Structural Optimization and Stability

结构优化与稳定

• 批准号: 0324628
• 负责人: Yitshak Ram
• 金额: $ 25万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-10-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0324628&HistoricalAwards=false
• 关键词: Structural; Optimization; Stability

AbstractIn many mechanical and aerodynamic systems structural strength, stability and lightness are of primaryimportance. The stability of a structure with a specified support and external loading can be characterized byan eigenvalue problem whose solution determines the non-trivial equilibrium configurations of the system.The maximum external load that can be imposed on the structure is determined by the least eigenvalue of thesystem. The problem of designing an optimal structure that can support the largest load is more involved. It requiresthe determination of structural parameters, e.g., the variable cross-sectional area of the structure, whichmaximize the least eigenvalue of the system. An important example is due to Lagrange, who attempted todetermine the shape of the strongest column with a specific length and mass. This apparently simple problemremained unsolved for more than one hundred and fifty years. Its analytical solution is still surrounded bycontroversy. The main thrust of this research is that the standard optimization procedure is by no means the best way toaddress the structural optimization problem involved. Depending on the failure criterion, there is a certainrelation between the structural mode of failure and the physical parameters of the optimal structure. In theLagrange problem the maximum bending stress in the ideal column is constant along its length. This conditionimplies that the square of the fundamental buckling mode is proportional to the cube of the cross-sectional areafor the optimal column. This relation was vital in determining the exact analytical solution to the problem. Italso plays a major role in the new methodology proposed here, which consists of two stages:(a) Determining the relation between the mode-shape of failure and the physical parameters of the optimalstructure. This relation leads to an eigenvalue problem where elements of the stiffness matrix are knownfunctions of an eigenvector of the system, and(b) Solving the inverse eigenvalue problem of determining the unknown parameters in the stiffness matrixsubject to the eigenvector constraint.The project has practical engineering applications in new and emerging technologies related to fabricationof microstructures and their integration in new generation of mechanical components. Another importantapplication of the proposed research is in design of safe, reliable, and lightweight aerospace structuresThe proposed activity will also contribute to the curriculum development of Machine Design Lab andStress Analysis. The students will take part in a design competition involving optimal design of structuresThe project will support disadvantaged minority students by (a) directly involving them in the research,and (b) stimulating their interest in advancing themselves to pursue graduate study

在许多机械和空气动力系统中，结构的强度、稳定性和轻便是最重要的。具有给定支承和外载荷的结构的稳定性可以用一个特征值问题来描述，该问题的解决定了系统的非平凡平衡构形，结构所能承受的最大外载荷由系统的最小特征值决定。设计一个能承受最大载荷的最优结构的问题涉及较多。它需要确定结构参数，例如，使系统最小特征值最大化的变截面结构。一个重要的例子是由于拉格朗日，谁试图确定的形状最强的柱与特定的长度和质量。这个看似简单的问题一百五十多年来一直没有得到解决。它的解析解至今仍有争议。本研究的主旨是，标准的优化程序绝不是解决结构优化问题的最佳方法。根据失效准则，结构的失效模式与最优结构的物理参数之间存在一定的关系。在拉格朗日问题中，理想柱的最大弯曲应力沿其长度沿着是常数.这个条件意味着基本屈曲模态的平方与最优柱横截面积的立方成正比。这个关系对于确定问题的精确解析解至关重要。它也起着重要的作用，在这里提出的新方法，它包括两个阶段：（a）确定之间的关系的模式形状的破坏和最佳结构的物理参数。这种关系导致了一个特征值问题，其中刚度矩阵的元素是系统的特征向量的已知函数，以及（B）解决确定刚度矩阵中的未知参数的逆特征值问题，受到特征向量的约束。该项目在与微结构的制造及其在新一代机械部件中的集成有关的新兴技术中具有实际的工程应用。本研究的另一个重要应用是在安全、可靠、轻量化的航空航天结构设计中，本研究也将有助于机械设计实验室和应力分析的课程开发。学生们将参加一个设计竞赛，涉及结构的最佳设计。该项目将通过以下方式支持弱势少数民族学生：（a）直接让他们参与研究，（B）激发他们对深造的兴趣