Edge Cables Research Articles

A fibre Bragg grating accelerometer with temperature insensitivity for cable force monitoring of FAST

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) currently holds the distinction of being the largest single-aperture telescope worldwide. To ensure its secure functioning, it is crucial to monitor the cable force on its active reflecting surface cable network structure. In this paper, a fibre Bragg grating (FBG) accelerometer is developed to acquire low-frequency vibration signals of the cables. The sensor’s cantilever beam structure enables high sensitivity measurement of low-frequency signals, while the symmetrical double fibre grating structure effectively eliminates the impact of temperature. The sensor’s specific limiting structure ensures its survival during transportation and installation. A series of laboratory tests have been performed, and they demonstrate the excellent measurement performance, temperature insensitivity and practical usefulness of the accelerometer. Ninety FBG accelerometers are successfully installed on the site of the FAST project, where they are precisely measuring and documenting the magnitude of force exerted on the edge cables.

Form-finding of tensile membrane structures with strut and anchorage supports using physics-informed machine learning

Due to their aesthetic appeal, light weight, and capacity to span vast expanses of space, tensile membrane structures (TMS) are very popular these days. TMS are usually supported by frames and boundary edge cables, but sometimes also by struts and anchorage supports. Traditional mesh-based form-finding algorithms, typically developed for the first two boundary types, suffer from convergence issues stemming from the choice of initial shape, choice of pseudo material properties, mesh distortion, hyper-parameter selection, etc. In order to address the issues with conventional mesh-based form-finding frameworks as stated above, a mesh-free form-finding framework for TMS is proposed utilizing a gradient-enhanced physics-informed neural network. The theory of functional connections is employed to precisely meet the TMS boundary conditions without depending on an additional penalty function used in conventional physics-informed neural network frameworks, thereby eliminating errors related to boundary constraints. The challenge of incorporating compressive strut supports in TMS form-finding is addressed by employing the principle of inverted forces, and modelling them as tension elements. 24 numerical studies, with a diverse set of TMS shapes and boundary supports, including benchmark problems, are presented demonstrating the effectiveness and accuracy of the proposed method. This method also allows the designer to explore various parametric (architectural) designs of TMS.

Form-finding analysis and optimization of cable membrane structure based on iterative correction of tension process

The current form-finding analysis of cable membrane structures does not consider the actual tensioning process, thus leading to a difference between the form-finding prestressed and tensioning working states. It will affect the morphology accuracy of membrane structures in use, especially in the field of space structures. This work proposes a form-finding optimization method based on the iterative correction of the tensioning process, which considers membrane stress and edge shape optimizations in order. The method focuses on two evaluation indices: the average membrane stress difference and the root mean square (RMS) of the position difference of the edge cables. This sequential optimization analysis is illustrated based on the examples of a sunshade structure for aerospace applications. The results show that these design requirements on the two evaluation indices can be satisfied after one membrane stress optimization and one edge shape optimization. Subsequently, the influence of the seams on the optimization analysis of tensile cable membranes is also investigated. Although seams increase the inhomogeneity of the membrane stress and edge shape difference, the proposed optimization framework based on the iterative correction of the tension process can still ensure that the design requirement can be satisfied. The work in this paper could form the basis for a high-precision study of tensile membrane structures in space.

Nonlinear structural behavior and vibration control of a double curved cable net under the dynamic excitations

The paper is regarding to the structural dynamics of a saddle shaped cable-net structure with two high points and two low points at the corners. The net cables are pre-stressed by stretching the four edge cables that are supported at the corner points. A series of parametric nonlinear dynamic analysis is utilized to evaluate the dynamic response of the system under the different structural masses and geometries, pretensions and alignments of cables and the amplitudes of dynamic excitation. An equivalent single-degree-of-freedom model is presented as a simplified method to estimate the dynamic response of the full finite element model. The simulation results show that the equivalent model can accurately estimate the displacement response of multi-degree-of-freedom model under dynamic excitation. Furthermore, a nonlinear active control algorithm is applied to decrease the structural response under the transient wind excitation and the results indicate the effectiveness of the proposed control algorithm.

