【作者】 刘霞；

【导师】 沈蒲生；

【作者基本信息】 湖南大学 ， 结构工程， 2007， 博士

【摘要】 结构优化设计目前正处于蓬勃发展时期,工程师们越来越多地意识到合理设计方法的重要性,追求以最小的代价获取最大的利益。过去几十年间连续结构的拓扑优化方法有很大的发展,应用范围不断拓广,特别是在航空航天、机械制造等领域重量的减轻对设计相当重要,优化方法的应用已颇为成熟。与其它领域相比,工程结构优化设计理论和应用的重要性尚未得到足够的重视,发展相对缓慢,结构设计仍停留在依靠工程师个人经验分析试算的阶段。目前我国仍处在建设高潮期,据建设部的预测,至2020年建筑工程面积将达到300亿平米,这种情况对于我们这样一个资源相对匮乏的国家,在建筑工程领域发展和应用最优设计方法已迫在眉睫,为此本文针对结构优化设计中较难的拓扑优化问题展开研究。目前求解拓扑优化问题能力较强的算法有演化结构优化算法(ESO算法)、均匀化方法、密度函数法、仿生学算法等,其中演化结构优化算法(ESO算法)以其概念清晰、规则简单、计算方便的优点受到很多学者的青睐,但同时又因不能保证所得解为最优解受到一些学者的质疑。遗传算法(GA)属于仿生学算法,近年来的研究表明它具备找到最优解的长处。但遗传算法本身并不具有明确的结构优化设计的背景,虽然在计算数学层面上它能有效地解决组合优化的一些问题,具体应用于结构工程时,由于计算太耗时仅限于桁架结构的优化,无法进一步拓展到平面或空间结构。本文在这两种算法的基础上首次提出了一种新的拓扑优化方法“遗传演化算法(GESO算法)”,遗传演化算法继承了演化结构优化算法的灵敏度计算方法和基本步骤,从一个包含了最优解的初始设计域出发,根据遗传算法优胜劣汰的思想,以选择、变异、杂交等遗传算子决定单元的取舍,避免了错误的单元舍去,保证了算法所得解的最优性。新的遗传演化算法所得解的质量均好于原有的演化结构优化算法,同时计算效率又高于遗传算法。本文在提出新算法后,详细研究了算法中各计算参数对算法性能的影响,结果表明新算法鲁棒性好,最优解对计算参数不敏感,采用不同计算参数时均能找到最优解。本文所做的另一项具有创新性的工作是利用Michell准则与遗传演化算法联合寻优。Michell准则是澳大利亚工程师Michell 1904年用数学解析方法研究的最优结构应满足的条件,符合这一条件的结构称为Michell桁架。然而直接由Michell准则建立Michell桁架十分难,目前缺乏有效的求解方法。本文一方面采用已有的多个符合Michell准则的虚应变场检验校核了遗传演化算法所得解的最优性,另一方面通过遗传演化算法得到了新的符合Michell准则的实际结构,为进一步获得不Ⅱ同类型Michell桁架打下基础。本文重点研究了两点或多点铰支条件下平面结构在各种荷载作用下的优化拓扑,根据Michell准则和遗传演化算法计算结果,归纳并发现这类结构的优化拓扑所应遵循的规律。本文作者认为两点或多点铰支条件下的平面结构的优化拓扑主要分为两类,一类由直线和圆组成,一类结构由曲线组成,曲线形状大多类似于理论推导过的“Michell悬臂”曲线或圆滚线,这些结论对工程结构优化的概念设计具有重要意义。遗传演化算法被证明能方便地用于钢筋混凝土结构的配筋优化,钢筋混凝土结构由两种不同的材料组成,而且由于混凝土开裂和钢筋的屈服,材料表现出非线性特性,配筋优化计算时是否考虑两种材料的区别,是否考虑材料的非线性成为焦点。为此,本文设计了三套方案进行配筋优化,运算表明,不区分两种材料的差别,不考虑材料的非线性的方案是最适合遗传演化算法的方案,计算简单,结果实用。因为遗传演化算法擅长建立桁架模型,构件达到承载力极限状态时,荷载可认为是通过由钢筋拉杆和未开裂的混凝土压杆组成的拉压模型传递,构件的破坏是由于传力路径的破坏造成的。所以遗传演化算法配筋优化的过程是先求得构件的拉压杆模型,再在拉杆位置布置钢筋。本文利用遗传演化算法完成了不同跨高比的简支梁、深受弯构件、牛腿、框架节点等构件的配筋优化,提出了配筋优化方案,具有实际意义。更多还原

