Cable-strut Tensile Structure Research Articles

Research on the recovery performance of SMA tendon and the active control effect of adaptive cable dome

Cable dome is a widely used cable-strut tensile structure, and whose form is controllable. The shape and internal force of the structure can be adjusted by adjusting the length of the cable elements to enhance its load-bearing capacity. Shape memory alloy (SMA), as a new type of intelligent material, has excellent driving performance and is widely used in aerospace engineering, biotechnology, and construction engineering. In order to achieve active control of cable elements in cable domes using SMA, this paper conducted uniaxial tensile tests on SMA wires. Based on the test results, this paper designs and manufactures a SMA tendon suitable for active control and establishes a recovery performance model specifically for SMA tendon. Subsequently, tests on recovery performance are conducted to delve into the recovery force and displacement of the steel tendon. Finally, the SMA tendon is connected in series with the steel wire rope to obtain the active control cable elements, which is used to replace the diagonal cable in the Levy cable dome. Apply full span load to the structure, conduct active control tests by heating SMA tendon, record cable stress and node displacement during the test, and compare the results with finite element results and control methods in literature to study the control effect of SMA tendon. The test results show that the SMA tendon has good recovery performance and can be used as the control device of the control cable elements in the cable dome structure. The control effect is stable and reliable. Adjusting length of the diagonal cable can achieve Levy cable dome structural shape adjustment and improve the relaxation phenomenon of the ridge cable.

Research on the control limits of cable length errors of cable-strut tensile structures for prestressed relaxation under load effect

Cable-strut tensile structures (CSTS) are mainly composed of cables, and the cable length errors are bound to exist in the manufacturing of cables. The cable length errors have significant impacts on the mechanical properties of CSTS under load effects. Meanwhile, CSTS generally uses flexible membrane material as roofs, therefore cable length errors will result in the wrinkle of roofs and then cause the secondary accumulation effects of rain and snow load. Therefore, it is necessary to reasonably control the manufacturing errors of cable length. In order to solve the problem, the method of solving the control limits of cable length errors of CSTS is proposed due to the prestressed relaxation under load effects. The reliability index of CSTS is firstly given based on the reliability theory. Then, based on the reliability index and the criterion of prestress relaxation under load effect, the critical state equation and constraint inequality group are constructed, and the coefficient matrix of constraint inequality group is derived. Meanwhile, the nonlinear finite element method for solving the coefficient matrix of constraint inequality group is proposed. The procedure of solving the control limits of cable length errors of CSTS is given based on the proposed method. The crossed spoke cable-truss structure is taken as an example to verify the feasibility of the new method. The research contents provide an effective solution for controlling cable length errors of CSTS for prestressed relaxation under load effect.

Analysis of new wave-curved tensegrity dome

The cable dome is one of the most widely used structures in cable-strut tensile structures. A new topology of the tensegrity system is firstly proposed, and combined with the circular wave surface, a new wave-curved tensegrity dome is then obtained, which has less members than traditional cable domes. Concurrently, based on a combination of Levenberg-Marquardt and quasi-Newton (LM-QN) methods, a form-finding algorithm for cable-strut tensile structures is proposed to solve nonlinear equilibrium equations by addressing the least-squares problem. Subsequently, the configuration of the wave-curved tensegrity dome is analyzed using the proposed form-finding method, which demonstrates that an integral feasible prestress exists in the new structural form. Finally, the static and dynamic performance of the new structure are analyzed, and its possible defects and weaknesses are subsequently examined based on the analysis results. The numerical results show that the proposed wave-curved tensegrity dome satisfies the necessary requirements and has high research relevance as a type of light roof. Moreover, the LM-QN method can overcome the singular problem of the tangent stiffness matrix and be used as one of the form-finding methods for the verification of new structures.

