Research On The Rigid Homogenization Theory Of Masonry Structures Based On Regular Tessellation Theory

Masonry rigid homogenization can be used by flexible meshing masonrystructure model in finite element software, and finally, the mechanical performanceand failure mechanism of various kinds of the masonry mode of masonry structurescan be analyzed. This method not only combines the advantages of the separate andthe whole continuous model, which avoids the the complexity modeling of former andthe rough calculation results of latter, but also provides a premise for theestablishment of a precise theory of masonry structure and meeting the detailedengineering analysis needs. In this paper, regular tessellation theory was firstlyintroduced to set up a method of selecting the RVE model of masonry rigidhomogenization, derivate the boundary and initial conditions in the numericalsimulation, and establish the link between the micromechanics and macro-mechanicalperformance of masonry. The main research achievements are as follows:(1) Because of the following three main problems: the diversity of masonrybuilding model, the lack of plane segmentation theoretical foundation and thelimitation of the describing of two-dimensional periodic material, regular tessellationtheory was firstly introduced to analyze masonry structure in this paper. The inherentlaws of common masonry mode under the hypothesis of plane stress has been studied,periodic plane segmentation has been done on all types of masonry based on regulartessellation theory, and component of regular tessellation has been studied. At thesame time, the deconstruction method of studying masonry structure was firstlyproposed, based on regular tessellation theory. As a result, three basic types(rectangle,parallelogram and rhombus element) have been found in all types of masonry mode,while a variety of different regular tessellation model exist in the same buildingpatterns of the same type and size of the component, so various types of component ofregular tessellation model can eventually be deconstructed into several simplest typesof skeleton elements. A basis for the periodic segmentation based on masonry rigidhomogenization theory was provided by this research, a premise for establishing themathematical relationship between element and corresponding RVE was provided too.At the same time, new ideas and methods for masonry rigid homogenization theorywere offered.(2) Due to different effect factors of component, the best selecting standard ofthe component need to be established. All types of reference frame of masonry component model and the edge conditions has been studied to find out not only thebest description of masonry’s two-dimensional periodic but also the best masonrycomponent, which combined with the conclusion of masonry theoretical analysis.(3) In this paper, in order to take a further exploration on the research formacroscopic homogeneous state of stress conditions and the realization of the processof masonry rigid homogenization used in calculation software, macroscopichomogeneous experimental conditions has been described, the combination ofgraphical interpretation of macroscopic homogeneous state of stress conditions hasbeen used to describe the deformation characteristics in mathematical language. Inaddition, effect factors should be considered in the realization of the process ofmasonry rigid homogenization.(4) The relationship in mathematical models between the basic elements andRVE has been explored, the basic elements and the corresponding RVE boundary andinitial conditions has been derived.