Efficient Symmetry Method for Calculating Integral Prestress Modes of Statically Indeterminate Cable-Strut Structures

Abstract

Novel statically indeterminate structures generally contain both self-stress modes and internal mechanisms, and have few or no load-bearing capacities before being prestressed. These structures could not maintain stable equilibrium states until appropriate initial prestresses are assigned. The initial prestress design is the basic and key step for novel kinematically indeterminate structures. In this study, an efficient symmetry method is proposed for determining integral prestress modes for various cable-strut structures with multiple independent self-stress modes. Group theory and its matrix representations are introduced to calculate the linear independent self-stress modes retaining full symmetry. Subsequently, integral prestress modes are directly extracted from the null space of the first block matrix of the symmetry-adapted equilibrium matrix. Manual classifications of member types and double singular value decompositions on large-sized matrices are avoided in the calculation process. Therefore, the symmetry method shows great advantage in terms of computation efficiency, especially for the structures with high-order symmetry, complex geometric configurations, or many independent self-stress modes. Illustrative examples are presented to verify the robustness and efficiency in calculating integral prestress modes for different types of symmetric cable-strut structures. The proposed method can play an important role in the force-finding analysis and optimum prestress design of various cable-strut structures.