Strategy for partition of space frames erected by mechanism method
Wei WANG1(),Hua DENG1,*(),Li HUANG2
1. Space Structures Research Center, Zhejiang University, Hangzhou 310058, China 2. Department of Real Estate and Engineering Management, Zhejiang University of Finance and Economics, Hangzhou 310018, China
A geometrical partitioning strategy was proposed to form the mechanism for space frames erected by "mechanism method", typical of Pantadome. The square sum of the elongations of all structural members was adopted as the index to describe the structural deformation and expressed as the quadratic form of nodal displacements. Considering that the partitioned mechanism must implement rigid body displacement from the design configuration to the working surface, i.e. moving trend, the eigenvectors of the quadratic matrix could be used to approximately construct the rigid body displacement. If the displacements which were constantly constructed using those eigenvectors with smaller eigenvalue as well as smaller angle to the moving trend, the structure would theoretically move towards the working surface with small deformations. Taking the direction of moving trend as the initial vector, these eigenvectors could be obtained by solving the Ritz vectors of the inverse of the quadratic matrix. From the design configuration, the space frame was forced to move towards and finally approached the working surface with the estimated displacement. The structural deformation could be generally controlled at a lower level. For the final configuration closest to the working surface, those areas distinctly deformed relative to the design configuration were identified to be the partitioning boundary of the space frame. A vaulted spatial truss and a space frame were adopted as the illustrative examples to prove the validity of the partitioning strategy.
Wei WANG,Hua DENG,Li HUANG. Strategy for partition of space frames erected by mechanism method. Journal of ZheJiang University (Engineering Science), 2019, 53(7): 1407-1414.
Fig.1Quantitative description for local deformation of node i
Fig.2Vaulted spatial truss and its eigenvalues at design configuration
Fig.3Final configuration and its distribution of ||E||2
Fig.4Partitioned vaulted spatial truss and its final configuration
Fig.5Variations of L when vaulted truss moving along dr and da, respectively
Fig.6Geometries of cutting shape space frame and assembly surface
Fig.7Nearest configuration of space frame to assembly surface
Fig.8Distribution of ||E||2 on upper-chord layer of space frame
Fig.9Partition of cutting shape space frame
Fig.10Mechanism converted by space frame and its final configuration
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