Circumferential Bending Research Articles

A Global Energy Approach for Analysis of a Propagating Buckle in Submarine Pipelines

This paper presents a unique approach to analyze the steady-state buckle propagation phenomenon in underwater pipelines. In previous work, we restudied the buckling of a very long pipeline subjected to external pressure and found that buckling happens only over a certain length of the pipeline. In this paper, the collapse mode of the pipeline obtained in previous studies is taken as the transition zone during steady-state buckle propagation. Kinematics in the transition zone is analyzed based on von Kármán–Donnell type of nonlinearity. Assuming linear elastic rigid plastic material properties, the mechanical responses in the transition zone are examined using the deformation theory. Two parameters, the yield coefficient and the membrane stretching factor, are introduced to depict the effects of transversal bending and the membrane stretching, respectively. Analytical solution of buckle propagation pressure is derived by considering the energy conversation calculated from shell theory. It is found that the buckle propagation performance is governed by the transversal bending, including the circumferential bending and longitudinal bending. The membrane stretching is significant only for thick wall pipeline, in particular when the ratio of radius-to thickness is small than ten. The analysis is in effect by comparing the obtained solutions with the well-established predictions and the experimental results.

Modal signal analysis of conical shells with flexoelectric sensors

Flexoelectricity is known as the electromechanical coupling effect between the strain gradient and the polarization. In this study, a flexoelectric sensor is laminated on conical shells to monitor the natural modal signal distributions. The sensing mechanism of a generic flexoelectric sensor patch is presented first. Then, the spatially distributed microscopic sensing signal with respect to coordinates is evaluated in detail to reveal the modal signal distributions. Due to the gradient effect, the bending strain component is the only contribution to the total sensing signal. The total signal consists of two components resulting from the circumferential and longitudinal bending strain components. Analytical results show that the flexoelectric sensing signal induced by the longitudinal bending strain is the dominant contribution to the total signal for lower order modes; the contribution of the circumferential bending strain components increases while increasing the circumferential mode number. In lower modes, the optimal location of flexoelectric sensor is at the minor end and shifts to the middle for shallow shells. In higher modes, the optimal location is at the middle of the shell, but first shifts to the major end and then shifts to the minor end while increasing the semi-apex angle.

Full-scale physical testing of a buried reinforced concrete pipe under axle load

The structural response of a 600 mm inner diameter reinforced concrete pipe buried in a dense, well-graded sand and gravel soil and subjected to surface load from a single design truck axle with 0.3, 0.6, and 0.9 m of soil cover above the pipe crown is quantified using full-scale physical testing. The pipe did not crack at its minimum burial depth of 0.3 m under working CL-625 and CL-800 single-axle highway design loads as the largest tensile strains were only 50%–60% of those at the onset of cracking. Application of the fully factored CL-625 single-axle load at a burial depth of 0.3 m resulted in a tensile crack and a maximum circumferential bending moment of 6 kN·m/m; however, no limit state was reached as the crack width was around one-half the value used to define pipe serviceability and the maximum moment was around 70% of the theoretical ultimate capacity. The decrease in pipe demand from surface load with increasing soil cover is also quantified. At 400 kN of single-axle force, the crown moment decreased to 65% and 35% of the value at 0.3 m burial when the depth of soil cover was increased to 0.6 and 0.9 m, respectively.

Research on Mechanical Deformation of Thrust Bearing

Finite Element Method numerical simulation has been carried out to analyze mechanical deformation of thrust bearing under the point and line supporting condition. The simulation results indicate that the torsion deformation of the point supporting is the larger, torsion deformation is mainly radial bending deformation, and circumferential bending deformation is small, it becomes more and more obvious with the decrease of bearing pad length-width ratio under the same working conditions for the same pad. Line supporting torsion deformation is mainly the circumferential bending deformation, and the left and right sides are symmetrical along the circumferential, the radial bending deformation is small, torsion deformation related to the length and width of supporting, with their size increasing the torsion deformation decreased.

