Design of Elastic Building Frame and Space Truss Structure for Constrained Strains via Inverse Problem Formulation

由于这项资助，取得了以下优异成绩。(1)在施工中，结构的已建部分因恒载而变形。然后，将新的构件依次添加到结构的这些部分，在这个过程中已经引入了结构的初始缺陷。本文提出了一种计算施工中恒载响应的解析方法。(2)采用子结构综合法，刚度矩阵的形成过程与结构的施工过程几乎相同。以预制组合空间桁架结构为例，说明了该方法的优越性。对结构施工过程中引入的缺陷进行了计算。(3)制定了满足规定等级的建筑结构的模糊设计问题。通过求解相应的优化设计问题，给出了目标函数模糊约束的确定方法。在该问题中，设计变量为模糊数，采用模糊理论的α-水平集。该模糊问题的解直接来源于相应的脆数优化设计问题的解。在设计过程中，封闭形式解对于确定结构构件非常有用，因为设计者只需选择尺寸在模糊设计变量范围内的构件。(4)制定了一组水平荷载作用下多层多跨框架的规定等级设计问题。该问题是一个模糊优化设计问题，同时采用了与塑性破坏荷载因子有关的模糊约束和与结构自重有关的模糊目标函数。提出了该问题模糊设计变量的精确闭型解的求导方法。

Thanks to the grant-in-aid, following excellent results were obtained.(1) Under construction, the already-constructed parts of the structure are deformed by dead loads. Then, new members will be added to these parts of the structure successively, initial imperfection has been introduced to the structure in this process. In this research, an analytic method is proposed to calculate the response by dead loads under construction.(2) By using substructure synthesis method, stiffness matrix is formed in the almost same process as that of the construction of the structure. An example of precast composite space truss structure is worked out to propose the advantages of this method. The imperfection introduced in the process of construction of the structure is calculated.(3) The fuzzy design problem of building structures which satisfy the specified grade is formulated. The determination method of fuzzy constraint for object function is presented, by using the solution to the corresponding optimum crisp design problem. In this problem, the design variables are fuzzy numbers and α-level set of fuzzy theory is used. The solution to this fuzzy problem is derived directly from the solution to the corresponding optimum design problem of crisp numbers. The closed form solutions are very useful for determining members of a structure in the design process, as designers have only to select the members whose dimensions are within the range of fuzzy design variables.(4) The specified grade design problem of multistory multispan frames under a set of horizontal loads is formulated. This problem is an fuzzy optimum design problem in which both the fuzzy constraint relating to plastic collapse load factor and the fuzzy objective function relating to the weight of the structure are adopted. The method is proposed for derivation of exact closed form solutions to the fuzzy design variables of that problem.