The Freeform Surface Of Single Rigid Structure Shape Optimization And Engineering Application

Free-form surface is unable to express in elementary mathematics analytic type precision of curved surface. Free-form surface as a kind of geometry, has the rich architectural expression and the creation of free space, thus gradually it gets the favor of architects and gets more and more application in the practical engineering. Free-form surface is not only in the use of the building function and the aesthetic demand, at the same time, the geometry of free-form surface which is a skeleton line of the structure affects the efficiency of the structure under load, and the structure of the economy, etc. Considering the practical engineering, the single rigid grid is a long-span space building one of the main forms of structure. Therefore, how to create not only meets the construction requirements, but also the structure is reasonable and can guarantee the free surface of single rigid grid structure is the key problem to research the free-form surface morphology. In recent years, with the development of structural morphology, looking for reasonable stress both elegant free-form surface provides an effective method. Based on the single rigid structure morphology optimization research status, this paper combined with the structure morphology point of view, and mainly carried out the following several aspects:1. In this paper, considering the actual construction design process, the non-uniform rational b-spline(NURBS) surface of forward calculation, reverse calculation, and surface trimming method for architects are taken to provide initial free curved surface fitting and geometry creation. This method can solve free or complex boundary and open hole free curved surface fitting problem among them which is the more close to the actual engineering application and expand the application range of the optimization method.2. Based on the structure of the overall minimum strain for the optimization goal, this paper used gradient method as optimization method, by moving the free-form surface control point coordinate of the rigid structure to modify the geometry of the surface. In the process of the whole optimization, according to the computing structure strain energy on the sensitivity of the control points to determine the control points to the size of the mobile amplitude. In the process of calculation, this paper deduces the whole composed of space beam element stiffness matrix of the expression of the control point’s derivation.3. In this paper, on the basis of the theory, numerical calculation software based on MATLAB compiled the free curved surface fitting with single rigid grid structure optimization program, and program was applied to two practical engineering projects, that fully illustrates the rationality of the curved surface fitting and structural optimization method is effective. And in the process of optimization, several problems on the application of the gradient method has carried on the preliminary discussion, for example, in the process of optimization, directly arrange the node load or cloth load, initial component value rationality to explore the size of cross section, how to quickly establish a single rigid grid structure finite element optimization model.4. In this paper a calculation analysis is made on the stability of before and after optimization for a stadium free-form surface single rigid structure roof. Research shows that the stability limit load of the optimized single rigid structure is greatly improved, but its stability limit load is sensitive to the initial geometric imperfection of structure.