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In this paper, a novel arch structure—circular box arch with sinusoidal corrugated webs (CBASCW)—is presented. Through the methods of theoretical derivation and finite element simulation, we studied its in-plane elastic buckling and in-plane elastoplastic stability. Through theoretical derivation, a shear stiffness formula of the arch section is determined, and the elastic buckling load when the arch is in pure compression state is proposed considering the shear deformation. We also introduced a simplified model, which can simulate the deformation and internal forces conveniently. The failure mode and global elastoplastic instability mechanism are investigated under uniformly distributed full-span radial load, uniformly distributed full-span vertical load, and uniformly distributed half-span vertical load. Furthermore, by introducing a regular slenderness ratio and stability coefficient, the stability curve of the arch under the state of pure compression is plotted. Subsequently, based on the stability curve and the numerical simulation results of a simplified model, a design formula for the stability bearing capacity is proposed for situations where global elastoplastic instability occurs. [ABSTRACT FROM AUTHOR]

This paper presents an arch structure called the circular box arch with sinusoidal corrugated webs (CBASCW). This study investigates the out-of-plane elastic buckling behavior and elastoplastic stability capacity of the arch through a combined approach of theoretical derivation and finite element simulation. The section stiffness of the arch, including flexural stiffness, shear stiffness, and torsional stiffness, is achieved through theoretical derivation. Additionally, the elastic buckling load in both pure compression and pure bending states is derived. A simplified model is also introduced, which can conveniently simulate the internal force and deformation of the arch. The elastoplastic instability mechanism and failure mode are studied under various loading conditions, including uniform radial load, end bending moment, vertical load uniformly distributed in full-span, and vertical load uniformly distributed in half-span. Furthermore, the stability curves of the arch under conditions of pure compression and pure bending are graphed by incorporating stability coefficient and regularized slenderness ratio. According to the simulation results obtained from the simplified model and the analysis of stability curves, a design formula for stability capacity is proposed. [ABSTRACT FROM AUTHOR]

The structural elements of buildings have recently required the development of efficient design solutions due to increased dynamic and thermal loads. The main solution for improving the efficiency of such elements involves creating lightweight non-uniform beam and arch structures from alloyed steel, which has better mechanical characteristics. The most promising approach is the use of welded beams and arches with perforated partitions and composite beams, which are often used together, for instance, as structural elements of cylindrical shells. The development of an effective cross-sectional shape for perforated beams and crane girders is considered, taking into account the strength, local stability, resistance to flat bending, and fatigue deformation. It has been shown that the effective form for perforated beams is a box-shaped structure made of perforated shvellers. Calculations for selecting a rational design from the assortment of hot-rolled shveller profiles have demonstrated that a significant reduction in the weight of the structure can be achieved by using the proposed cross-sectional shape. An evaluation of the fatigue strength of composite metal crane girders operating in harsh conditions has shown the effectiveness of using hot-rolled I-beams as their upper flange, as well as the necessity of using hot-rolled I-beams to ensure strength in their lower part. When choosing the rational parameters of an arch design, multiple recalculations of its bending with respect to technological cutouts in the thickness are necessary; hence, simplified calculation schemes are commonly used. Some authors simplify this process by replacing an arch with a cutout with a solid arch reduced in height by the cutout radius. We have shown that this model does not accurately describe the actual distribution of forces and displacements, leading to inadequate results. We have developed a simplified methodology for the preliminary calculation of a circular arch with a cutout, which includes correction coefficients calculated by us. A calculation of the flat stress–strain state of an elastic circular metal arch with a central semicircular cutout under various ratios of design parameters and uniform external pressure was conducted. A dependence of the stress concentration coefficient at the cutout's apex on the ratio of the cutout radius and arch thickness was obtained. These results can be generalized for reinforced non-uniform shells and for the fuzzy application of external influences. [ABSTRACT FROM AUTHOR]

This study aims to analyze the in-plane free vibrations of arches comprising the laterally symmetric functionally graded materials. Emphasis is placed on the circular arch whose material properties vary laterally symmetrically about the centroidal axis by a power-law function. The differential equations governing the mode shape of the arch were derived under the boundary conditions and were numerically solved to calculate the natural frequencies using the Runge–Kutta and Regula–Falsi methods. Calculation results of this study for natural frequencies compare well with those of the finite element method. The effects of various arch parameters on natural frequencies are highlighted and discussed in detail. [ABSTRACT FROM AUTHOR]