Static displacement expansion for cable-strut tensile structures by concurrently using mode compensation and optimization strategies

For a specific load, the displacements of a real cable-strut tensile structure can be approximately expressed by only a few contribution modes. The displacements can thus be quickly expanded based on finite sensor locations by the traditional contribution-mode based method (TCMM). However, the TCMM has two shortcomings. First, mode truncation errors occur by neglecting non-contribution modes. Second, too many sensors are needed when a load case has too many contribution modes. In this paper, two strategies named mode compensation strategy (MCS) and mode optimization strategy (MOS) are suggested, respectively. The MCS aims to compensate mode truncation errors observed in the TCMM, with all non-contribution modes treated as one integral compensation mode. The MOS attempts to reduce the quantity of contribution modes by finding the best virtual mass distribution. An improved contribution-mode based method (ICMM) using both the MCS and the MOS is thus proposed. An annular tensile cable-truss canopy structure with a span of 200 m is numerically analyzed. For the load case with 26 loading points and 16 contribution modes, the MOS can significantly reduce the number of contribution modes to 4. Besides, the ICMM presents high expansion accuracy with far less sensor locations than the TCMM and the Guyan method.

Robustness Analysis of a Flexible Cable-Strut Tensile Structure

Currently, the robustness analysis of structure is primarily related to rigid structures, and little has been done to study the robustness of spatial flexible cable-strut tensile structures with larger span, more complex forms, lower redundancy, more sensitivity to unexpected interference such as construction deviations, etc. Based on the $$ H_{\infty } $$ theory, this paper starts with the fundamental theory and develops analysis method for the robustness of flexible cable-strut tensile structures, and then the relationships between the structural robustness and some design parameters such as initial pre-stress level, load distribution form, structural span, cross-section area, rise-span ratio, etc. are analysed through a case study of a concrete cable-strut tensile structure in China. On this basis, the effects of construction errors such as element-length error and supporting node position error are further analysed. Finally, the importance of each kind of element is analysed by means of conceptual removal of element. The results show that the higher the initial pre-stress level, the larger the element cross-section, the smaller the structural span, the larger the rise-span ratio and the more uniform the load distribution, the stronger the structural robustness. In the limited construction error range, the element-length error and the supporting node position error have little effects on the robustness of the structure. The hoop cables are the more important elements and the elements in inner region of the structure are of comparatively lower importance in the cable dome structure in this study.

Identification and Adjustment of the Pretension Deviation in Cable-Strut Tensile Structures

Construction errors inevitably arise in real cable-strut tensile structures. Nevertheless, construction error analysis and evaluation, as well as methods to identify the source of the errors and proper adjustment methods to compensate for these errors, remain in their infancies. In this study, the relationship between pretension deviation and element length deviation is first established based on the three basic equations for pin-joint structures. On this basis, identification methods are proposed to identify the sources of the pretension deviation caused by the active cable length deviation and the pretension deviation caused by both the active and the passive cable length deviations. Using measured data, an adjustment method is developed for the pretension deviation under different scenarios. Furthermore, the effectiveness of the adjustment method for the pretension deviation is discussed using the evaluation indices. Finally, a case study is presented and demonstrates that the proposed identification method can identify the sources of the pretension deviations. The number of adjusted cables will affect the level of adjustment for the pretension deviation. During the adjustment of the pretension deviation, different adjustment methods will result in different shape deviations and different maximum displacements.

Determination of a Monitoring Scheme for Controlling Construction Errors of a Cable-strut Tensile Structure

Construction errors are inevitable in real cable-strut tensile structures. Nevertheless, the relevant work, especially the monitoring scheme design work, to control the construction errors is lacking. At present, the monitoring schemes always lay out the monitored members in the places with great internal force or great deformation, do not consider the method to control the construction errors and do not explain the method to lay out the monitored members in fundamental theory. To address this situation, the element length error, which is an important construction error affecting the bearing performance, is considered as the factor variable and the fundamental equation of pre-stress deviation and element length error is derived firstly. Next the methods to express the pre-stress deviation, which are only derived from the active cable length errors or from both the active cable and passive cable length errors, are discussed. After that, based on the condition that the errors can be solved and compensated, the least number of monitored members is determined. Moreover, those members sensitive to cable length deviation of active cables are selected as monitored members. In order to evaluate the effect level caused by passive cable length deviation, two evaluation parameters Δ and ρ are further discussed. Finally, one cable-strut tensile structure example is employed to verify the proposed method and the results of the example studies indicate that the least necessary number of monitored members can be achieved for the accurate solution and compensation of active cable length deviations. Different members have different sensitivities to the change of the length in active cables and those members with great sensitivities can be chosen in prior as monitored members. The evaluation parameters Δ and ρ can be used to analyze the source of errors and to evaluate the error effect level caused by the passive cable length deviation.

