad Mahdi Semnan Univ Dept Mech Engn Semnan Iran

The present paper proposes a fast and easy to implement level set topology optimization method that is able to adjust the complexity of resulting configurations. While the existing methods solve a large system of linear equations, the proposed method applies a density filter to the level set function in order to smoothen the optimized configurations. Considering the proposed method, the minimum total potential energy problem and optimum design problem of compliant mechanism will be studied in the present study. In topology optimization methods, the topological derivative determines the criteria of removing/adding material from/to the domain of definition of the problem. We utilize the definition of topological derivative to measure the sensitivity of a given objective function when an infinite small hole is inserted at an arbitrary location of the domain. It is shown that a first-order stress field appears in the topological derivative. Moreover, a comprehensive Airy stress function is proposed in order to solve the boundary value problem that governs the appeared first-order stress field. Finally, a simple matlab implementation is provided to confirm the effectiveness and utility of the proposed method.

关键词： Topology optimization Level set method Topological derivative Airy stress function Filtering regularization method matlab code

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An efficient 137-line matlab code for geometrically nonlinear topology optimization using bi-directional evolutionary structural optimization method

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2021年第5期63卷 2571-2588页

作者： Han, Yongsheng Xu, Bin Liu, Yuanhao Northwestern Polytech Univ Inst Struct Hlth Monitoring & Control Sch Mech Civil Engn & Architecture Xian 710072 Peoples R China

Topology optimization, as a powerful conceptual design method, has been widely adopted in both academic research and industrial applications. To further promote the development of topology optimization, many computer programs have been published for educational purposes over the past decades. However, most of the computer programs are constructed based on a linear assumption. On the basis of bi-directional evolutionary structural optimization (BESO) method, the paper presents a matlab implementation of the geometrically nonlinear topology optimization code for compliance minimization of statically loaded structures. Excluding 19 lines which are used for explanation, only 118 lines are needed for the initialization of the design parameters, nonlinear finite element analysis, sensitivity calculation, sensitivity filtration, and topological design variables update. Different design problems can be solved by modifying several lines in the proposed program. The complete 137-line code is included as an Appendix and is intended for educational purposes only.

关键词： Topology optimization matlab code Geometrically nonlinear BESO method Education

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"3D_Fault_Offsets," a matlab code to Automatically Measure Lateral and Vertical Fault Offsets in Topographic Data: Application to San Andreas, Owens Valley, and Hope Faults

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JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 2018年第1期123卷 815-835页

作者： Stewart, N. Gaudemer, Y. Manighetti, I. Serreau, L. Vincendeau, A. Dominguez, S. Matteo, L. Malavieille, J. Univ Cote Azur CNRS OCA IRDGeoazur Valbonne Sophia Antipoli France Univ Paris Diderot CNRS Inst Phys Globe Paris Sorbonne Paris Cite Paris France CNRS Geosci Montpellier Montpellier France

Measuring fault offsets preserved at the ground surface is of primary importance to recover earthquake and long-term slip distributions and understand fault mechanics. The recent explosion of high-resolution topographic data, such as Lidar and photogrammetric digital elevation models, offers an unprecedented opportunity to measure dense collections of fault offsets. We have developed a new matlab code, 3D_Fault_Offsets, to automate these measurements. In topographic data, 3D_Fault_Offsets mathematically identifies and represents nine of the most prominent geometric characteristics of common sublinear markers along faults (especially strike slip) in 3-D, such as the streambed (minimum elevation), top, free face and base of channel banks or scarps (minimum Laplacian, maximum gradient, and maximum Laplacian), and ridges (maximum elevation). By calculating best fit lines through the nine point clouds on either side of the fault, the code computes the lateral and vertical offsets between the piercing points of these lines onto the fault plane, providing nine lateral and nine vertical offset measures per marker. Through a Monte Carlo approach, the code calculates the total uncertainty on each offset. It then provides tools to statistically analyze the dense collection of measures and to reconstruct the prefaulted marker geometry in the horizontal and vertical planes. We applied 3D_Fault_Offsets to remeasure previously published offsets across 88 markers on the San Andreas, Owens Valley, and Hope faults. We obtained 5,454 lateral and vertical offset measures. These automatic measures compare well to prior ones, field and remote, while their rich record provides new insights on the preservation of fault displacements in the morphology.