Flexible lightweight arched structures are finding increasing use as components in smart engineering applications. Such structures are prone to various types of instability under moving transverse loads. Here, we study deformation and vibration of a hinged circular arch under a uniformly moving point load using geometrically-exact rod theory to allow for large pre- and post-buckling deformations. We first consider the quasi-statics problem, without inertia. We find that for arches with relatively large opening angle (∼ 160 ∘ ) a sufficiently large traversing load will induce an out-of-plane flopping instability, instead of the in-plane collapse (snap-through) that dominates failure of arches with smaller opening angle. In a subsequent dynamics study, with full account of inertia, we then explore the effect of the speed of the load on this lateral buckling. We find speed to have a delaying (or even suppressing) effect on the onset of three-dimensional bending–torsional vibrations and instability. Based on numerical computations we propose a power law describing this effect. Our results highlight the role of inertia in the onset of elastic instability. [ABSTRACT FROM AUTHOR]

The in-plane elastoplastic failure mechanism of plate-tube-connected steel circular arches with inverted triangular cross sections is investigated in this study by using theoretical derivation and numerical simulation. First, the in-plane elastic buckling load formula of the arch under full-span uniform radial load (FSURL) is presented. Then, the limited conditions of avoiding the connecting plate and chord local failure before global elastic instability are derived. Lastly, the elastic–plastic failure mechanisms of arches are studied under FSURL, full-span uniform vertical load (FSUVL), and half-span uniform vertical load (HSUVL). It is found that the arch will experience global failure, chord local failure, combined connecting plate and chord failure, and connecting plate local failure under FSUVL and HSUVL. The failure mode is mainly related to the stiffness of the connecting plate. The corresponding design formulas are proposed for the global failure of arches and local failure of the chord. The proposed formulas and FE results are in good agreement. [ABSTRACT FROM AUTHOR]

The in-plane elastoplastic failure mechanism of plate-tube-connected steel circular arches with inverted triangular cross sections is investigated in this study by using theoretical derivation and numerical simulation. First, the in-plane elastic buckling load formula of the arch under full-span uniform radial load (FSURL) is presented. Then, the limited conditions of avoiding the connecting plate and chord local failure before global elastic instability are derived. Lastly, the elastic–plastic failure mechanisms of arches are studied under FSURL, full-span uniform vertical load (FSUVL), and half-span uniform vertical load (HSUVL). It is found that the arch will experience global failure, chord local failure, combined connecting plate and chord failure, and connecting plate local failure under FSUVL and HSUVL. The failure mode is mainly related to the stiffness of the connecting plate. The corresponding design formulas are proposed for the global failure of arches and local failure of the chord. The proposed formulas and FE results are in good agreement.

This study investigates the failure mechanisms and strength of plate-tube-connected circular steel arches. The upper and lower chord of the arch are joined by a series of uniformly distributed steel plates in a radial direction. The chord of the arch mainly bears bending moment, shear force and axial force. The connecting plates mainly resist bending moment, so its failure mechanisms and strength design are different from the traditional truss arch with diagonal tubes and web-opening arches. In this paper, the finite element (FE) software ABAQUS is used to study the in-plane failure mechanism and stability bearing capacity of planar plate-tube-connected circular steel arches, which is subjected to full-span uniform radial load (FSURL), full-span uniform vertical load (FSUVL) and half-span uniform vertical load (HSUVL). The elastic buckling load formula of two-hinged plate-tube-connected circular steel arches is proposed under FSURL.. Also, the limited condition of avoiding local buckling is also proposed under FSURL. The stability bearing capacity design formula of the arch under FSURL is proposed. Studies have shown that under FSURL, the arch will be subjected to global elastoplastic failure, and the upper chord will exhibit a full-section yield at the scope of 1/4 L span and the lower chord will exhibit a full-section yield at the scope of 3/4 L span. Under F(H)SUVL, the global failure mode may occur. The global failure stability bearing capacity design formulas of the arch under FSUVL and HSUVL are also proposed. The FE results are in good agreement with these formulas. Finally, the design suggestions of plate-tube-connected circular steel arches are proposed. [ABSTRACT FROM AUTHOR]

