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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 ***, utilizing PBCs to

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

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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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Structural topology optimization subject to overhang angle constraint with overhang length relaxation in additive manufacturing

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Science China(Technological Sciences) 2022年第6期65卷 1213-1231页

作者： ZHANG KaiQing cheng gengdong WANG Yu Department of Engineering Mechanics Dalian University of TechnologyDalian 116023China State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of TechnologyDalian 116023China

This paper studies additive manufacturing(AM) oriented structural topology optimization(TO).The minimum compliance design subject to overhang angle constraint with overhang length relaxation and horizontal minimum length control is *** the overhang length relaxation allows additional flexibility for AM product design,there have been very limited studies on *** paper elucidates that the overhang angle constraint we proposed can identify the lower boundary element that violates the overhang angle *** advantage of this fact,we achieve the overhang length relaxation by specifying that the volume fraction of the elements that violate the overhang angle constraint in each local area of the design domain is less than a specified upper bound.A formula for estimating the maximum allowable overhang length of this method is proposed and *** horizontal minimum length constraint is also employed in this *** controlling the horizontal length size of the structural member,this constraint together with the overhang angle constraint with overhang length relaxation suppresses the hanging *** gradient-based optimization algorithm method of moving asymptotic(MMA) is used to solve the TO *** examples show the effectiveness of this *** is observed that the new constraint alleviates the main issues of traditional overhang angle constraints,i.e.,gray element issue,stress concentration issue,and shattered structure *** with the strict traditional overhang angle constraint,the new formulation reduces structural compliance.

关键词： topology optimization overhang angle constraint overhang length relaxation design for manufacturability additive manufacturing

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Memorial to Xuesen Qian

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Acta Mechanica Sinica 2010年第1期26卷 1-2页

作者： gengdong cheng Dalian University of Technology Dalian 411023 China

Xuesen Qian （Hsue-Shen Tsien）, the father of China＇s rocketry and space technology, was born in Shanghai on 11 December 1911. He graduated from the Shanghai Jiaotong University in 1934 and received a degree in mechanical engineering there. He then spent an internship at Nanchang Air Force Base. Qian left China for the United States in 1935 to study mechanical engineering and earned Master＇s Degree of Science from MIT 1 year later.

关键词： Memorial to Xuesen Qian

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HOMOGENIZATION-BASED METHOD FOR BENDING ANALYSIS OF PERFORATED PLATE

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Acta Mechanica Solida Sinica 1998年第2期11卷 172-179页

作者： Liu Shutian cheng gengdong Gu Yuanxian Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Beijing Inst Radio Measurement Beijing 100854 Peoples R China

Owing to the existence of distributed holes, it is difficult tosolve the bending problem of perforated plates by the conventionalfinite element method. A homogenization-based method for this problemis presented in this paper. As an example, the bending analysis of acircular perforated plate with distributed step-wise cylindricalholes is made. The deflection and the fundamental frequen- cyobtained by present method are in good agreement with experimentaldata, this implies that the method is effective.

关键词： perforated plate bending analysis homogenization-based method

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Topology optimization of simplified convective heat transfer problems using the finite volume method

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Science China(Technological Sciences) 2023年第5期66卷 1352-1364页

作者： YAN Kun WANG YunYu PAN Yu SUN Guo CHEN Jian CAI XianHui cheng gengdong School of Chemical Machinery and Safety Dalian University of TechnologyDalian116024China Science and Technology on Scramjet Laboratory National University of Defense TechnologyChangsha410073China State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsDalian University of TechnologyDalian116024China

Topology optimization of simplified convective heat transfer has been widely studied,but most existing studies are based on the finite element method(FEM);methods based on the finite volume method(FVM)have been less *** this paper,a topology optimization method based on FVM was proposed for a simplified convective heat transfer *** developed a novel adjoint sensitivity analysis method applicable to FVM,which included adjoint equations,corresponding boundary conditions,and sensitivity analysis ***,a program for the proposed topology optimization method was developed in open field operation and manipulation(OpenFOAM)and portable,extensibletoolkit for scientific computation(PETSc).Thus,large-scale topology optimizations could be performed in ***,numerical examples of the classical two-dimensional(2D)and 3D optimization problems were *** results verified the effectiveness and feasibility of the proposed *** results of large-scale 3D examples show an interesting phenomenon that for the optimized designs with few features,the large-scale topology optimization is still valuable for obtaining more effective structural shapes.

