Study On Tessellation And Deconstruction Of Masonry Structures And Boundary Conditions Of The Basic Cells Based On Rigid Homogenization Method

The mechanical performance and failure mechanism of masonry structures are complicated, and establishing a system of analysis theory of masonry structures with knowledge in physics and mathematics becomes an issue widely concerned by people in the engineering field. The homogenization method which is an effective multi-scale calculated method can establish the analysis model of masonry structures on meso-level. And it provides an effective approach for the precise analysis of masonry structures. In this paper, the rigid homogenization method based on regular tessellation theory is applied to analyze inherent laws of tessellation and deconstruction in flemish bond masonry walls and running bonding masonry walls, get all of the basic elements and their corresponding RVE of the two masonry patterns, and derivate the boundary conditions of them. This work not only provides a theoretical basis for the establishment of the periodic boundary conditions of RVE and the selection of loading, but also lays a theoretical foundation for analyzing masonry structures accurately. The main research achievements are as follows:(1) The inherent laws of tessellation in flemish bond masonry walls and running bonding masonry walls under the hypothesis of plane stress have been studied, periodic plane segmentation has been done on this two types of masonry based on regular tessellation theory, and every component gotten from the segmentation has been deconstructed.The result indicates that the number of elements of flemish bond masonry walls and running bonding masonry walls respectively is 24 and 21, while 3 and 4 types are respectively included.This reseach provides a basis for establishment of the mathematical relationship between every component and their corresponding RVE.(2) The tessellation graphy is used to describe deformation characteristics of masonry structures which are in macroscopically homogeneous stress state. And the two conditions must be qualified in the masonry structures:the stress vectors are continous and the strains are compatible. This provides a basis for the realization and appliation of the process of masonry rigid homogenization in finite element software. (3) Mathematical models are applied to express tessellation relationships between the basic component and its RVE, the tessellation relationships between the basic component and itself. Conclusions are that the periodicity and symmetry of the same type of RVE may be different, while the periodicity and symmetry of different types of RVE may be the same. In addition, boundary conditions of all the 45 basic elements of flemish bond masonry walls and running bonding masonry walls have been derived. It provides a theoretical basis for the selections of periodic boundary conditions of RVE and loading in finite element simulation.