In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details. [ABSTRACT FROM AUTHOR]

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis. [ABSTRACT FROM AUTHOR]

The procedure of automation of calculation of the strained-deformed state of circular arches is considered in the calculation of bending and tensile-compression deformations concentrated and distributed external loads. The aim of the work is to apply the possibilities of the boundary element method (BEM) to solve quite labor-intensive tasks of the strained-deformed state of circular arches and arch structures. To achieve the goal, a static calculation of the tensely-deformed state of circular arches in the MATLAB environment is performed. For this purpose, a system of differential equations of flat deformation of a circular rod is made and solved taking into account bending and stretching deformations along radial and tangential dis-placements. As a result of the calculation, it was concluded that numerous problems in the calculation of rings and ring systems can be solved by means of the boundary element method (BEM) equation in a coherently presented method, taking into account bending and ten-sile-compression deformations.

The aim of this study is to devive an analytical solution to predict the buckling load of the thin-walled arch under a point load at mid-span position. A deflection function and the energy method are adopted to build the nonlinear equilibrium formulae, by solving which, the analytical solution is expressed explicitly. Subsequently, a numerical simulation is established to track the load-displacement paths of equilibrium. The simulation results indicate the load drops significantly after its maxima (critical buckling load) and follows multiple branches characterized by load limits and displacement limits. A comparison is taken between the numerical and analytical results, and a good accordance is depicted. Moreover, parameters that may affect the buckling load are analyzed, with the inclusion of rotational stiffness supports, the central angle, as well as the normalized thickness on the load capacity. Finally, both the proposed theoretical formule and simulation results agree excellently with the test results and other closed-form expressions published elsewhere. [ABSTRACT FROM AUTHOR]

This article investigates how the material composition can affect the in-plane stability of circular arches with bi-layered rectangular cross-section. The Euler-Bernoulli beam theory is used. The materials are linearly elastic and isotropic. The one dimensional mechanical model is geometrically nonlinear: moderately large rotations are assumed. The end-supports are ideal pins and out-of plane displacements are restricted. The loading is a concentrated force at the crown. Evaluations are carried out graphically. It is found that not only the geometry but the material distribution has considerable effects on the critical load. [ABSTRACT FROM AUTHOR]

Abstract Natural frequencies of circular deep arches made of functionally graded materials (FGMs) with general boundary conditions are obtained in this research based on the unconstrained higher-order shear deformation theory taking into account the depth change, complete effects of shear deformation, and rotary inertia. The material properties are assumed to vary continuously through the thickness direction of the arch. Displacement field within the arch is obtained through expansion up to an arbitrary order. Governing differential equations of the in-plane vibration are derived using Hamilton's principle. These equations are solved numerically utilizing the differential quadrature method (DQM) formulation. In order to illustrate the validity and accuracy of the presented results, results are compared with the available data in the open literature. Afterwards, novel numerical results are given for free vibration behaviour of the FGM deep arches with various boundary conditions. Highlights • Displacement of the arch is estimated by means of a higher order theory up to an arbitrary order. • Different types of boundary conditions are covered in this research. • GDQ method is used to solve the governing equations. • Properties are distributed across the depth of the arch using a power law function. [ABSTRACT FROM AUTHOR]

In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.

