Research On Feasibility And Engineering Applicability Of Reciprocal Configurations From Single-layer Spherical Grids

Reciprocal structure is a kind of spatial structure system composed of members which overlap each other.Due to it's unique overlapping relationship of members,reciprocal structure is aesthetically pleasing in form,and because of it's simple structure,low technical requirements,and convenient construction,it has received widespread attention in the engineering community,and has become a new research interest in academic community in recent years.However,it's difficult to determine the shape due to the mutual overlap of reciprocal structural members,especially on a given large-span curved surface.Therefore,solving the problem of morphological generation of reciprocal structural members is an urgent task to promote the engineering application of reciprocal structural.Under this background,single-layer spherical reciprocal grid is taken as the research object in this dissertation,and six types of commonly used single-layer spherical grids are directly converted by three types of direct configuration methods.Then explore the feasibility of its turning to reciprocal configuration.Analytical formulas for geometric parameters of feasible solutions are obtained,and then CAD three-dimensional models and solid models are made,and by analyzing the correlations between the parameters,the range of reciprocal configuration parameters in the feasible solutions is given.The specific work of this dissertation is as follows:Chapter 1 introduces the concept,historical development and latest research progress process of reciproal structure,focusing on the current geometric configuration research of reciprocal structure,discusses and combs the geometric configuration method of reciprocal structure on a given curved surface,and then expounds the overall ideas and main contents of the research in this dissertation.Chapter 2 introduces reciprocal unit block,spherical initial grid and three types of direct configuration methods.Firstly,the geometrical parameters of the basic unit in the reciprocal configuration—reciprocal unit block are described in detail.Then six types of commonly used single-layer spherical reticulated shells are introduced and the geometrical descriptions of the grid are given.Finally,three types of direct configuration methods are explained in detail and their specific operations are explained.Chapter 3 adopts the pre-judgment method and spherical reciprocal judgment methods to comprehensively judge reciprocal grids generated by the rotation method,extended translation method and contraction method of six types of commonly used single-layer spherical grids.Finally,only the reciprocal grids generated by the extended translation method of ribbed spherical grid meet the requirements of the reciprocal configuration.Chapter 4 analyzes the feasible solution obtained in Chapter 3,gives the reciprocal configuration diagram,and obtains the analytical formulas of the eccentricity and the length of the feasible solution through parameter analysis.Then,the CAD three-dimensional model and the solid model were made,and the accuracy of the MATLAB program written was verified by comparison and analysis.Chapter 5 analyzes the engineering applicability of feasible solutions.Firstly,puts forward a series of structural requirements and indicators,and analyzes the effects of initial parameters on the difference in cross-sectional dimensions of members,the length change rate of members,and the slenderness ratio of members through three-dimensional charts.Then the parameter range of the reciprocal configuration with good engineering applicability in the feasible solution is given.Finally,through making 3D modeling with a set of data in the selected range,the accuracy of the conclusion is verified.Chapter 6 summarizes the main research contents of this dissertation,points out the limitations and shortcomings of the research work,and finally gives my own suggestions for the follow-up research of reciprocal structure.