Distributed indeterminacy evaluation of cable-strut structures: formulations and applications

Abstract

Abstract:The indeterminacy evaluation is an effective method for system identification; it can predict the mechanical behaviors of flexible structures in the primary design. However, the conventional indeterminacy evaluation based solely on geometry and topology has neglected the influence of material properties on mechanical behavior and the contribution of each component to the total indeterminacy. To address these issues, a distributed indeterminacy evaluation taking account of the effect of component stiffness was carried out with a view to providing reasonable interpretations and feasible applications for two concepts, i.e., the distributed static indeterminacy (DSI) and the distributed kinematic indeterminacy (DKI). A unified method for the DSI is proposed, and a comparative analysis between this and an existing method revealed that the proposed method has a wider range of applicability and is essentially identical in the kinematically determinate case. It can be concluded that since the DSI is representative of symmetric properties, a simple but efficient grouping criterion can be established which can improve the efficiency of the specific force finding method entitled double singular value decomposition (DSVD). On the other side, an evaluable method for the DKI is proposed suggesting that DKI is a useful indicator for the assessment of nodal mobility and can provide a feasible solution to the form transforming study.

Area-loss effect analysis of pin-jointed structures

“…In structural safety studies, the mechanical performance of pin-jointed structures was studied with both geometric and material properties of structural members. Chen et al (Chen et al, 2014; Zhou et al, 2015) carried out a distributed indeterminacy evaluation considering the effect of member stiffness. And Jiang et al (2019) studied the influence of members’ material variation on the structural mechanical performance.…”

Efficient Update of Redundancy Matrices for Truss and Frame Structures

“…Another more recent work on the redundancy matrix was published by Liu et al 2005, who used the redundancy matrix and its counterpart, the 'importance indices', to assess the importance of structural elements in truss and frame structures. The idea of the redundancy matrix was extended to kinematically indeterminate structures (Tibert 2005;Zhou et al 2015;Y. Chen et al 2018) and to continuous representations of structures by a connection between concepts from applied mathematics and classical structural mechanics (Gade et al 2021).…”

Efficient Update of Redundancy Matrices for Truss and Frame Structures

“…Another more recent work on the redundancy matrix was published by Liu and Liu (2005), who used the redundancy matrix and its counterpart, the 'importance indices', to assess the importance of structural elements in truss and frame structures. The idea of the redundancy matrix was extended to kinematically indeterminate structures (Tibert 2005;Zhou et al 2015;Chen et al 2018) and to continuous representations of structures by a connection between concepts from applied mathematics and classical structural mechanics (Gade et al 2021). Further references for the calculation and application of the redundancy matrix can be found in the works by von and Gade et al (2021).…”

“…A concept of redundancy in statically indeterminate truss and frame structures was proposed on the basis of the analogy between Gaussian adjustment calculus in geodesy and structural mechanics (Linkwitz 1961;Bahndorf 1991;Ströbel 1997). Recently, the idea of the redundancy matrix was extended to kinematically indeterminate structures (Tibert 2005;Zhou et al 2015;Chen et al 2018) and to continuum mechanical framework (Gade et al 2021). A more extensive literature overview on the calculation and application of the redundancy matrix can be found in the work by von Scheven et al 2021.…”