Spatial Electrostrictive Actuations of Flexible Circular Tubes

This paper is aimed to study dynamic actuation of circular tubular shell structures coupled with distributed electrostrictive actuator segments. A mathematical model of the hybrid elastic/electrostrictive circular tubular shell, including the electrostrictive/elastic/control couplings, is derived. The generalized electrostrictive control actuation induced by an arbitrary electrostrictive actuator segment consists of three contributing components: the circumferential membrane control action, the longitudinal bending control action, and the circumferential bending control action. In particular, spatial modal actuation characteristics of the total actuation and the three contributing components corresponding to various design parameters (e.g., actuator thickness, shell radius, and thickness) are evaluated and compared with respect to actuator patch sizes. Analysis data suggest that the electrostrictive membrane control actuation dominates the overall control action in lower shell modes; however, the control moment becomes important in higher shell modes. Optimal placements of electrostrictive actuator segments on the circular tubular shell are identified. Modal filtering behaviors, due to cancellation of internal attenuation/amplification effects, occur when large-size actuators are used, rendering the actuation less effective.

Failure of non-conventional composite pipes — an experimental and numerical approach

This paper discusses an experimental and numerical study to investigate the failure behavior of innovative and newly designed non-conventional cross-sectional fiber reinforced composite pipes subjected to internal pressure and bending loads. An adaptive filament winder for non-conventional pipes is exclusively designed and built to fabricate the test samples used in this investigation. Experiments are conducted on triangular and rectangular cross-sectioned samples as per ASTM standards to find the internal burst pressure, bending strength, and failure modes of the pipes. Numerical analysis for the pipe loading process has been developed based on the finite element method for linear orthotropic conditions for composite pipes. The finite element analysis is used to build the model and predict the stresses imposed on the non-conventional pipes. The relationships between the applied internal pressure and peak circumferential stress, bending load, and bending strength with reference to the fillet radius are determined; and generally a good correlation is found between the experimental and numerical results. This study has extended the use of non-conventional composite pipes in structural applications.

Experimental study of thin-walled TiNi tubes under radial quasi-static compression

TiNi tubes with various sizes and boundary constraints subjected to radial quasi-static compression were systematically studied. The contour curves of the tubes were extracted from the real-time charge-coupled device (CCD) images, and the circumferential strain, bending moment, and phase composition distribution were calculated based on the contour curves and some assumptions. It was found that the load–displacement curves had hysteretic loops, and all specimens could recover to their initial shape after unloading, which was attributed to the effects of austenite–martensite phase transformation and phase transformation hinges (THs). For single-tube experiments, the numbers of TH were observed to be twice the numbers of constraints. For vertical double-tube experiments, the main deformation of each tube was concentrated on its upper half circle. The energy dissipation rate (EDR) and the dissipated specific energy (SE) in single-tube case increased with decrease of the diameter–wall thickness ratio (DTR; D/ t) or increase of the constraint number. With a four-directional constraint condition and same D/ t, the EDR and SE of vertical double tubes were greater than that of a single tube and close-packed seven tubes. The present results could give a reference for designing repeatedly used shock-resistant element with higher energy absorption capacity.

Effect of Semi-Geodesic Winding on the Vibration Characteristics of Filament Wound Shells of Revolution

The effect of semigeodesic winding on the free vibration characteristics of filament wound shells of revolution is studied. For this purpose multisegment numerical integration technique is extended to the solution of the free vibration problem of composite shells of revolution which are wound along the semigeodesic fiber paths counting on the preset friction used during the winding process. Sample results are obtained for truncated conical and spherical shells of revolution and the effect of preset friction on the vibration characteristics of filament wound shells of revolution is particularly analyzed. Results show that when the preset friction is increased natural frequencies of higher circumferential vibration modes also increase irrespective of the initial winding angle, and the circumferential bending stiffness stands out as the dominant parameter governing the natural frequencies of higher circumferential vibration modes.

