Analyzing the Form-Finding of a Large-Span Transversely Stiffened Suspended Cable System: A Method Considering Construction Processes

The precise control of the shape of transversely stiffened suspended cable systems is crucial. However, existing form-finding methods primarily rely on iterative calculations that treat loads as fixed known conditions. These methods are inefficient and fail to accurately control shape results. In this study, we propose a form-finding method that analyzes the load response of models under different sag and stress levels, taking into account the construction process. To analyze the system, a structural finite element model was established in ANSYS, and geometric nonlinear analysis was conducted using the Newton-Raphson method. The form-finding analysis results demonstrate that the proposed method achieves precise control of shape, with a maximum shape error ranging from 0.33% to 0.98%. Furthermore, the relationships between loads and tension forces are influenced by the deformed shape of the structures, exhibiting significant geometric nonlinear characteristics. Meanwhile, the load response analysis reveals that the stress level of the self-equilibrium state in the transversely stiffened suspended cable system is primarily governed by strength criteria, while shape is predominantly controlled by stiffness criteria. Importantly, by simulating the initial tensioning process as an initial condition, this method solves for a counterweight that satisfies the requirements and achieves a self-equilibrium state with the desired shape. The shape of the self-equilibrium state is precisely controlled by simulating the construction process. Overall, this work presents a new method for analyzing the form-finding process of large-span transversely stiffened suspended cable system, considering the construction process which was often overlooked in previous studies.

A SIMPLIFIED CALCULATING METHOD OF NONLINEAR FREQUENCY OF CABLE NET UNDER MEAN WIND LOAD

The cable net supported glass curtain wallas the most advanced technique in dot point supported glass curtain wall, is widely used in China. Because of its large deflection and high nonlinearity under wind load, the dynamic performance of the cable net is greatly different from that of the conventional linear structures. The continuous membrane theory is used to construct the nonlinear vibration differential equation of the cable net, and the harmonic balance method is used to solve the analytic formula of the nonlinear frequency. In order to verify the accuracy of the above analytic formula, the results of the formula and the nonlinear FEM time-history method are compared and found to be in good agreement. Furthermore, the nonlinear vibration differential equation and the nonlinear frequency obtained in this paper are the basis for the wind-induced response analysis of a cable net under fluctuating wind load.

Dynamic performance of cable net facade with consideration of glass panels under earthquake

Shaking table tests and theoretical analysis were conducted to study the dynamic performance of cable net facade with consideration of glass panels under earthquake. Firstly,the dynamic response of cable net faade under earthquake was investigated with shaking table test. Then the working mechanism of glass panels in coordination with cable net was proposed. Accordingly,a numerical simulation model of glass panel's working in coordination with cable net was built for the dynamic analysis.And then the seismic response was analyzed with this model theoretically. The study indicates that the seismic response of the cable net with glass panels on most occasions is mainly decided by the symmetric modes,and the first vibration mode is dominant. The damping of cable net facade is mainly decided by glass panels. And it is very good for cable net faade to restrain its dynamic response under earthquake.

EIGENFREQUENCY ANALYSIS OF CABLE STRUCTURES WITH INCLINED CABLES

The approximate eigenfrequencies for the in-plane vibrations of a cable structure consisting of inclined cables, together with point masses at various points were computed. It was discovered that the classical transfer matrix method was inadequate for this task, and hence the larger exterior matrices were used to determine the eigenfrequency equation. Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matrices were made.

SVD Approach for Actuator and Sensor Placement in Active Vibration Control of Large Cable Net Structures

The actuator and sensor placement problem for active vibration control of large cable net structures is investigated in this paper.Since the structures exhibit closely spaced modes in the range of low frequencies,the number of modes to be considered is quite large after modal truncation,while only a limited number of actuators and sensors are to be placed.This makes it hard to determine the actuator and sensor locations with the existing placement methods in the literature such as the methods based on the controllability/observability grammian.To deal with this issue,an actuator and sensor placement method based on singular value decompositions(SVD)of the input and output matrices is proposed,which guarantees the modal controllability and observability of the system.The effectiveness of the SVD based method is verified through numerical simulations in which comparisons are conducted between randomly-chosen locations and the optimal ones obtained by a genetic algorithm.

