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The purpose of this paper is to analyze the cable-supported bridges more efficiently by building the finite element model with the spatial combined cable element.

The spatial combined cable element with rigid arms and elastic segments was derived. By using the analytical solution of the elastic catenary to establish the flexibility matrix at the end of the cable segment and adding it to the flexibility matrix at the ends of the two elastic segments, the flexibility matrix at the end of the cable body is obtained. Then the stiffness matrix of the cable body is established and the end force vector of cable body is given. Using the displacement transformation relationship between the two ends of the rigid arm, the stiffness matrix of the combined cable element is derived. By assigning zero to the length of the elastic segment(s) or/and the rigid arm(s), many subdivisions of the combined cable element can be obtained, even the elastic catenary element.

The examples in this field and specially designed examples proved the correctness of the proposed spatial combined cable element.

The combined cable element proposed in this study can be used for the design and analysis of cable-stayed bridges. Case studies show that it is able to simulate cable accurately and could also be used to simulate the suspenders in arch bridges as well in suspension bridges.

The purpose of this paper is to present a finite element formulation of enhanced two‐node parabolic cable element for the static analysis of cable structures.

Unlike the assumed polynomial displacement interpolation functions, the present approach uses the analytical cable dynamic stiffness matrix to obtain the explicit expression of the static stiffness matrix of an inclined sagging cable by setting the frequency at zero. The Newton‐Raphson‐based iterative method is used to obtain the solution.

It is demonstrated that the present results agree well with those obtained from the nonlinear analytical theory of a parabolic cable and previous reported methods in the literature.

This paper proposes a two‐node parabolic cable element. For comparable accuracy with the truss element method, fewer numbers of such cable elements are needed.

THE Department of Aeronautical Engineering in the University of Bristol was founded in 1945, when the Bristol Aeroplane Company generously presented the University with funds sufficient for the endowment of a Chair, to be known as the Sir George White Chair of Aeronautical Engineering. This was the fourth aeronautical Chair to be founded in Great Britain, having been preceded some quarter of a century earlier by the Mond Chair at Cambridge and the Zaharoff Chair at Imperial College, and a decade earlier by the Wakefield Chair, subsequently abolished, at University College, Hull. In addition, before 1945, a number of universities and colleges—in particular, Queen Mary College1—had offered courses with an aeronautical content, but not in independent departments headed by a professor. The present writer was appointed to the new Chair at Bristol in the summer of 1945; but owing to his commitments at the Royal Aircraft Establishment was not able to take up the appointment until January 1946. Meanwhile the first students, to a total of five, had been recruited and, in October 1945, had begun their general engineering studies in other departments of the Faculty of Engineering.

The purpose of this paper is to recover the deficiency of existing tie force (TF) methods by considering the decrease in section strength due to cracking and by selecting limit state of collapse according to section properties.

A substructure is selected by isolating the connected beams from the entire structure. For interior joints, the TFs in the orthogonal beams are obtained by catenary action. For corner joints, the TFs are assessed by beam action. For edge joints, however, the resistance is gained by greater of the resistance under catenary action for periphery beams and beam action for all the connecting beams in both directions. For catenary action, the TF capacities must satisfy Equation (20). On the other hand, for beam action, the TF must satisfy Equation (16), while R is calculated from Equation (17). In the case where the length of the connecting beams is similar, Equation (19) can be used.

Closed form solutions are available for TFs on both beam and catenary stages.

The proposed formulation makes designing more practical and convenient. However, the proposed formulation had good agreement with experimental results.

The purpose of this paper is to provide an accurate dynamic model for the flexible cable capture mechanism and to analyze the dynamic characteristics in the capturing process.

The absolute nodal coordinate formulation (ANCF) that based on the continuum mechanics approach is applied in the capture task using flexible cables. An ANCF cable element in which axial and bending strain energy are taken into account is presented to model the flexible cables. The generalized coordinates of ANCF are absolute displacements and slopes and make no small deformation assumptions; therefore, this element has a remarkable superiority in the large rotation and deformation analysis of flexible cables compared to the conventional floating frame of reference formulation (FFRF). The mass matrix of the cable element is constant, which will reduce the degree of non-linearity of the dynamic equations. The contact force between the steel cables and capture rod is calculated by the non-linear contact dynamic model, in which material and geometry properties of contact bodies are considered.

The stress distribution of steel cables is investigated in the numerical studies which show that the closer to the ends of the cable, the larger axial forces and smaller bending moments they will be. The reduction of grasping velocity will lead to a decrease in the contact force and the oversize peak value of contact force is more likely to be avoided when reducing the elastic modulus of steel cables to obtain a greater soft capture capability.

The work shows a practical possibility to improve modeling accuracy of the capture mechanism. Results of the analyses can provide references for the design and analysis of the capture task.

The ANCF is first used in the analysis of the capture task with flexible cables, and some useful results which have not been published before are obtained.