Hanger arrangements suitable for timber network arch bridges with light timber decks on transverse crossbeams have been studied. The focus was on radial hanger patterns for glulam arches with circular shapes. The premise for the patterns are that the hangers always are attached in pairs to the transverse crossbeams, which are evenly distributed along the deck. The arrangement of hangers in network arch bridges is crucial for the structural performance of the bridges, as well as the stress distribution among the hangers. In the paper the performance of network bridges with classical radial patterns as well as introduced modified patterns under various load positions are compared. The underlying research is based on two-dimensional parametric numerical models of the network outlines. The parameters which have been varied are arch rise, hanger spread angle and location of a focal point for hanger creation. A comparison of stress ranges in hangers as well as bending moments in the arch for the considered patterns have been emphasized. The paper shows how the introduced pattern modifications influence the network arch performance. The intention is to provide a rational basis for better material utilization and design. In general it is recommended to apply a design modification leading to separate centres for the arch and the focal point for the hanger creation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the formulation of the Hencky bar-chain model (HBM) for shape optimization of pinned-pinned circular arches under uniform radial pressure for maximum buckling capacity. The so-called HBM is a discrete model which comprises a finite number of rigid curved segments connected by frictionless hinges and elastic rotational springs. The different rotational spring stiffnesses along the arch represent the varying cross-section of the arch. Therefore, the optimization of the rotational spring stiffnesses of a HBM leads to the optimal shape of a circular arch. With a sufficiently large number of springs, one may obtain the optimal continuous shape of the arch. HBM has a great advantage over other numerical methods in seeking the optimal solution because it allows one to obtain the analytical optimality conditions in a set of recursive equations that requires minimal computational effort to solve the problem. Although HBM has been used by Krishna and Ram [1] and Zhang et al. [2] for column shape optimization, this is the first time that HBM is developed for arch optimization. [ABSTRACT FROM AUTHOR]

This paper studies network arch timber bridges. The network patterns considered in the paper are suitable for bridges with a light deck on evenly spaced transverse crossbeams. Therefore, the equidistant distribution of hangers fastening points along the deck is assumed. In bridges made of steel and concrete, hangers are usually equally distributed along the arch. In presented cases, hangers distribution along the arch results from values of parameters like: a number of hangers, an arch rise, a bridge span and hangers inclination. This paper introduces a new network pattern as a modification of a radial pattern. The presented analyzes were performed as a parametric study of variable geometric parameters, on a vast set of 2D FEM models of the network arch with modified radial pattern. The focus was on bending moment distribution on the arch, as it is highly sensitive to even small changes in hanger arrangement. In addition, as a light deck may increase hanger relaxation, the number of relaxed hangers was also analyzed. Values of bending moments were obtained from static analyzes of different load cases, with symmetrical and unsymmetrical load applied on the deck. The results indicate, that introduced radial network pattern modification can improve the performance of the network arch. [ABSTRACT FROM AUTHOR]

Vierendeel steel truss arches are often used in lighting zones of the spatial roof to obtain good permeability and lighting effects. They are different from conventional steel truss arches in terms of failure mechanism and strength design because they have only transverse tubes without diagonal tubes between chords. The chords of the Vierendeel truss arch undertake axial, bending and shear actions while the transverse tubes only resist the bending action. Hence, their structural design against strength is different from conventional steel truss arches. However, this aspect is not well analyzed in literature. This study analyzed the in-plane instability mechanism, failure mode and corresponding strength of the Vierendeel truss arch under a uniform radial load, a full-span uniform vertical load, a half-span uniform vertical load and their combinations. The global in-plane elastic buckling load of the arch under a uniform radial load is derived firstly and an interaction design formula for predicting the global in-plane strength of the arch under a uniform axial compression is proposed. It is found that the chords of the arch may fail in fully sectional plastic moment mode. Transverse tubes may fail because of the end moments. Slender enough arches may also undergo global failure. Strength design equations for local chord failure and for global failure of arches are developed. All of the equations proposed for predicting global in-plane elastic buckling, global in-plane ultimate strength and chord local strength of the arch agree quite well with the finite element results. [ABSTRACT FROM AUTHOR]

Generalised functions have been widely adopted in structural mechanics to treat singularities of beam-like structures. However due to the curved geometry, that couples axial and transversal displacements, their use has never been explored for curved beams. In this paper the capability of distributions of leading to closed form exact solutions for multi-cracked circular arch is shown. The exact closed-form solution of a circular Euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained. Damage, under the form of concentrated cracks, has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of Dirac's delta functions. The resulting nontrivial generalised six order differential equations have been derived and solved in closed form. Independently of the number of along arch concentrated cracks, the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression. This latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem. The results have been validated through some comparisons with finite element numerical simulations: examples referred to multi-cracked Euler arches with different boundary conditions, damage and load scenarios are presented. [ABSTRACT FROM AUTHOR]