Dynamic Analysis of Suspension Bridges and Full Scale Testing

This paper is concerned with the earthquake analysis of suspension bridges, in which the effects of large deflections are taken into account. The first part of the study deals with an iteration scheme for the nonlinear static analysis of suspension bridges by means of tangent stiffness matrices. The concept of tangent stiffness matrix is then introduced in the frequency equation governing the free vibration of the system. At any equilibrium stage, the vibrations are assumed to take place tangent to the curve representing the force-deflection characteristics of the structure. The bridge is idealized as a three dimensional lumped mass system and subjected to three orthogonal components of earthquake ground motion producing horizontal, vertical and torsional oscillations. By this means a realistic appraisal is achieved for torsional response as well as for the other types of vibration. The modal response spectrum technique is applied to evaluate the seismic loading for the combination of these vibrations. Various numerical examples are introduced in order to demonstrate the method of analysis. The procedure described enables the designer to evaluate the nonlinear dynamic response of suspension bridges in a systematic manner.

STATIC ANALYSIS OF CABLE STRUCTURE

Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and tension distribution defined in Eulerian coordinate system was accurately obtained. The nonlinear algebraic equations caused by cable structure were solved directly using the modified Powell hybrid algorithm with high precision routine DNEQNE of Fortran. For example, a cable structure consisting of three cables jointly supported by a vertical spring and all the other ends fixed was calculated and compared with various methods by other scholars.

A CATENARY ELEMENT FOR THE ANALYSIS OF CABLE STRUCTURES

Based on analytical equations, a cat ena ry element is presented for the finite element analysis of cable structures. Com pared with usually used element(3_node element, 5_node element), a program with the proposed element is of less computer time and better accuracy.

Reduced technique for modeling electromagnetic immunity on braid shielding cable bundles

In this paper, an efficient multi-conductor simplification technique is proposed to model the electromagnetic immunity on cable bundles within a braid shielding structure over a large frequency range. By grouping together the conductors based on the knowledge of Z-Smith chart, the required computation time is markedly reduced and the complexity of modeling the completely shielding cable bundles is significantly simplified with a good accuracy. After a brief description of the immunity problems in shielding structure, a six-phase procedure is detailed to generate the geometrical characteristics of the reduced cable bundles. Numerical simulation is carried out by using a commercial software CST to validate the efficiency and advantages of the proposed approach. The research addressed in this paper is considered as a simplified modeling technique for the electromagnetic immunity within a shielding structure.

Static analysis of elastic cable structures under mechanical load using discrete catenary theory

In this paper,the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory.A cable net is discretized into multiple nodes and edges in our numerical approach,which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation.A fully implicit framework is proposed based on the discrete differential geometry(DDG)theory.The equilibrium configuration of a target object is derived by adding damping force into the system,known as the dynamic relaxation method.The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation.A more intricate scenario is further discussed in detail,where a structure consisting of multiple slender cables is connected through joints.Utilizing the robustness and efficiency of our discrete numerical framework,a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers.Finally,an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties,material characteristics,component numbers,and cable orientations.Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures,and could motivate innovative designs in both mechanical and civil engineered equipment.

Form-fnding methods for deployable mesh reflector antennas

Deployable high-frequency mesh reflector antennas for future communications and obser- vations are required to obtain high gain and high directivity. In order to support these new missions, reflectors with high surface accuracy are widely required. The form-finding analysis of deployable mesh reflector antennas becomes more vital which aims to determine the initial surface profile formed by the equilibrium prestress distribution in cables to satisfy the surface accuracy requirement. In this paper, two form-finding methods for mesh reflector antennas, both of which include two steps, are pro- posed. The first step is to investigate the prestress design only for the cable net structure as the circum- ferential nodes connected to the supporting truss are assumed fixed. The second step is to optimize the prestress distribution of the boundary cables connected directly to the supporting truss considering the elastic deformation of the antenna structure. Some numerical examples are carried out and the simulation results demonstrate the proposed form-finding methods can warrant the deformed antenna reflector surface matches the one by design and the cable tension forces fall in a specified range.

Green Construction of National Speed Skating Oval

1 Background As the basic principle of the world economy,environment,and social development,sustainable development is the focus of the international community today.In the Olympic Agenda 2020 published by the International Olympic Committee(IOC),sustainable development was officially listed as one of the core concepts of the Olympic Games.Since the beginning of the bid,the concept of ctathlete-centered,sustainable and economical”was proposed,which was highly consistent with the idea of the Olympic Agenda 2020.To implement the concept of holding“green”Olympic Games and meet the sustainability requirements of the IOC,the Organizing Committee of Beijing Winter Olympic Games issued a series of documents related to the sustainability of sports venues such as Sustainability Policies for 2022 Beijing Winter Olympic Games and Winter Paralympic Games,and strived to realize the sustainable development of sports venues in the whole life cycle of planning and design stage,construction stage,operation stage,and post-game utilization.

Nonlinear analysis of cable structures using the dynamic relaxation method

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.