Nonlinear analysis of cable structures using the dynamic relaxation method

doi:10.1007/s11709-020-0639-y

Front. Struct. Civ. Eng.

2021, Vol. 15

Issue (1) : 253-274 https://doi.org/10.1007/s11709-020-0639-y

RESEARCH ARTICLE

Nonlinear analysis of cable structures using the dynamic relaxation method

Mohammad REZAIEE-PAJAND(

), Mohammad MOHAMMADI-KHATAMI

Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran

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Abstract

The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers. Because they have highly nonlinear behavior, it is difficult to find solutions to these problems. Thus far, different assumptions and methods have been proposed to solve such structures. The dynamic relaxation method (DRM) is an explicit procedure for analyzing these types of structures. To utilize this scheme, investigators have suggested various stiffness matrices for a cable element. In this study, the efficiency and suitability of six well-known proposed matrices are assessed using the DRM. To achieve this goal, 16 numerical examples and two criteria, namely, the number of iterations and the analysis time, are employed. Based on a comprehensive comparison, the methods are ranked according to the two criteria. The numerical findings clearly reveal the best techniques. Moreover, a variety of benchmark problems are suggested by the authors for future studies of cable structures.

Keywords nonlinear analysis cable structure stiffness matrix dynamic relaxation method

Corresponding Author(s): Mohammad REZAIEE-PAJAND

Just Accepted Date: 16 October 2020 Online First Date: 11 February 2021 Issue Date: 12 April 2021

Cite this article:

Mohammad REZAIEE-PAJAND,Mohammad MOHAMMADI-KHATAMI. Nonlinear analysis of cable structures using the dynamic relaxation method[J]. Front. Struct. Civ. Eng., 2021, 15(1): 253-274.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0639-y
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I1/253

Fig.1 Simple truss element.

Fig.2 Element of Deng et al. [³²].

Fig.3 Jayaraman element in 2-D space.

Fig.4 Element of Thai and Kim [³⁶].

Fig.5 Yang element.

Tab.1 Proposed strategies for cable element

Fig.6 Simple cable net.

Fig.7 Static equilibrium path of simple cable net.

Fig.8 Hyper net.

Fig.9 Static equilibrium path of hyper net.

Fig.10 Inverted cable dome.

Fig.11 Static equilibrium path of inverted cable dome.

Tab.2 Number of iterations and analysis time for solving simple cable net

Tab.3 Number of iterations and analysis time for solving hyper net

Tab.4 Number of iterations and analysis time for solving inverted cable dome

Fig.12 2-D view of rectangular grid.

Fig.13 3-D view of rectangular grid.

Tab.5 The z-coordinates of the rectangular grid (m)

Fig.14 Static equilibrium path of rectangular grid.

Tab.6 Number of iterations and analysis time in solving rectangular grid for first boundary condition

Tab.7 Number of iterations and analysis time in solving rectangular grid for second boundary condition

Tab.8 Number of iterations and analysis time in solving rectangular grid for third boundary condition

Tab.9 Number of iterations and analysis time for solving spatial net

Fig.15 Spatial net.

Fig.16 Static equilibrium path of spatial net.

Tab.10 The z-coordinates of the saddle net (m)

Fig.17 Saddle net.

Fig.18 Static equilibrium path of saddle net.

Fig.19 Simple cable.

Fig.20 Static equilibrium path of simple cable.

Tab.11 Number of iterations and analysis time for solving saddle net

Tab.12 Number of iterations and analysis time for solving simple cable

Fig.21 Tetrahedral grid.

Fig.22 Static equilibrium path of tetrahedral grid.

Tab.13 Number of iterations and analysis time in solving tetrahedral grid for first boundary condition

Tab.14 Number of iterations and analysis time in solving tetrahedral grid for second boundary condition

Tab.15 Number of iterations and analysis time in solving tetrahedral grid for third boundary condition

Fig.23 Annular roof.

Fig.24 Static equilibrium path of annular roof.

Tab.16 Number of iterations and analysis time for solving annular roof

Tab.17 The z-coordinates of the rhombus net (m)

Fig.25 Rhombus net.

Fig.26 Static equilibrium path of rhombus net.

Tab.18 Number of iterations and analysis time for solving rhombus net

Fig.27 Cylindrical net.

Fig.28 Static equilibrium path of cylindrical net.

Tab.19 Number of iterations and analysis time in solving cylindrical net for symmetric load

Tab.20 Number of iterations and analysis time in solving cylindrical net for asymmetric load

Tab.21 General comparison of methods based on required number of iterations

Tab.22 General comparison of methods based on analysis time

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