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IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints


IASS Symposium 2014

SESSION: Computational Methods

Tangent stiffness separation method and its application in dynamic analysis of spatial latticed structures

< Table of Contents for Computational Methods
  • Proceedings Name: IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints
  • ISSN: (Electronic Version) 2518-6582
  • Session: Computational Methods
  • Title: Tangent stiffness separation method and its application in dynamic analysis of spatial latticed structures
  • Author(s): Lei WANG, Yongfeng LUO
  • Keywords: Geometrical nonlinearity. full scale method. Tangent stiffness separation method.Spatial latticed structures
Abstract
Nonlinear dynamic analysis is unavoidably encountered when the seismic design should be conducted for a structure. In terms of multi-storey buildings, the material nonlinearity is the main source of structural nonlinearity. When comes to long span spatial structures, the geometrical nonlinear effect is also significant, and sometimes even the main source of nonlinearity. In nonlinear dynamic analysis,the structural tangent stiffness matrix, which is derived by conventional incremental method, maintains clear and complete physical concept. However, the corresponding motion equationsdo not have simplified expressions up to now, so a lot of time will be spent on solving the equations, especially for the structures with large number degree of freedoms. The tangent stiffness separation method divides the coupled tangent stiffness matrix into two matrices in form, which are the linear matrix and the nonlinear matrix respectively. When the product of the nonlinear matrix and the displacement vector, which taken as additional load vector, is moved to the right hand of the motion equation, as result, the left hand of motion equation will show linear feature. Then, the explicit formulations of tangent stiffness separation method are derived in this paper. Compared with the procedure of step by step integration of conventional full scale method, the equivalent stiffness matrix derived from the tangent stiffness separation method keeps constant, so that, time for decomposing equivalent stiffness matrix in every load step is saved. Meanwhile, the linear form of motion equation provides a base for studying simplified dynamic model of spatial latticed structures. In final, the Gedesike shell is taken as an example to verify that the tangent stiffness separation method isthe same accuracyas the conventional full scale method.

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