This paper presents numerical and experimental investigations of the in-plane strength and design of pin-ended circular arches having a sinusoidal corrugated web under combined in-plane loads. Finite-element models are developed that account for the effects of the corrugated web, initial geometric global and local imperfections of the arch and its web and flanges, residual stresses, the included angle and curvature of the arch, and different combined load cases. These are validated by test results and used together with the experiments to investigate the failure modes and strengths of such arches. It is found that an I-section arch with a corrugated web may fail in a global mode or in a web shear buckling mode. There are two types of global failure modes for arches under combined loads. In most cases, corrugated arches may fail in an elastoplastic buckling mode. However, when wind load plays an important role in the combined loads, corrugated arches may fail in a plastic yielding mode. An interaction design equation is proposed for predicting the global in-plane strength of steel arches with a sinusoidal corrugated web under combined axial and bending actions. The design equation provides lower bound predictions for the strengths of corrugated arches. General procedures are also proposed for the practical strength design of steel I-section arches with a sinusoidal corrugated web. [ABSTRACT FROM AUTHOR]

This paper reports experimental and numerical investigations used to develop a simple and accurate design method for the in-plane strength of circular steel I-section arches having a sinusoidal corrugated web under a uniform vertical load over the entire span. In deference to a flat web that can resist both shear and normal stresses, a sinusoidal corrugated web can resist only shear stresses, since its axial and bending stiffnesses are quite small. Tests are carried out to investigate the global in-plane elasto-plastic behaviour and strength of a circular steel I-section arch with a sinusoidal corrugated web under symmetric loading. A finite element model is also developed, validated by the test results, and then used to further investigate the global in-plane elasto-plastic behaviour and strength of the steel arches. Based on the test and finite element results, a design equation for predicting the global in-plane strength of circular steel I-section arches with a sinusoidal corrugated web subjected to a uniform vertical load over the entire span is proposed. It is found from the finite element results that in addition to an in-plane global failure mode, a circular steel I-section arch with a corrugated web may also fail in an elasto-plastic web shear buckling mode. Hence, elasto-plastic shear buckling of the sinusoidal corrugated web in arches must also be considered in their design. [ABSTRACT FROM AUTHOR]

• The mode shape functions for out-of-plane displacement of arches with different elastic rotational restraints are analytically determined. • Analytical solution for instability regions with elastic rotational restraints under a localized uniform radial periodic load is presented. • The analytical solution of dynamic instability regions are verified by frequency sweep transient finite element analyses (FEA). • Affected parameters on dynamic instability regions are comprehensively analyzed. Out-of-plane dynamic instability of a circular arch with elastic rotational constraints under localized uniform radial periodic load is studied in this paper which has not been yet reported in the literature. In the out-of-plane dynamic instability analysis, the coupled equation of motion associated with lateral displacement and twist angle is derived by using an energy method and Hamiltonian principle. Then the mode shape functions of arches with different elastic rotational restraints are deduced and analytical solution for unstable regions with a period of 2 T are obtained by using Bolotin's method. Finite element numerical analysis is employed to justify the dynamic unstable regions by frequency sweeping simulation and the results show a desirable agreement. It is found that when the flexibility of out-of-plane elastic rotational restraints decreases, the unstable region moves towards the direction of higher frequencies owing to the increase in rigidity of the arch, with the out-of-plane dynamic stability of the arch being improved. The load localized parameter significantly impacts the dynamic stability for the arches with various flexibility of out-of-plane restraints. These results give us a deep understanding of the instability mechanism of engineering structures with arches and provide insight into the effective design of arch structures. [ABSTRACT FROM AUTHOR]

