Form-finding method for symmetric cable-strut structures based on fully symmetric subspace stiffness submatrix

Abstract

The invention discloses a symmetric rope pole structure form finding method based on a fully-symmetric subspace stiffness sub-matrix. According to a symmetric rope pole structure with a support boundary condition, cluster theories are introduced, a symmetric group of the symmetric rope pole structure is determined, node displacement increment corresponding to fully-symmetric subspace is acquired according to the stiffness sub-matrix and unbalanced node force corresponding to the fully-symmetric subspace, a displacement increment coefficient is determined according to the reducing principle oftotal potential energy of the structure, so that node coordinates are continually updated, and a balanced and stable rope pole structure is finally acquired. The method mainly includes the steps: firstly, defining an initial configuration according to symmetry to obtain a coordinate-transformation matrix corresponding to the fully-symmetric subspace of the structure; acquiring the stiffness sub-matrix and the unbalanced node force corresponding to the fully-symmetric subspace; updating a structure configuration through the node displacement increment acquired according to the stiffness sub-matrix and the unbalanced node force; finally acquiring a positive definite balance structure of a stiffness matrix.

Description

technical field [0001] The invention belongs to the fields of space structure, symmetrical cable-strut structure design and development, etc., and relates to a form-finding method for a symmetrical cable-strut structure based on a fully symmetrical subspace stiffness submatrix. Background technique [0002] In the traditional structure, the structure obtains its stiffness from the geometry and materials, and this kind of structure mainly obtains the stiffness from the geometry and materials, which is the so-called rigid structure. The cable-strut structure mainly obtains the stiffness from the prestress, and the analysis to determine the geometric shape and prestress state of the cable-strut structure is the so-called form-finding analysis, also known as the initial shape analysis, where the shape is the initial geometric shape, and the state is initial prestressed state. [0003] Most of the existing form-finding methods are aimed at the self-balancing cable-strut system, ...

AI Technical Summary

Problems solved by technology

For the cable-strut structure with support boundary constraints, some scholars convert the support constraints into bar constraints by adding virtual members, thereby transforming the structure into a self-balancing tensegrity structure for analysis, but the virtual member Different settings have a greater impact on the results

Images