Support node construction error analysis of a cable-strut tensile structure based on the reliability theory

A support node construction error sensitivity analysis was conducted, and the allowable value of node error was determined in this study based on the reliability theory and using the ANSYS software. First, the node construction error sensitivity analysis method was proposed based on Latin hypercube sampling, and detailed procedures were described. Then, a method for determining an allowable error value with a reliability index not less than 1.5, an internal force deviation of the cable not greater than 10%, and a normal serviceability limit state was presented. An exemplary tensile structure with different error distribution and error values was employed to verify the proposed method. Finally, a cable-strut tensile structure model with a diameter of 5.0 m was designed and fabricated. The research showed that different directions of the node construction error had different error sensitivities, and that each direction of the node error had different error sensitivities for different elements. The allowable node construction error can be obtained using a linear searching method with a reliability index not less than 1.5, an internal force deviation of the cable not greater than 10%, and a normal serviceability limit state. The theoretical results were generally consistent with the experimental results, which indicated that the proposed error sensitivity analysis method was accurate. Thus, this study has value for both theoretical research and engineering applications.

Optimal Construction Scheme for Controlling Construction Errors of a Cable-strut Tensile Structure

In a real cable-strut tensile structure, construction errors are inevitable. To explore the optimal construction scheme and control construction errors, this study optimized the construction scheme of a cable-strut tensile structure. First, a mathematical model of the element length error was investigated based on stochastic theory. By combining the balance equation, geometric equation and physical equation, the fundamental relationship between the pre-stress deviation and element length error was derived. Because the pre-stress in the active cable can be controlled exactly and the cable’s pre-stress deviations were zero during construction, the relationship between the pre-stress deviation of a passive cable and the element length error was obtained. Then, the statistical characteristics of the pre-stress deviation were obtained under different construction schemes using statistical theory. Finally, an example was analysed as a case study. The study showed that different elements have different error sensitivities and that different construction schemes have different error effects. Using the method proposed in this paper, the error effect of different construction schemes can be analysed, and the optimal construction scheme, with lower error effects and lower construction costs, can be selected for actual construction projects.

Optimization of the construction scheme of the cable-strut tensile structure based on error sensitivity analysis

Optimization of the construction scheme of the cable-strut tensile structure based on error sensitivity analysis is studied in this paper. First, the element length was extracted as a fundamental variable, and the relationship between element length change and element internal force was established. By setting all pre-stresses in active cables to zero, the equation between the pre-stress deviation in the passive cables and the element length error was obtained to analyze and evaluate the error effects under different construction schemes. Afterwards, based on the probability statistics theory, the mathematical model of element length error is set up. The statistical features of the pre-stress deviation were achieved. Finally, a cable-strut tensile structure model with a diameter of 5.0 m was fabricated. The element length errors are simulated by adjusting the element length, and each member in one symmetrical unit was elongated by 3 mm to explore the error sensitivity of each type of element. The numerical analysis of error sensitivity was also carried out by the FEA model in ANSYS software, where the element length change was simulated by implementing appropriate temperature changes. The theoretical analysis and experimental results both indicated that different elements had different error sensitivities. Likewise, different construction schemes had different construction precisions, and the optimal construction scheme should be chosen for the real construction projects to achieve lower error effects, lower cost and greater convenience.