• Eigenproperties of a multi-cracked Euler-Bernoulli inextensible circular arch. • Cracks are accounted for in governing equation by means of the distribution theory. • Governing equation defined over a unique integration domain regardless n° cracks. • Integration via Laplace transform is adopted to infer closed form mode shapes. • Both validations and parametric analyses are presented. Despite the numerous explicit solutions of free vibration of arches with regular cross sections, in case of concentrated defects such as cracks, no procedure is available to analyse arch vibrations without sub-division of the integration domain. As a result, curved sub-elements comprised between crack and external constraints, or successive cracks, are considered. In this paper a distributional approach is adopted to provide a formulation of the free vibration differential governing equations of circular inextensible arches over a unique integration domain in presence of multiple concentrated open (non-breathing) cracks. Discontinuities due to the presence of an arbitrary number of cracks are modelled by means of Dirac's deltas. An integration procedure is devised to offer closed form solutions of the relevant vibration modes together with the relevant frequency determinantal equation. Natural frequencies and mode shapes of damaged arches with different damage and restraint configurations have been evaluated and compared with experimental results available in the literature as well as finite element numerical simulations. The presented closed form solutions are also employed for two parametric studies to evaluate the influence of an increasing number of along axis concentrated cracks as well as of the location of cracks along the arch span. [ABSTRACT FROM AUTHOR]

This paper investigates the global in-plane failure and local web shear failure mechanism and strength of steel I-section circular arches with a sinusoidal corrugated web. In reference to a flat web that can resist both the shear and axial forces, the sinusoidal corrugated web can resist the shear force only. As a result, the sinusoidal corrugated web may fail in an elastic-plastic shear buckling mode. This study considers pin-ended circular steel arches with a sinusoidal corrugated web under a uniform radial load or a uniform vertical load to elucidate numerically their different failure modes. It is found that local web failure occurs suddenly without warning, and all aspects pertaining to the local web shear failure are investigated thoroughly with an equation for the ultimate shear-carrying capacity of nonuniformly sinusoidal corrugated webs being proposed. It is also found that the effects of the shear deformations of corrugated web on global in-plane buckling and the strength of steel arches are significant. A strength design equation for arches under nominal uniform axial compression and an interaction equation for arches under a uniform vertical load are developed. Strength design procedures for steel arches with a sinusoidal corrugated web against global failure and web shear failure are proposed. All of the equations proposed for global in-plane buckling, local web shear buckling, global in-plane strength, and web shear strength agree with finite-element results. [ABSTRACT FROM AUTHOR]

For the command of robotic systems different solutions are employed, generally electrical or mechanical. Amongst mechanical solutions, the most commonly met is the cam command. Since cams are mechanical parts requiring dedicated technology for execution on one side and extremely little interchangeability on the other side, they present a high cost. The present paper proposes the employ of circular arcs for the profiles of rotary cams, arcs intended to approximate the regions of the profile characteristic to ascending and descending phases. The general methodology for obtaining the characteristics of approximation circles is presented. [ABSTRACT FROM AUTHOR]

Ideally, structural health monitoring of civil infrastructure consists of determining, by measured parameters, the location and severity of damage in the structure. Many structural vibration parameters have been used to identify and quantify damage. Using parameters based on structural vibration phase space features for damage detection is a new field in structural health monitoring. In this article, a new parameter based on topology changes of the phase space of vibration signals is proposed to identify structural damage, and an index named changes of phase space topology derived from vibration time history is used to locate the damage. A circular arch structure is used to demonstrate the method. Both numerical simulation and experimental tests of dynamic responses of a scaled arch structure to impact loads are carried out. The obtained structural response data are used to detect structural damage. Both the experimental and numerical results indicate that this method can successfully locate damage. It also demonstrated that this proposed method is more sensitive to damage but less sensitive to noise than modal-based parameters. The proposed damage index can be a good candidate in an online structural health monitoring system, as it depends on global vibration measurements but is more sensitive to structural damage than other global vibration-based parameters such as vibration frequencies and mode shapes. [ABSTRACT FROM AUTHOR]

Dynamic instability of a non-shallow circular arch, under harmonic time-depending load, is investigated in this paper both in analytical and experimental ways. The analytical model is a 2-d.o.f. reduced model obtained by using a Galerkin projection of a mono-dimensional curved polar continuum. The determination of the regions of instability of the symmetric periodic solution and the discussion of the post-critical behavior are carried out, comparing the results with the experimental evidence on a companion laboratory steel prototype. During post-critical evolution, both periodic and non-periodic solutions are obtained varying the excitation control parameters. The theoretical and experimental models are analyzed around the primary external resonance condition of the first symmetric mode, in the case of a nearly 2:1 internal resonance condition between the first symmetric and anti-symmetric modes. When the motion loses regularity, synthetic complexity indicators are used to describe, in quantitative sense, the nonlinear response. [ABSTRACT FROM AUTHOR]

