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Effect of boundary conditions on shakedown analysis of heterogeneous materials

Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 39-68页

作者： Xiuchen GONG Yinghao NIE Gengdong CHENG Kai LI State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentInternational Research Center for Computational MechanicsDepartment of Engineering MechanicsDalian University of TechnologyDalian 116023Liaoning ProvinceChina

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis lea

关键词： heterogeneous material self-equilibrium stress field(SSF) shakedown analysis effect of boundary conditions

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Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve

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Theoretical & Applied Mechanics Letters 2024年第1期14卷 16-22页

作者： Zongliang Du Tanghuai Bian Xiaoqiang Ren Yibo Jia Shan Tang Tianchen Cui Xu Guo State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentDepartment of Engineering MechanicsDalian University of TechnologyDalian 116023China Ningbo Institute of Dalian University of Technology Ningbo 315016China

Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.

关键词： MetamaterialPattern-transformationConstitutive curveInverse design

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Data-driven modeling on anisotropic mechanical behavior of brain tissue with internal pressure

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Defence Technology（防务技术） 2024年第3期33卷 55-65页

作者： Zhiyuan Tang Yu Wang Khalil I.Elkhodary Zefeng Yu Shan Tang Dan Peng State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentDalian University of Technology116023DalianPR China The department of Mechanical Engineering The American University in CairoNew Cairo11835Egypt department of Neurology The Second Hospital of Dalian Medical UniversityDalian116023PR China

Brain tissue is one of the softest parts of the human body,composed of white matter and grey matter.The mechanical behavior of the brain tissue plays an essential role in regulating brain morphology and brain function.Besides,traumatic brain injury(TBI)and various brain diseases are also greatly influenced by the brain's mechanical properties.Whether white matter or grey matter,brain tissue contains multiscale structures composed of neurons,glial cells,fibers,blood vessels,etc.,each with different mechanical properties.As such,brain tissue exhibits complex mechanical behavior,usually with strong nonlinearity,heterogeneity,and directional dependence.Building a constitutive law for multiscale brain tissue using traditional function-based approaches can be very challenging.Instead,this paper proposes a data-driven approach to establish the desired mechanical model of brain tissue.We focus on blood vessels with internal pressure embedded in a white or grey matter matrix material to demonstrate our approach.The matrix is described by an isotropic or anisotropic nonlinear elastic model.A representative unit cell(RUC)with blood vessels is built,which is used to generate the stress-strain data under different internal blood pressure and various proportional displacement loading paths.The generated stress-strain data is then used to train a mechanical law using artificial neural networks to predict the macroscopic mechanical response of brain tissue under different internal pressures.Finally,the trained material model is implemented into finite element software to predict the mechanical behavior of a whole brain under intracranial pressure and distributed body forces.Compared with a direct numerical simulation that employs a reference material model,our proposed approach greatly reduces the computational cost and improves modeling efficiency.The predictions made by our trained model demonstrate sufficient accuracy.Specifically,we find that the level of internal blood pressure can greatly influence stress distribution and

关键词： Data driven Constitutive law Anisotropy Brain tissue Internal pressure

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Optimization Design of the Multi-Layer Cross-Sectional Layout of An Umbilical Based on the GA-GLM

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China Ocean Engineering 2024年第2期38卷 247-254页

作者： YANG Zhi-xun YIN Xu FAN Zhi-rui YAN Jun LU Yu-cheng SU Qi MAO Yandong WANG Hua-lin Institute of marine machinery College of Mechanical and Electrical EngineeringHarbin Engineering UniversityHarbin 150001China State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentDepartment of Engineering MechanicsDalian University of TechnologyDalian 116024China Ningbo Institube of Dalian University of Technology Ningbo 315040China

Marine umbilical is one of the key equipment for subsea oil and gas exploitation,which is usually integrated by a great number of different functional components with multi-layers.The layout of these components directly affects manufacturing,operation and storage performances of the umbilical.For the multi-layer cross-sectional layout design of the umbilical,a quantifiable multi-objective optimization model is established according to the operation and storage requirements.Considering the manufacturing factors,the multi-layering strategy based on contact point identification is introduced for a great number of functional components.Then,the GA-GLM global optimization algorithm is proposed combining the genetic algorithm and the generalized multiplier method,and the selection operator of the genetic algorithm is improved based on the steepest descent method.Genetic algorithm is used to find the optimal solution in the global space,which can converge from any initial layout to the feasible layout solution.The feasible layout solution is taken as the initial value of the generalized multiplier method for fast and accurate solution.Finally,taking umbilicals with a great number of components as examples,the results show that the cross-sectional performance of the umbilical obtained by optimization algorithm is better and the solution efficiency is higher.Meanwhile,the multi-layering strategy is effective and feasible.The design method proposed in this paper can quickly obtain the optimal multi-layer cross-sectional layout,which replaces the manual design,and provides useful reference and guidance for the umbilical industry.