Innovative CAD-integrated Isogeometric Simulation of Sliding Edge Cables in Lightweight Structures

The focus of the paper is twofold: About the practical structural problem of membrane structures mechanically prestressed by edge cables, which are allowed to slide tangentially, and about an innovative CAD integrated simulation technique. The structural problem is well recognized but the new technique most elegantly resolves the challenges of standard discretization approaches when dealing with the formulation and solution of the sliding contact of two bodies discretized by individual, non-matching meshes moving relatively to each other. The proposed formulation takes advantage of the parameter space of NURBS patches and extends the weak coupling formulation by adding a degree of freedom in the parameter space and thus inherently satisfies the sliding constraints. Indeed, the presented contact formulation is of most general importance and may be applied to many other contact problems of structural mechanics. The special case of an edge supported membrane structure, however, is a most illustrative case to demonstrate how this technique is embedded into CAD and the sliding contact can immediately be considered in the early stages of architectural design. As a consequence, the effect to the stresses and displacements can immediately be studied and controlled. The contribution briefly presents and verifies the newly proposed approach with some examples and demonstrates the applicability in different real-world problems.

Multi-fidelity fluid–structure interaction analysis of a membrane blade concept in non-rotating, uniform flow condition

Abstract. In order to study the aerodynamic performance of a semi-flexible membrane blade, fluid–structure interaction simulations have been performed for a non-rotating blade under steady inflow condition. The studied concept blade has a length of about 5 m. It consists of a rigid mast at the leading edge, ribs along the blade, tensioned edge cables at the trailing edge and membranes forming the upper and lower surface of the blade. Equilibrium shape of membrane structures in the absence of external loading depends on the location of the supports and the prestresses in the membranes and the supporting edge cables. Form-finding analysis is used to find the equilibrium shape. The exact form of a membrane structure for the service conditions depends on the internal forces and also on the external loads, which in turn depend on the actual shape. As a result, two-way coupled fluid–structure interaction (FSI) analysis is necessary to study this class of structures. The fluid problem has been modelled using two different approaches, which are the vortex panel method and the numerical solution of the Navier–Stokes equations. Nonlinear analysis of the structural problem is performed using the finite-element method. The goal of the current study is twofold: first, to make a comparison between the converged FSI results obtained from the two different methods to solve the fluid problem. This investigation is a prerequisite for the development of an efficient and accurate multi-fidelity simulation concept for different design stages of the flexible blade. The second goal is to study the aerodynamic performance of the membrane blade in terms of lift and drag coefficient as well as lift-to-drag ratio and to compare them with those of the equivalent conventional rigid blade. The blade configuration from the NASA-Ames Phase VI rotor is taken as the baseline rigid-blade configuration. The studied membrane blade shows a higher lift curve slope and higher lift-to-drag ratio compared with the rigid blade.

Investigation of Prestress-Dependent Aerodynamic Performance of a Double Membrane Sailwing

This paper investigates the aerodynamic performance of a semiflexible membrane wing concept using twoway coupled fluid–structure interaction simulations. The sailwing concept consists of a rigid leading-edge mast, ribs, tensioned edge cables, and membranes forming the upper- and lower-wing surfaces. For membrane structures like the sailwing, the exact shape of the membrane surface in the absence of external loading depends on the prestress levels of both membranes and supporting edge cables. A form-finding analysis is used for calculating the equilibrium shape of prestressed membrane surfaces with no external loading. The exact shape of the sailwing in operating condition depends on the pressure distribution on the membrane’s surface, which itself depends on the wing’s shape and the structural parameters. For faster design space exploration, the fluid problem is modeled using an unsteady vortex panel method. Among all the factors influencing the fluid–structure interaction problem, the role of the prestress level is specifically investigated. A nonlinear dynamic analysis of the structural problem is performed using the finite element method. The influence of the wing’s flexibility on its aerodynamic performance and structural response is examined by changing the prestress level in the membranes. Aerodynamic characteristics of the membrane wing are compared with an equivalent conventional rigid wing. A higher lift slope for the membrane wing and improvement of the lift coefficient due to trailing-edge flexibility are observed.