关键词： fault offsets matlab code topographic data San Andreas Fault Owens Valley fault Hope fault

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Topology optimization of micro piezoelectric actuators and energy harvesters at femto-st institute: summary and matlab code implementation

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JOURNAL OF MICRO AND BIO ROBOTICS 2024年第2期20卷 6-6页

作者： Homayouni-Amlashi, Abbas Schlinquer, Thomas Kipkemoi, Peter Byiringiro, Jean Bosco Rakotondrabe, Micky Gauthier, Michael Mohand-Ousaid, Abdenbi Univ Franche Comte Inst FEMTO Dept AS2M SUPMICROTECH F-25000 Besancon France ESEO Engn Sch F-21231 Dijon France Dedan Kimathi Univ Technol Dept Mechatron Engn Nyeri Kenya Univ Toulouse Natl Sch Engn Tarbes ENIT INPT LGP Lab F-65000 Tarbes France

This paper primarily summarize the research efforts conducted within the AS2M department of the FEMTO-ST institute, focusing on topology optimization of piezoelectric structures. In this regard, the principles and the possibilities offered by topology optimization with a specific emphasis on the SIMP approach (Solid Isotropic Material with Penalization) are highlighted. The design processes of piezoelectric micro-actuators and energy harvesters are described, The optimized piezoelectric structures are presented and the improvements over classical designs are assessed. Moreover, in this paper, we present the eigenvalue optimization of the piezoelectric energy harvester by tuning the mass of attachment as an optimization variable. The theoretical development is accompanied by the developed matlab code to implement the topology optimization algorithm. This code is the update and extension of the previously published codes by authors for piezoelectric structures while it will be the first published code of its kind that considers the tuning of the natural frequency of the piezo structure. Finally, the paper discusses the feasibility and the potential of multi-material topology optimization.

关键词： Piezoelectric micro-actuator Piezoelectric energy harvester Topology optimization matlab code

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The matlab code of the method based on the Full Range Factor for assessing the safety of masonry arches

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METHODSX 2019年 6卷 1521-1542页

作者： Galassi, Stefano Tempesta, Giacomo Univ Florence Dept Architecture Piazza Brunelleschi 6 I-50121 Florence Italy

In most masonry arches stresses are very low and, therefore, collapse does not occur because of material failure. As a consequence, the safety of arches should not be assessed by means of a safety factor based on material strength as for conventional structures. In 1969 Heyman was the first to state that the safety of masonry arches relies on their geometry and proposed a method for computing the so-called "geometrical factor of safety" based on the comparison between the shape of the thrust line and the profile of the arch. In this context, we have recently developed a method capable of computing the line of thrust closest to the geometrical axis and defining a safety factor based on the comparison between such a line of thrust and the profile of the arch, which we have denoted as "performance factor". In this paper, that supplements the author ref. (Tempesta and Galassi, 2019 [411), the matlab code of our method is provided for unlimited and unrestricted use by researchers as well as academics for educational purposes. The method (denoted as FRS Method) is inspired by the method proposed by Heyman in 1969 Unlike the original iterative method, the FRS Method computes the line of thrust using a one-step procedure, which is less time consuming and provides the exact solution The original geometrical factor of safety is replaced by a performance factor, that characterizes the range of the equilibrium thrust lines within the profile of the arch effectively and the safety factor in a targeted way (C) 2019 The Author(s). Published by Elsevier B.V.

关键词： Discrete arches Line of thrust Finite differences Safety assessment Heyman Geometrical factor Performance factor matlab code

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An automatic quadrature method for semi-infinite integrals of exponentially decaying functions and its matlab code

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 437卷

作者： Hasegawa, Takemitsu Sugiura, Hiroshi Univ Fukui Dept Informat Sci Fukui Fukui 9108507 Japan Nanzan Univ Dept Mechatron Showa Ku Nagoya Aichi 4668673 Japan

For the integral of a function f over a semi-infinite interval [0, & INFIN;) with f (x) decaying exponentially as x & RARR;& INFIN;, an automatic quadrature scheme is constructed and implemented in matlab. Three limit formulae of Clenshaw-Curtis-type rules in our recent work (Numerical Algorithms, vol.90, 2022, pp.3-30) are exploited that converge fast for analytic functions. Each formula is expressed by a weighted infinite sum of function values at nodes and so its truncated finite sum is used. The best of the three formulae in accuracy is used as an approximation whose error is estimated with other two formulae and no additional function evaluations, since nodes of the other formulae are included in those of the best one. Numerical results indicate that our automatic scheme is better in performance than the QUADPACK routine for several types of test integrals. Particularly, it copes quite well with oscillatory integrals including the sinusoidal function and/or the Bessel function that are known to be difficult to approximate. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： Integral on an unbounded interval Limit formulae of Clenshaw-Curtis-type rules Automatic quadrature matlab code

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