The differential quadrature (DQ) methodology introduced by the authors [see, Comput. Methods Appl. Mech. Engng. 191 (2002a) 3509; Int. J. Solids Struct. 39 (19) (2002b) 4927; Int. J. Numer. Methods Engng. 54 (3) (2003a) 847; J. Sound Vibrat. 263 (2) (2003b) 415] is employed for out-of-plane static analysis of circular arches under a wide spectrum of boundary conditions. In addition to the classical boundary conditions, elastic restraints against translation and rotation are also considered. Different loading conditions are examined. Several examples of arches with uniform, continuous or stepped varying cross-sections are presented to demonstrate the accuracy of the methodology. The domain decomposition technique in conjunction with the present DQ methodology is examined for certain cases. The results are compared with those of exact solutions for several uniform or stepped sections arches and also for arches on elastic foundations. Accurate converged numerical solutions are obtained with only few grid points. [Copyright &y& Elsevier]

• Analytical solution for flexural–torsional buckling load of an arch in linear temperature field is obtained. • The shear deformation has significant effect on buckling load at bigger temperature differential. • Neglect of shear deformation causes a lower buckling load at bigger temperature differential. • The buckling load decreases with an increase of the slenderness ratio. • The rotational support-spring stiffness substantially affect buckling load of arch at bigger temperature differential. When subjected to a constant temperature gradient, a steel circular arch will experiences non-uniform thermal expansion in its axial direction. This expansion will produces complex internal forces in the arch, which in turn will affect its flexural–torsional buckling behavior under a central concentrated radial load. Hitherto, research studies of the flexural–torsional buckling of such arches are scarce. The position of the effective centroid and shear center do not coincide with the geometric centroid of the section in a temperature gradient field, and this influences the flexural–torsional buckling response. In this paper, the flexural–torsional buckling of shear deformable circular arches with in-plane elastic rotational end restraints subjected to a central concentrated radial load at a constant temperature gradient field is studied. The theoretical solutions for the buckling load of the arch including the effect of the temperature gradient field are obtained and validated by ANSYS simulations. It is found that the buckling load decreases with an increase of the temperature differential when the included angle is small and increases with an increase of the temperature differential in case the included angle is larger than a certain value. The buckling loads including shear deformations are higher than those ignoring shear deformations at a bigger temperature differential. The influences of shear deformations on the buckling load are more significant at a bigger temperature differential. [ABSTRACT FROM AUTHOR]

• The material property is distributed non-symmetrically through the cross-section. • The FGM arch shows different stability performance from the homogeneous arch. • The temperature rise has an evident effect on the mechanical behavior of the FGM arch. • Numerical verification agrees well with the derived analytical predictions. • Parametric studies are conducted comprehensively. Several recent applications, i.e. space-structures and fusion reactors, involve the adoption of functionally graded materials (FGM) in their basic elements, such as the thin-walled cylinders, arches, beams, plates, and so on. These elements may be under a temperature variational environment due to the season's change, day and night temperature variation, or even fire disasters. The load capacity and/or buckling behavior of these thin-walled structures may be different from the ones only under mechanical loadings. Based on this fact, this study refers to the in-plane asymmetric buckling of the heated circular FGM arches under uniform pressure fields. The material of the FGM arch is thermo-elastic. A thermal radially-outward deflection occurs before the pressure field is introduced. This deflection may result in different buckling mechanisms from the arch under pure pressure loading. Analytical predictions on the buckling pressure are derived by combining the thin-walled shell schemes, admissible displacement functions, and the energy theory. Subsequently, a finite element simulation is introduced to trace the kinematic movement of the crown point. The pressure-displacement plots are obtained, from which, the buckling pressure is reachable. It is found the thermal field affects considerably the static stability of the FGM arch. Finally, a discussion refers mainly to the influence of material inhomogeneity on the buckling pressure, especially focusing on the influence of different power-law indexes on the internal forces, stresses, and strains. [ABSTRACT FROM AUTHOR]

The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL’s dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future. [ABSTRACT FROM AUTHOR]