An Approach for the Analysis of Collapse Onset in Elastic Tube Flows

An experimental study conducted for the determination of the onset of collapse of an elastic tube of a Starling resistor conveying air is presented herein. The collapse was induced under the action of external pressure p e applied to the tube walls. The influence of length L, thickness h, and modulus of elasticity E of the tube on collapse were determined by using a variety of silicone rubber and latex-Penrose tubes. The experiments were conducted under the presence of constant upstream head with the absence of a longitudinal strain of the tube in a range of flow Reynolds number (Re) 16750 < Re < 70280. At each air flow rate Q through the tube, p e was increased gradually. The inlet and exit pressures of the tubes p 1 and p 2 were measured. The variation of Q with p e was used to determine the onset of collapse. The magnitude of p e at the onset of collapse was defined as p e,c. The visually observed collapse was associated with a flow rate reduction, followed by so-called oscillating and non-oscillating cases. The experimental data at the onset of collapse were expressed in terms of a correlation between Re (h/L) and a non-dimensional pressure parameter defined as (p e,c − p 2)/K p including circumferential bending stiffness of the tube K p.

FRP rupture strains in the split-disk test

The strengthening of concrete and concrete-filled steel columns by applying externally-bonded fibre-reinforced polymer (FRP) composite jackets has become a popular retrofit technique. Failure of such FRP-wrapped columns is usually governed by rupture of the FRP in the hoop direction. Two common material test methods have been used to obtain the hoop strength and rupture strain of FRP composites used in these applications: tensile tests of flat coupons and split-disk tests. The FRP rupture strain obtained from a split-disk test is usually less than that obtained from a flat coupon test, but there is neither a well-defined relationship between the two nor a comprehensive explanation for why they are different. This paper presents an investigation, using finite element (FE) analysis, into FRP hoop strains in the split-disk test with the aim of explaining possible reasons of the reduction of the FRP rupture strain in the test. The FE results show that the local strains in an FRP ring in a split-disk test are increased by the geometric discontinuities at the ends of the FRP and by circumferential bending of the FRP ring at the gap due to change of curvature there caused by the relative moment of the two half disks. The FRP ruptures once the strain at one of these locations reaches the FRP coupon rupture strain, leading to a lower apparent tensile strength than that obtained from flat coupon tests. The influence of parameters such as adhesive properties, FRP stiffness, geometry of the overlapping zone and FRP-to-split disk friction are examined.

Springback Variation Principles in Materials Forming Processes

The conceptions of springback anti-couple systems and equations are initially given. By the use of the weighted residual method to the springback anti-couple equations, the springback principles of minimum potential energy and minimum complementary energy are established. Meanwhile, the springback principle of minimum potential energy is applied to calculating springback deformations of a curved beam under the radial and circumferential forces and end bending moments.

Procedures for the strain based assessment of pipeline dents

A criterion for strain-based assessment of dents in gas pipelines has been recently proposed in the ASME B31.8 code. This work initially presents a critical review of the equations for estimating strains presented in Appendix R of that code. Next, a procedure based on B-spline curves is presented that interpolates dent geometry from data measured by in-line inspection (ILI) tools and evaluates strain components. The paper proceeds with studies to assess the influence of the ILI tool resolution and positioning on the estimation of the circumferential bending strain. Finally, the evaluation of longitudinal membrane strains is assessed by taking two alternative definitions for dent length that enters in the formula proposed in Appendix R of the aforementioned code, and comparing with results provided by Finite Element analyses. The comparison suggests that directions on how to measure the dent length might be incorporated in a revision of the ASME B31.8 Code.

Determination of Homeostatic Elastic Moduli in Two Layers of the Esophagus

The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt a theory based on small perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of 59.4 +/- 13.2 deg). The neutral axis was located 27% +/- 1.9%away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.

Finite element analysis under different boundary conditions of the filling of cylindrical steel silos having an eccentric hopper

A three-dimensional finite element analysis was made of the filling of cylindrical silos having an eccentric hopper, using different boundary conditions—silos supported at the transition or on discrete columns. The analysis included the options of the presence or absence of reinforcement in the transition and walls. The results for the pressures on the wall for a flexible wall and all the boundary conditions were compared with those for a silo with a rigid wall. The membrane stresses and meridional and circumferential bending moments were then evaluated in the silo wall and in the reinforcing elements. Lastly, the influence of the eccentricity of the hopper in a silo of intermediate eccentricity was analysed, and conclusions were drawn for the optimal design of these structures.