关键词： simplified convective heat transfer topology optimization large scale adjoint sensitivity analysis OpenFOAM

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An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures

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Frontiers of Mechanical Engineering 2015年第2期10卷 126-137页

作者： Shutian LIU Quhao LI Wenjiong CHEN Liyong TONG gengdong cheng State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian 116024 ChinaE-mail: stliu@*** School of Aerospace Mechanical and Mechatronic EngineeringUniversity of Sydney NSW 2006 Australia

Additive manufacturing （AM） technologies, such as selective laser sintering （SLS） and fused deposition modeling （FDM）, have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simply- connected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method （VTM）. In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simplyconnected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

关键词： additive manufacturing topology optimiza-tion manufacturability constraints design for additivemanufacturing simply-connected constraint

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结合基降阶策略的高效安定分析数值算法

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机械工程学报 2023年第18期59卷 154-164页

作者：王雨程耿东李凯大连理工大学工业装备结构分析国家重点实验室大连116024

结构安定分析是结构设计和完整性分析的一个重要问题。原对偶本征应力驱动算法(Primal-dual eigenstress-driven method,PEM)是一种有效的两水平嵌套的结构安定分析算法,可与商业有限元集成应用于实际工程问题,但计算效率仍存在进一步... 详细信息

结构安定分析是结构设计和完整性分析的一个重要问题。原对偶本征应力驱动算法(Primal-dual eigenstress-driven method,PEM)是一种有效的两水平嵌套的结构安定分析算法,可与商业有限元集成应用于实际工程问题,但计算效率仍存在进一步提升的空间。结合基降阶策略和原对偶本征应力驱动方法提出了高效安定性分析数值算法,利用PEM法每轮迭代形成的残余应力场作为基向量,与相应载荷顶点的弹性应力场叠加将安定分析问题简化为一维优化问题,降低优化变量的数量,利用一维搜索0.618法,结合PEM方法为安定乘子提供了更为准确的估计。该算法避免繁琐的塑性增量分析,仅进行有限次的弹性分析与迭代及高效的一维搜索,可以显著提高算法计算效率,并获得准确的残余应力场。结合ANSYS APDL二次开发实现算法,通过圆孔方板、Bree板、三维框架三个例题,进一步验证此算法的有效性。

关键词：安定分析基降阶原对偶本征应力驱动方法弹塑性一维搜索0.618法

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利用系统可靠度约束下的优化设计求解公差分配问题

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机械强度 2006年第6期28卷 839-844页

作者：许林程耿东易平大连理工大学工业装备结构分析国家重点实验室大连116024

一个较好的公差分配方案可以有效地提高产品的性价比。然而目前所采用的公差分配方法或者并不能真正反映出产品的性能状况,或者计算的效率较低。文中研究系统可靠度约束下优化设计的序列近似规划求解方法及其在机械公差分配问题中的应... 详细信息

一个较好的公差分配方案可以有效地提高产品的性价比。然而目前所采用的公差分配方法或者并不能真正反映出产品的性能状况,或者计算的效率较低。文中研究系统可靠度约束下优化设计的序列近似规划求解方法及其在机械公差分配问题中的应用。分析文献中经常出现的算例,最终结果用MonteCarlo模拟证实,基于系统可靠度的优化方法比文献常用的简化方法在公差的分配方面更经济合理,不同算法的比较结果表明计算方法的有效性。结果分析为机械公差分配方法的工程应用提供建议。

关键词：可靠度分析优化设计序列近似规划法公差分配公差分析 Monte Carlo模拟

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周期性蜂窝材料微极等效模型及其微观应力的一种快速算法

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固体力学学报 2008年第2期29卷 109-120页

作者：牛斌阎军程耿东大连理工大学工业装备结构分析国家重点实验室工程力学系大连116024

将周期性蜂窝材料等效为具有非局部本构的微极连续介质,以解释实验中出现的尺度效应和边界层效应.在评论相关的多种不同方法(能量法、体积平均的均匀化法等)之后,提出了一种基于位移连续和单胞力平衡的推导微极等效本构参数的新方法.以... 详细信息

将周期性蜂窝材料等效为具有非局部本构的微极连续介质,以解释实验中出现的尺度效应和边界层效应.在评论相关的多种不同方法(能量法、体积平均的均匀化法等)之后,提出了一种基于位移连续和单胞力平衡的推导微极等效本构参数的新方法.以正方形单胞制成的结构为例,在不同的结构与单胞尺寸比下,考虑承受集中点载荷、均布轴力和均布剪力三种载荷工况,比较了离散完全计算、经典连续介质等效和不同微极连续体等效本构的计算结果,建议了较好的微极本构参数值.数值模拟表明,集中点载荷和剪切载荷作用时,在加载点附近和边界部分,微极等效可以显著提高计算精度.最后,给出了一种映射算法,可以根据微极等效连续体分析的结果,快速计算出对应微观单胞构件的应力,以开有圆孔的方板应力集中为例,验证并考察了所提快速算法的有效性和计算精度.

关键词：蜂窝材料微极连续介质等效性能尺度效应

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