关键词： umbilical cross-sectional layout multi-layers GA-GLM optimization

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求解多约束离散变量结构拓扑优化的序列保守近似整数规划算法

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Acta Mechanica Sinica 2024年第1期40卷 138-154页

作者：孙凯程耿东张凯庆梁缘 department of Engineering Mechanics Dalian Universiy of TechnologyDalian 116023China Sate Key Laboraory of Structural Analysis Optimzaton and CAE Sofware for Industrial EquipmentDalian 116023China

序列近似整数规划方法通过求解一系列可分离的近似整数规划子问题成功求解多类大规模拓扑优化问题.然而,这些近似子问题的解析求解依靠正则松弛算法,正则松弛算法要求子问题必须由二次或线性的目标函数以及线性的约束函数构成.同时,序... 详细信息

序列近似整数规划方法通过求解一系列可分离的近似整数规划子问题成功求解多类大规模拓扑优化问题.然而,这些近似子问题的解析求解依靠正则松弛算法,正则松弛算法要求子问题必须由二次或线性的目标函数以及线性的约束函数构成.同时,序列近似整数规划方法依赖于体分比下降策略,这使得其难以处理不包含体分比约束的拓扑优化问题.为进一步地完善序列近似整数规划算法,我们受移动渐近线方法的启发,引入经典的序列保守近似规划,以获得一系列可行性稳步提升的设计,这个新方法称作序列保守近似整数规划算法.新方法会产生一系列包含倒数设计变量的非线性的近似整数规划子问题,并通过调整渐近线控制子问题的保守性。由于正则松弛算法不能求解非线性子问题,一种基于KKT(Karush-Kuhn-Tucker)条件的简单的设计变量更新准则被给出.基于上述思想,序列保守近似整数规划算法不依靠体分比约束等线性约束就可以获得稳定的优化过程,由此可以用来求解复杂的离散变量拓扑优化问题.多类不同需求的拓扑优化问题被解决,包括考虑等式约束及非等式约束的、以及考虑有效的及无效的体分比约束的问题.数值结果证明,由于保守性的引入,整个优化收敛进程可以自适应地调节无需额外的结构分析.

关键词：松弛算法整数规划规划算法拓扑优化移动渐近线方法等式约束方法依赖线性约束

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Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials

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Computer Modeling in Engineering & Sciences 2024年第8期140卷 1831-1861页

作者： Xu Xu Xiaoteng Wang Haitian Yang Zhenjun Yang Yiqian He State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentDepartment of Engineering MechanicsDalian University of TechnologyDalian116024China Hubei Key Laboratory of Geotechnical and Structural Safety School of Civil EngineeringWuhan UniversityWuhan430072China Mechanik–Materialtheorie Ruhr-Universität BochumBochum44801Germany

The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

关键词： Three-dimensionalmultiscale viscoelastic analysis numerical base functions octree SBFEM image-based analysis temporally piecewise adaptive algorithm

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数据驱动的曲面构件形状-拓扑协同优化方法

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航空学报 2024年第2期45卷 275-286页

作者：高天贺田阔黄蕾张澍李增聪大连理工大学工业装备结构分析优化与cae软件全国重点实验室工程力学系大连116024

针对紧凑设计空间下曲面构件极致轻量化需求,提出一种数据驱动的曲面构件形状-拓扑协同优化方法,主要包括离线、在线和更新3个阶段。离线阶段中,首先通过拉丁超立方采样方法在设计空间内采样,并利用网格变形技术进行参数化建模,获得样... 详细信息

针对紧凑设计空间下曲面构件极致轻量化需求,提出一种数据驱动的曲面构件形状-拓扑协同优化方法,主要包括离线、在线和更新3个阶段。离线阶段中,首先通过拉丁超立方采样方法在设计空间内采样,并利用网格变形技术进行参数化建模,获得样本点对应的网格模型。然后对上述网格模型分别进行拓扑优化,获得优化后的应变能。基于上述步骤获得的样本数据,训练径向基函数代理模型,其中形状设计变量为输入,拓扑优化获得的应变能为输出。在线阶段中,将基于离线阶段获得的代理模型开展优化设计,采用协方差矩阵自适应进化策略来提高优化效率。更新阶段中,计算代理模型优化结果的真实响应,并将其加入样本数据集进行代理模型更新。最后,通过简支梁和航天器舱门算例开展算法验证。结果表明相比针对固定形状获得的拓扑优化结果,提出方法优化获得的应变能结果分别降低了20.08%和37.93%,表明提出方法具有更优的设计能力。