The purpose of this study is to present a multi-scale analysis methodology for calculating the effective stiffnesses and the micro stresses of helically wound structures efficiently and accurately. The helically wound structure is widely applied in ocean and civil engineering as load-bearing structures with high flexibility, such as wire ropes, umbilical cables and flexible risers. Their structures are usually composed of a number of twisted subcomponents with relatively large slender ratio and have the one-dimensional periodic characteristic in the axial direction. As the huge difference between the axial length and the cross-section size of this type of structures, the finite element modeling and theoretical analysis based on some assumption are usually unavailable leading to the reduction of computability; even the optimization design becomes infeasible.

Based on the asymptotic homogenization theory, the one-dimensional periodic helically wound structure is equivalent to the one-dimensional homogeneous beam. A novel implementation of the homogenization is derived for the analysis of the effective mechanical properties of the helically wound structure, and the tensile, bending, torsional and coupling stiffness properties of the effective beam model are obtained. On this basis, a downscaling analysis formation for the micro-component stress in the one-dimensional periodic wound structure is constructed. The stress of micro-components in the specified geometry position of the helically wound structure is obtained basing on the asymptotic homogenization theory simultaneously.

By comparing with the result from finite element established accurately, the established multi-scale calculation method of the one-dimensional periodic helically wound structure is verified. The influence of size effects on the macro effective performance and the micro-component stress is discussed.

This paper will provide the theoretical basis for the efficient elastoplastic analysis of the helically wound structure, even the fatigue analysis. In addition, it is necessary to point out that the axial length of the helically wound structure in the general engineering problems that such as deep-sea risers and submarine cables.

A long, small diameter piezoelectric cable has become available for use as a sensor device. The long length of the cable is exciting in that measurement can take place anywhere along its length. This is an excellent characteristic when measuring the dynamic behaviour of a continuous system. Measuring at a point (for example using strain gauges) is often not satisfactory as the point may or may not correspond to a node (or nodes) associated with one or more modes of vibration of the system. By monitoring over a length however, this problem is overcome. The disadvantage with measuring over a length is that the output signal is a summation of all the events along the length and a quantity that does not indicate an exact position.

The robustness of building structures in a fire has recently drawn wide attention. This study presents the progressive collapse analysis of steel frame building structures under localised fire. The main objective of this study is to propose methods to enhance the structural collapse resistance of such structures in fire.

A modelling method was developed and validated against both experimental and analytical studies. Then, a series of robustness analyses were performed to investigate the interaction among the members and the pattern of load distribution within the structures. These analyses show that lateral resistance and load redistribution have a vital role in the robustness of the building. Thus, two approaches have been adopted to enhance the robustness of the focused steel frame during a fire.

It is found that increased size of floor beams and vertical bracing systems are effective measures in preventing whole structure collapse. The larger beam section is able to prevent catenary action so that the load in the failed columns can safely transfer to the adjacent columns without buckling. On the other hand, the bracing system improves the lateral resistance that can accommodate the lateral force when catenary action occurs in the beam.

Previous studies have focused on the collapse mechanism of steel frame structures. However, the parameters affecting the structural robustness in a fire have not yet been explored. To address this gap, this study adopted numerical modelling to undertake parametric studies to identify effective methods to improve the robustness of such structures under fire conditions.

First, a synopsis of the major changes of natural science, mathematics and philosophy within the 17th century shall highlight the birth of the new age of science and technology. Based on Fermat's principle of the shortest light‐way and Galilei's first attempt of an approximative solution of the so‐called Brachistochrone problem using a quarter of the circle, Johann Bernoulli published a competition for this problem in 1696, and six solutions were submitted by the most famous scientists of the time and published in 1697, even though the variational calculus was only published in 1744 by Euler for the first time. Especially the analytical solution of Jakob Bernoulli contains already the main idea of Euler's variational calculus, i.e. to vary only one function value at a time using a finite difference method and proceeding to the infinitesimal limit. Also Leibniz' geometric solution is very remarkable, realizing a direct discrete variational method geometrically which was invented numerically much later in the 19th century by Ritz and Galerkin and generalized to the finite element method by introducing test and trial functions in finite subspaces. A new finite element solution of the non‐linear Brachistochrone problem concludes the paper. It is important to recognize that besides the roots of variational calculus also the first formulations of conservation laws in mechanics and their applications originated in the 17th century.

The purpose of this paper is to present a solution strategy for the analysis of cable networks which includes an extension to the force density method (FDM) in an attempt to support cable elements when they become slack. The ability to handle slack cable elements in the analysis is particularly important especially in cases where the original cable lengths are predefined, i.e. the cable structure has already been constructed, and there is a need for further analysis to account for additional loading such as wind. The solution strategy is implemented in a software application.

The development of the software required the implementation of the FDM for the analysis of cable networks and its extension to handle constraints. The implemented constraints included the ability to preserve the length in the stressed or the unstressed state of predefined cable elements. In addition, cable statics are incorporated with the development of the cable equation and its modification to be able to be handled by the FDM .

The implementation of the solution strategy is presented through examples using the software which has been developed for these purposes.

The results suggest that for cable networks spanning large distances or cable elements with considerable self-weight the neglect of the cable slackening effects is not always conservative.