【Abstract】 The subject of optimum structures is currently undergoing something of a boom. Engineers have realized the importance of the gains that can be made by a rational approach to design, which quantifies a principle of minimum cost. Topology optimization methods for continuum structures have achieved significant progress in the last two decades. These techniques have increasingly been used in aeronautical, mechanical and automotive industries in which the weight reduction of structures is very important. However, the potential of structural optimization techniques has not been realized by civil engineering industry and most works are designed by trial and error based on individual engineering experiences. As officers of the Ministry of Construction estimated, civil engineering industry is promising in China and the total of 30 billions m2 buildings will be constructed until 2020. As the relative lack of resources in our country the development and application of optimal theory is very important task for construction industry. On this background this thesis focuses on the structural topology optimization.Topology optimization methods include evolutionary structural optimization (ESO), homogenization, density function, genetic algorithm (GA), et al, among which evolutionary structural optimization attained more attention for its simple concepts and easy programming. But ESO often came under some suspicious remarks for no guarantee of optimum structures. GA is excellent in optimization by using Darwinian’s theory of survival of the fittest though having no definite mathematic background. The time-consuming characteristics of GA in engineering limited its application to truss structures instead of plane or space structures. However, a new method deal with topology optimization of plane structures was proposed in this dissertation on the basis of ESO and GA. The new algorithm is named genetic evolutionary structural optimization (GESO) which starts from an original design field consist of all potential optimum structures and computed sensitivity numbers as done in ESO, selected and deleted elements from a ground structure by genetic operation such as mutation and crossover. Combination of the genetic operations and the process of ESO decrease the possibility of improper element being deleted. Compared with the results acquired by ESO, the topologies obtained by the new GESO are more exact while the time consumed is lesser than that of GA. It is shown in succeeding studies that the acquired optimums are insensitive to the value of parameters, so the robustness of the new method is proved.Another innovative work in the dissertation is connecting GESO with Michell theory. The Michell theory of least-weight trusses for one load condition and a stress constraint was established in a milestone contribution by Michell (1904, Australia). Michell theory plays an important role in structural topology optimization. In general, Michell truss is a kind of framework with continuous distributions of members. It is often called“truss-like continuum”which is difficult to be deduced by mathematics analysis. In the dissertation the numerical studies of the new method use the classical Michell trusses for verifying their results. On the other hand, with the numerical calculations by GESO new“Michell type”structures are presented. Two or more pin-point supported plane structures under different loadings attained more attentions in the studies of discovering their optimal principle of topology. A large number of numerical experiments gained two main kinds of optimums for pin-point plane structures that is the structure composed of straight lines and circles and the structure made up of“Michell cantilever”and cycloids. These conclusions are of significant importance to structural concept design.GESO can be conveniently applied to reinforcement layout optimization in reinforced concrete structure. Reinforced concrete is a composite material and the nonlinear behavior of reinforced concrete is characterized by the cracking of concrete and the yielding of steel reinforcement. The key problem for which solutions are obtained are whether the stiffness of reinforcing steel and the nonlinear behavior of reinforced concrete can be considered in the finite element model. Three schemes were then designed for the question. The answer is that the stiffness of reinforcing steel and the nonlinear behavior of reinforced concrete cannot be taken into account in the finite element model. After extensive cracking of concrete, the loads applied to a reinforced concrete member are mainly carried by the concrete struts and steel reinforcement. The failure of a reinforced concrete member is mainly caused by the breakdown of the load transfer mechanism, rather by that the tensile stress attains the tensile strength of concrete. The design task is to develop an appropriate strut-and-tie model for the structural concrete member in order to reinforce it. Simple supported beams with different span-to-depth ratios, deep beams, corbels and beam-column connections are discussed for acquiring optimal reinforcement layout which can be used in engineering structures.更多还原