关键词：形状-拓扑协同优化网格变形数据驱动曲面构件径向基函数

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高置信水平结构逆可靠度分析与优化方法研究进展

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力学学报 2024年第2期56卷 310-326页

作者：郝鹏杨浩冯少军王博工业装备结构分析优化与cae软件全国重点实验室辽宁大连116024 大连理工大学工程力学系辽宁大连116024

不确定性客观存在于工程结构生产制造以及服役等各环节之中并对结构的承载性能影响显著.特别是对于服役条件苛刻的航空航天承载装备,在设计阶段考虑多源不确定性的影响对于结构安全至关重要.在众多不确定性分析方法中,逆可靠度分析方法... 详细信息

不确定性客观存在于工程结构生产制造以及服役等各环节之中并对结构的承载性能影响显著.特别是对于服役条件苛刻的航空航天承载装备,在设计阶段考虑多源不确定性的影响对于结构安全至关重要.在众多不确定性分析方法中,逆可靠度分析方法在效率和稳健性方面具有一定优势.为此,国内外学者在高置信水平结构逆可靠度分析与优化方法方面开展了大量研究并取得了长足进步,包括自适应迭代控制算法、先进可靠度优化策略与非充分样本下的高置信水平设计方法等.本文首先对国内外逆可靠度分析与优化方法取得的进展进行了系统梳理与总结,特别是逆可靠度分析方法的发展历程以及面临的挑战问题,主要包括强非线性功能函数、多设计点以及低失效概率问题.进一步,针对长期困扰可靠度方法实际应用的小样本问题,重点从结构高置信水平可靠度分析与优化理论角度开展系统介绍,详细论述了小样本诱发的认知不确定性到可靠度置信水平的传播链条.最后,基于现有成果和国家重大前沿需求,重点围绕航天装备可重复使用需求对结构可靠度未来研究方向进行了思考与展望,期望相关研究成果能够进一步助力我国航空航天结构实现高可靠性与极致轻量化设计.

关键词：航空航天结构逆可靠度分析可靠度优化设计置信水平优化设计小样本

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基于弹性力学第一性原理的数据驱动力学建模

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计算力学学报 2024年第1期41卷 73-80页

作者：郑勇刚吴哲同张涵博刘振海叶宏飞张洪武大连理工大学工程力学系工业装备结构分析优化与cae软件全国重点实验室大连116024

提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和... 详细信息

提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程,得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件,同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合,克服了传统建模方法的局限性和对人类经验的强依赖性,为建立简洁的力学模型提供了一种新途径。

关键词：结构力学模型数据驱动方程识别 Timoshenko梁第一性原理

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含裂纹纳米板振动问题的哈密顿体系方法

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计算力学学报 2024年第1期41卷 66-72页

作者：屈建龙周震寰徐新生大连理工大学工程力学系工业装备结构分析优化与cae软件全国重点实验室大连116024

基于裂纹处范德华力效应,采用非局部弹性理论构造纳米板模型,并通过导入哈密顿体系建立含裂纹纳米板振动问题的对偶正则控制方程组。在全状态向量表示的哈密顿体系下,将含裂纹纳米板的固有频率和振型问题归结为广义辛本征值和本征解问... 详细信息

基于裂纹处范德华力效应,采用非局部弹性理论构造纳米板模型,并通过导入哈密顿体系建立含裂纹纳米板振动问题的对偶正则控制方程组。在全状态向量表示的哈密顿体系下,将含裂纹纳米板的固有频率和振型问题归结为广义辛本征值和本征解问题。利用哈密顿体系具有的辛共轭正交关系,得到问题解的级数解析表达式。结合边界条件,得到固有频率与辛本征值的代数方程关系式,进而直接给出固有频率的表达式。数值结果表明,非局部尺寸参数和裂纹长度对纳米板振动的各阶固有频率有直接的影响。对比表明,辛方法是准确且可靠的,可为工程应用提供依据。

关键词：哈密顿体系含裂纹纳米板非局部理论振动固有频率

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