Elastic Buckling of Pontoons of Single Deck Floating Roofs subjected to Circumferential Bending Load

Elastic Buckling of Pontoons of Single Deck Floating Roofs subjected to Circumferential Bending Load

Load-Carrying Capacity of Circular Plates Made of a Fiber-Reinforced Composite

The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.

A magnetoelastic theoretical model for soft ferromagnetic shell in magnetic field

With the aid of a generalized variational method, in this paper, a theoretical model for soft ferromagnetic shells is derived to describe their magnetoelastic behavior in an applied magnetic field. Having made a quantitative comparison between the numerical predictions given by several theoretical models and the experimental results on strains of a cylindrical shell, we find that the predictions got by our model are in good agreement with the experimental data. It is also found that the Moon’s model is a special case of the model derived in this paper when the relative magnetic permeability μ r>10 4, which confirms that it is reasonable for the Moon’s model to calculate strains of the soft ferromagnetic shells. Having displayed the distribution of the equivalent magnetic force in the length of the cylindrical shell and its circumferential bending strains with different elastic end constraints, we give an explanation for the discrepancy between Moon’s analytical results and his experimental ones.

The design of bells with harmonic overtones.

Musical bells have had limited application due to the presence of inharmonic partials in the lower part of their acoustic spectra. A series of bells has been designed that contains up to seven partial frequencies in the harmonic series beginning at the fundamental frequency. This was achieved by choosing geometries for finite-element analysis models in which as many purely circumferential bending modes as possible occurred at frequencies below any mode with an axial ring node. The bell models were then fine tuned using gradient projection method shape optimization and the resulting profiles were cast in silicon bronze. A range of bell geometries and timbres is analyzed using psycho-acoustic models and is discussed in relation to European carillon bells.

A Timoshenko-beam-on-Pasternak-foundation analogy for cylindrical shells

A Timoshenko-beam-on-Pasternak-foundation model is developed for the analysis of thin elastic cylindrical shells. This model aims to bridge the gap between the Love–Kirchhoff theory and the approximate beam-on-elastic-foundation model of Vlasov (“long-wave” model), which accounts for only longitudinal stretching and circumferential bending. The new model improves on the assumptions of the “long-wave” model by accounting for the effects of two additional actions, namely, in-plane shearing and twist. The model is used to derive “explicit” design formulae for (1) the fundamental natural frequencies for vibration of a uniform cylindrical shell having six sets of end restraints, and (2) the circumferential modenumbers associated with the fundamental mode. A comprehensive comparative study of the predictions of both models against available results in the literature and results obtained by the finite-element method has shown that the proposed model significantly extends the limits of the validity of the “long-wave” model.

MICRO-SENSOR ELECTROMECHANICS AND DISTRIBUTED SIGNAL ANALYSIS OF PIEZO(ELECTRIC)-ELASTIC SPHERICAL SHELLS

Spatially distributed modal voltages and sensing signal generations of a distributed piezoelectric sensor layer bonded on spherical shells of revolution are investigated in this study. The generic sensing signal equation is derived based on the direct piezoelectric effect, the Gauss theory, the open-circuit assumption, the Maxwell equation and also the generic double-curvature thin shell theory. Owing to difficulties in analytical solution procedures, assumed mode shape functions based on the bending approximation theory are used in the modal signal expressions and analyses. Spatially distributed micro-electromechanical characteristics resulting from various meridional and circumferential membrane/bending strain components of infinitesimal sensor neurons are evaluated and major signal sources are identified. Analytical results suggest that the spatially distributed modal voltages clearly illustrate the distinct modal behaviour, similar to mode shapes. The major signal source of a free-edge hemispherical shell is the circumferential bending component. Accordingly, circumferential layout of distributed sensor strips would provide effective monitoring and diagnosis of free hemispheric shells.