Theoretical analysis and experimental study on sensitivity of element-length error in cable-strut tensile structures

In a real cable-strut tensile structure, the element-length errors are inevitable. To understand their effects on the bearing capacity of a cable-strut tensile structure, the element-length error sensitivity analysis was investigated in this study. First, mathematical model of the element-length error was proposed based on stochastic theory. By combining the balance equation, geometric equation, and physical equation, the fundamental equation between the pre-stress deviation and element-length error was derived. After that, pre-stress deviation statistics characteristic was achieved with the help of statistical theory and the element-length error sensitivity analysis method was formulated. Then, a cable-strut tensile structure model with a diameter of 5.0 m was designed and fabricated to validate the proposed method. The element-length was set adjustable in order to simulate the element-length errors. Making use of the measured internal forces induced by element-length errors, the error sensitivity of each kind of element was achieved. In addition, a finite element model was also established with the commercial software ANSYS. The element-length errors were simulated by the changes of element-length due to temperature variations. The results of the three models coincided with each other satisfactorily, verifying the effectiveness of the proposed mathematical model. It was found that different elements had different error sensitivities. The error sensitivity of the hoop cables was most prominent, the ridge cables and diagonal cables the second, and the struts the third.

Experimental Research on the Prestress and Static Behavior of a Cable-Strut Tensile Structure Model

A cable-strut tensile structure model with the diameter of 5.0m was designed and made to study the prestress and static behavior on the base of theory analysis. New schemes of the boundary compression ring, the cables and struts with the adjustable length, the connection nodes were designed and the least square method to fit the element force and strain curve was proposed. The initial prestress distribution and the responses of the model under full-span node load, half-span node load and 1/4-span node load were investigated. The experimental results indicate the cable-strut tensile structure will achieve the designed initial prestress while every element was tensioned to designed length. The outer planar stiffness of the structure is poor and easy to lost stability when subjected to asymmetric loads. The measured values and computed ones are almost consistent, which indicates the validity of the model design and the accuracy of the proposed methods.

Reliability analysis of cable-strut tensile structures based on response surface method

Reliability analysis of cable-strut tensile structures based on response surface method

Ultimate Bearing Capacity Analysis of Schwedler Suspendome

Prestress suspendome structure is a new two-double space structure system, which is composed of single-layer spherical reticulated shells and cable-strut tensile structure, and taking full advantages of two systems. Compared to single-layer shells, stiffness and stability are improved effectively. Compared to cable dome, designing, constructing and joint treatments are simplified much more easily. In this paper, taking geometrical nonlinearity and material nonlinearity into account, the stable ultimate bearing capacity of Schwedler suspendome was analyzed theoretically by employing a nonlinear finite element method. Structural parameters of the suspendome, such as prestresses of cables, heights of struts, rise-span ratio and cable layout, which influence the structural stable ultimate load-carrying capacity, having been analyzed by employing the two-double computational mode of Schwedler suspendome of 40m span. Some valuable and reasonable conclusions are drawn for practical engineering design by theoretically analysis.

Numerical Simulation Algorithm for the Forming Process of Tensile Cable-Strut Structure

Numerical simulation of forming process is an issue that finds the solution of a series of unstable equilibrium states of cable-strut tensile structures with specific unstressed length. This is a long well unsolved theoretic question, which mostly lies in the couple of mechanism and elastic deformation. On the basis of the unstressed length, the theoretic parabolic curve element was adopted to simulate the cable with elastic tension and deformation. The vector of unbalance nodal force was subsequently formulated with the explicit branch-node matrix of topology in force-density method. And the dynamical relaxation method was used to solve the nonlinear equation to avoid the singular stiffness of equation. Numerical examples indicated that the proposed algorithm could calculate the unstable equilibrium state and simulate the forming process with the unstressed length of the active cables changing, and has some theoretical significance.

Research on Analysis Method and Distributing Principle of the Optimal Prestress in Sunflower-Patterned Cable Dome

Sunflower-patterned cable dome which gets stiffness by prestress tensioning and force self-balance is a kind of cable-strut spatial tensile structure. If distribution of prestress in each layer of the structure is appropriate in construction, its deformation under vertical loads will be uniform. In finite element analysis software ANSYS, principle and method of selecting the optimal prestress distribution of sunflower-patterned cable dome were obtained through applying several different kinds of prestress on each layer of loop cable in calculation model and analyzing its deformation uniformity under full-span load respectively.