Existing Eurocodes Applied to a Membrane Structure

This article tries gaining insight in the effect of the partial factor starting by the analysis of a steel cable net structure according to Eurocode 3. Eurocode specifies a value of 1.35 for the partial factor for prestress. A cable net structure built in 1958, was used as a case study. In spite of the lack of design guidelines and calculation tools 58 years ago, the analysis according to the current design standard Eurocode 3 for steel shows that the results match quite well with the original calculation. Generally speaking, a reduction in the cross-section areas is observed using Eurocode 3. For the considered steel cable net structure a weight saving of 17% for a partial factor for prestress 1.35 is obtained. If a partial factor for the prestress 1.0 could be considered, the weight reduction would be 4% more. Furthermore, the article investigates the effect of the partial factor for prestress (1.0 or 1.35), there prestress contributes to the stiffness in the non-lineair structural behaviour of membrane structures. The value of the partial factor for prestress to be considered is a source of disagreement between experts in different countries. With a similar geometry as the steel cable net structure, a membrane structure is designed and analysed. For the primary steel structure the partial factor for prestress 1.35 has to be applied. A 2% weight saving for the pretension factor 1.0 versus 1.35 is obtained if the tensile surface including the membrane and the edge cables is considered separate from the primary structure. A sound conclusion though requires a thorough in-depth study for different shapes and for different membrane types.

圧縮部材を用いたケーブルネットワークによる衛星搭載用アンテナの鏡面設計法

Antenna surface forming by cable network is an essential design method to achieve high performance for communication services or high resolution observation for radio astronomy. The precision of the surface can be determined by a facet approximation error depending on their size. Uniform tensile force distribution among cables is measured by adjusting tension ratio of the edge cables and the center cables of the reflector. In general, the tensile forces of the edge cables become several times greater than those of the center cables. Therefore, total strain energy of the cables is decided based on the tensile force distribution including the edge cables. When the number of the cables of the network increases, the total strain energy of the cables raises. Consequently, a support structure, e.g., truss rib structures or hoop structures, must be improved its rigidity to prevent deformation of the surface. This paper describes a new surface forming concept in which the cable network is assembled by tensile and compression members. Several compression members are equipped instead of tensile cables. As a result, the total strain energy of the cables can be reduced, and the retentive force applied to the support structure can also be reduced by using this method.

Effects of different prestress intensities on the displacement of membrane structures under point loads

Membrane structures exhibit large displacements under external loads. These are a consequence of the low stiffness of the membrane. One of the ways to increase the stiffness of the structure is to increase the prestress intensity of the membrane or of the cables. This paper presents a research done on the influence of the prestress intensities on the displacements under point loads since point loads have a significant impact on the displacements in membrane structures. In this research the prestress of the membrane and the prestress of the edge cables have been investigated separately. Ten different intensities of the membrane prestress, and five different intensities of the cable prestress, combined with four positions of the point load have been modeled. The intensity of the point load has been kept constant in all loads cases. The research is conducted on numerical models in software Sofistik. Displacements under given parameters of the membrane structure and the point loads were recorded and maximal displacements were compared. The obtained results provide a better understanding of the relation between the prestress intensities and displacements of saddle shaped membranes. The outcome of the research can be used to better predict and to reduce the displacements of membranes under point loads.

Analytical structural reliability analysis of a suspended cable

Suspended cables, including transmission lines, suspension bridge cables, and edge cables of roof structures, feature in high profile and large span projects for architectural reasons, for their functional efficiency, and for ease of construction, particularly over large spans. A suspended cable predominantly reacts external loads by means of axial tension, and is, therefore, able to make full use of the material strength. Because of the slenderness of the suspended cable, the structural response is nonlinear, even if the material property is within the elastic range. From a mechanics perspective, therefore, these types of structure exhibit high levels of geometric non-linearity. For this reason, the nonlinear relationships between tension force, normal displacement, and the external loads need to be considered. In aiming to determine the structural safety of a suspended cable, and to understand which uncertainty features have the greatest influence, these relationships are written within a probabilistic framework.This article briefly sets the analysis of suspended cables within the context of geometrically nonlinear elastic structures and corresponding finite element analysis methodologies. Analytical solutions to the tension and normal displacement of a suspended cable subjected to external loading are presented. Nonlinear performance functions, in the form of either the cable tension or normal displacement are stated. Analytical expressions for the required gradients of the performance function of a suspended cable with respect to the basic variables under static loads are developed. The structural reliability of a suspended cable is studied using a first-order reliability method (FOSM) and verified by comparison with Monte Carlo simulation (MCS) and Monte Carlo simulation based optimization principles (MCOP) for a number of examples. Load cases including, wind, snow, and temperature variation are included.

