共查询到15条相似文献,搜索用时 859 毫秒
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多约束作用下连续体结构的拓扑优化 总被引:2,自引:1,他引:1
基于ICM(独立、连续、映射)方法建立了以结构重量最小为目标,以屈曲临界力、位移及应力三种约束同时作用的连续体拓扑优化模型:采用独立的连续拓扑变量,借助泰勒展式、过滤函数将目标函数作二阶近似展开。借助瑞利商、泰勒展式、过滤函数将屈曲约束化为近似显函数,借助于过滤函数,将位移约束用莫尔定理显式化;将应力这种局部性约束采用全局化策略进行处理,即借助第四强度理论、过滤函数将应力局部性约束转化为应变能约束,大大减少了灵敏度分析的计算量;将优化模型转化为对偶规划,减少了设计变量的数目,并利用序列二次规划求解,缩小了模型的求解规模。数值算例表明,ICM方法在解决屈曲、位移及应力三种约束共同作用的连续体拓扑优化问题上有优势。 相似文献
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连续体结构屈曲约束的ICM方法拓扑优化 总被引:4,自引:2,他引:2
基于ICM(独立、连续、映射)方法解决具有屈曲约束的连续体拓扑优化问题。建立以结构重量为目标,以屈曲临界力为约束的拓扑优化模型;采用独立的连续拓扑变量,借助泰勒展式将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将约束化为近似显函数,避免了灵敏度的计算;将优化模型转化为对偶规划,并利用序列二次规划求解,减少了设计变量的数目,缩小了模型的求解规模。给出三个算例,结果表明:该方法可有效地解决屈曲约束的连续体拓扑优化问题,能够得到合理的拓扑结构,并有较高的计算效率。 相似文献
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考虑性态约束时多工况桁架结构拓扑优化设计 总被引:9,自引:0,他引:9
本文提出了一种适用于桁架结构的拓扑优化设计方法。它以杆内力为设计变量,以结构重量为目标函数。该方法的主要特点是:第一,通过引入杆内力为设计变量,既克服了已有方法要求预定位移场这一主要困难,又为在拓扑优化过程中考虑应力、位移等性态约束创造了条件;第二,将多工况的拓扑优化问题描述为一个非光滑的数学规划问题,再通过一个变量代换将其转化为一般的规划为题,进而将原问题的求解又转化为几个线性规划问题的求解;第三,基于结构力学的三个基本方程,将位移与应力约束提成为线性不等式约束,这些约束同重量的目标函数一起构成了拓扑优化设计的线性规划模型。最后,将本方法应用于几个工程算例,得到了满意的数值计算结果。 相似文献
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Liu Tao Deng Zichen 《Acta Mechanica Solida Sinica》2006,19(3):264-274
In this paper, a method for the design optimization of elasto-plastic truss structures is proposed based on parametric variational principles (PVPs). The optimization aims to find the minimum weight/volume solution under the constraints of allowable node displacements. The design optimization is a formulation of mathematical programming with equilibrium constraints (MPECs). To overcome the numerical difficulties of the complementary constraints in optimization, an iteration process, comprising a quadratic programming (QP) and an updating process, is employed as the optimization method. Furthermore, the elasto-plastic buckling of truss members is considered as a constraint in design optimization. A combinational optimization strategy is proposed for the displacement constraints and the buckling constraint, which comprises the method mentioned above and an optimal criterion. Three numerical examples are presented to show the validity of the methods proposed. 相似文献
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基于混合能理论构造了二次规划问题求解的新算法,并在杆系弹塑性增量分析中进行了成功的应用。所提出的算法一改传统的对单一规划变量(如位移或应力等)的求解策略,将问题演变成混合变量的形式,在混合空间下对问题进行算法构造,使问题的下一个增量步的求解可以充分利用增量步前的信息,由此极大地提高了算法的求解效率,对杆系弹塑性问题的数值分析充分地证实了这一点。 相似文献
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The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the load-carrying capabilities and the thermal insulation properties. The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved. 相似文献
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A new algorithm for the solution of quadratic programming problems is put forward in terms of the mixed energy theory and
is further used for the incremental solution of elastic-plastic truss structures. The method proposed is different from the
traditional one, for which the unknown variables are selected just in one class such as displacements or stresses. The present
method selects the variables in the mixed form with both displacement and stress. As the method is established in the hybrid
space, the information found in the previous incremental step can be used for the solution of the present step, making the
algorithm highly efficient in the numerical solution process of quadratic programming problems. The results obained in the
examples of the elastic-plastic solution of the truss structures verify what has been predicted in the theoretical analysis.
Project supported by the National Natural Science Foundation of China (No. 50178916, No. 19732020 and No. 19872016), the National
Key Basic Research Special Foundation (No. G1999032805), the Special Funds for Major State Basic Research Projects and the
Foundation for University Key Teachers by the Ministry of Education of China. 相似文献