Four Catenary Architectures to Triangularly Stretch a Circular Membrane Aperture

Theoretically discussed and analytically compared are four structural paradigms for the isotropic stretching of circular membrane apertures with three-point tensioning of regular (120 deg) symmetry. These are 1) a film triangle with parabolic catenary systems on the sides, 2) a circular arc-triangular sheet with edge cables, 3) the latter with circular corner cutouts, and 4) directly tensioning the film disk around the circumference with radial catenaries, as here named. The last two are newly proposed to increase structural efficiency: to reduce suspension forces for a given support system footprint (equivalently, to reduce the support footprint for given suspension loads). Mechanics and geometries are rigorously formulated with key design relations symbolically derived. Of the four options, the radial catenary is found with a wide margin to be the most efficient, followed by the arc-circular perimeter with corner cutouts. The parabolic catenary is next, with simple arc-circular perimeter cables being the least efficient. Finally, derivative configuration options and some hardware engineering considerations are briefly touched upon. The latter include quantitative impact on support structure mass, physical feasibility, and system design concerns.

The Experimental Observation of the Prestress Forces in the Structural Elements of a Tension Fabric Structure

The periodic experimental observation of the prestress forces in some selected structural elements of the tension fabric structure is mentioned in this paper. The described experiment was focused to the tension fabric roof which covers the tram stop K Barrandovu in Prague. So far the observation was performed three times and it was every time aimed on three types of basic structural elements support cables anchored to the ground, edge cables placed in a fabric pocket and fabric membranes. The used non-destructive experimental procedures are based on the geometrical nonlinearity and the frequency method, the applied measurement system was developed by authors. The dependence of cable forces on temperature changes can be found out from the obtained results.

Tecnología de pasarelas con estructura de membrana

The paper presents this technology, that responds to the author’s initial idea of using tension advantages in footbridges. It begins with a brief analysis of the membrane structures and the challenges associated to this new application. Emphasis is made on a research project associated to the design, construction and testing of a membrane footbridge in Callus (Barcelona). Its global objective was making real the idea, materialising such a footbridge on the ground and thus verifying its functional, structural and constructive aptitude. There were also partial objectives linked to structural analysis (suitable formfi nding method for membrane and edge cables), design, construction process, environmental impact and serviceability behaviour, so leaving to specifi c conclusions. Of course, such research (due to an agreement between CSIC, FECYT and the Council of Callus) is described with some detail in all its stages: 1, Footbridge design (mainly, the structural membrane). 2, Footbridge construction at Callus. 3. Footbridge testing. The results were positive and the prototype fulfi lled its mission of making real an idea. Starting from it, the main conclusion was to continue the study of this membrane technology (something not at all obvious before the Callus project). Finally, after an evaluation of the technology, a brief discussion about continuity and prospective of such a work line is presented. In this way, the perspective of reaching long spans by using this technology (much improved) is pointed out.

Intracellular filament bundles in whole mounts of chick and human myoblasts extracted with Triton X-100

The method of Triton X-100 extraction and critical point drying of whole mounts of cultured chick and human myoblasts was used to study the presence of intracellular bundles of filaments within these cells. Observation by means of transmission and scanning electron microscopy demonstrated a complex system of filament bundles which appeared morphologically and spatially heterogeneous. Most obvious were long dense bundles or cables traversing along the ventral surface of developing myoblasts, presumably the ‘stress fibers’ seen in light microscopy. Other bundle types occurred which were composed of loose aggregates of filaments coursing through the remnant cell body. A prominent accumulation of filaments was also seen at the lateral edges of these myoblasts. These lateral edge cables were thicker and denser than any other type of filament bundle observed in the myoblasts. Reaction of unextracted myoblasts directly to human antiplatelet myosin conjugated to rhodamine demonstrated that the most intense reaction also occurred along the lateral edges of both human and chick myoblasts. During development of chick myoblasts the filament bundles became oriented parallel to the cell axis giving the cell a fusiform morphology. It is possible that the various filament bundle structures and their differing structural and spatial dispositions could be related to functional differences among the diverse population of intracellular bundles of filaments.

Discrete data smoothing by spline interpolation with application to initial geometry of cable nets

The problem of smooth-surface approximation from discrete data values is discussed. For the particular interpolation requirements of the cable net generation problem, a method of polar-coordinate smoothing spline functions is developed. Next a Newton-iterative method of automatic equal mesh generation is developed which uses the polar spline representation of the cable net surface. This method produces complete specification of the cable grid node locations and cable segments, including the irregular-length grid elements intersecting the net edge cables. Examples are presented to illustrate how the interpolation procedure functions and how the mesh generation procedure couples with the surface interpolation procedure to produce a satisfactory complete initial geometry specification.