Search

The simultaneous presence of bending moments and torques produced by the lateral and vertical contact forces between the wheel and the rail generates a complex strain state on the rail surface, which makes it difficult to identify the strain signals produced purely from the lateral contact force. In this study, a new strain gauge configuration is proposed to decouple strain signals of the wheel–rail lateral contact force from wayside measurements by analyzing the bending strains on the rail web using a full Wheatstone bridge. For this purpose, a finite element modeling of the wheel–rail contact is performed to analyze the bending strains on the rail web and to optimize two instrumented sections for eight electric resistance strain gauges. Laboratory testing is also used to examine the installation scheme of the strain gauges at the two optimal instrumented sections. A good agreement is observed between the experimental data and the simulation results. Strain signals are evenly distributed for about 10 cm in the middle region between the two optimal instrumented sections and only account for the lateral contact force.

Given the influence of near-fault vertical seismic action, we established a girder-spring-damping-rod model of a double-span continuous girder bridge and used the transient wave function expansion method and indirect modal function method to calculate the seismic response of the bridge. We deduced the theoretical solution for the vertical and longitudinal contact force and displacement response of the bridge structure under the action of the near-fault vertical seismic excitation, and we analyzed the influence of the vertical separation of the bridge on the bending failure of the pier. Our results show that under the action of a near-fault vertical earthquake, pier-girder separation will significantly alter the bridge’s longitudinal displacement response, and that neglecting this separation may lead to the underestimation of the pier’s bending damage. Calculations of the bending moment at the bottom of the pier under different pier heights and cross-sectional diameters showed that the separation of the pier and the girder increases the bending moment at the pier’s base. Therefore, the reasonable design of the pier size and tensile support bearing in near-fault areas may help to reduce longitudinal damage to bridges.

This paper presents a parameterized structural track model for the simulation of dynamic vehicle-turnout interaction in a multi body simulation environment. The model is demonstrated by performing simulations for different vehicle speeds, crossing geometries and fixations between crossing rail and sleepers with different stiffness. Results are presented for dynamic wheel-rail contact forces, bending moments in crossing rail and sleepers and sleeper-ballast contact pressure. The main conclusions are that (a) the peak dynamic bending moment in the sleeper under the crossing transition is significantly higher with a stiff direct fixing compared to a softer indirect fixing and (b) the structural loading in terms of bending moment in the crossing rail, bending moment in the underlaying sleeper and sleeper-ballast contact pressure increases proportionally and significantly with increased impact angle and vehicle speed for wheels passing over the crossing transition.

With the advancement of technology, various types of downhole tools have been developed. It is necessary to ensure that downhole tools can be tripped to the predetermined well depth through a drilling and completion string without any damage. However, mathematical models to predict the downhole tool deformation under axial loading are lacking. In this paper, an eccentric tube deflection model is established according to the geometric characteristics of downhole tools. First, six contact cases of an eccentric tube under axial loading in a curved wellbore are considered. The model solves the eccentric tube deflection in the different contact cases through the beam-column model and energy method. Second, using this model, the critical axial load in the contact cases is examined along with the deflection, bending moment, and contact force of the eccentric tube. The results show that the deflection, bending moment, and contact force of the eccentric tube are related to the contact case. The bending moment and contact force of the eccentric tube in wrap contact under axial compression are higher than those in other contact cases. In particular, when the eccentric tube is subjected to wrap contact under axial compression, the maximum bending moment and contact force increase sharply, and this aspect can help evaluate the accessibility of the downhole tool. Finally, this paper proposes a new method based on the eccentric tube deflection model to analyze the accessibility of a completion string in the context of eccentric downhole tools. The effectiveness of the proposed method is demonstrated through a field case.

Within the offshore oil and gas industry, the subsea pipelines in riser configuration are the main choice for petroleum transportation till the processing platform. The subsea pipeline is subject to considerable loads ranging from hydrodynamics forces from the sea current to seabed contact forces. Those contact forces are very important in risers design life, since high and concentrated bending moment stresses are observed in the region where the pipeline starts to be supported by the seafloor. The proper representation of the soil behavior in contact with the structure comprises a very important topic of study in subsea pipelines. In this context, a consistent pipeline–seabed interaction model based on Kerr-type foundation is presented. A finite element formulation for the soil, where the stiffness matrix is derived from a variational formulation of a three parameter elastic foundation model, is proposed. The pipeline is modeled as a planar beam undergoing large displacements using a co-rotational approach. The unilateral contact between soil and pipeline is dealt with a step-loading procedure. The proposed model is able to solve problems where the pipeline is initially placed above the foundation surface and subsequent contact with the seafloor is induced by large displacement of the structure. Numerical examples are presented in order to validate the foundation formulation and explore the proposed contact solution between a pipeline and the seabed. A static analysis of a steel catenary riser (SCR) is presented using the proposed soil–structure interaction model.

Based on theoretical analyses, the development of buckling mode of steel core is revealed for buckling restrained braces (BRBs) with fixed ends. The formulae are derived for the bending moments of the stiffening part of the core and restraining member of BRBs. Then a global stability design method of fixed-end BRBs is proposed. The results of the contact force, flexural response and buckling half wavelength with finite-element analysis agree with the theoretical analysis. The design criteria as well as the buckling half wavelength were validated by the quasi-static tests of five BRBs. Compared to existing methods, the proposed design approach can ensure a proper safety margin of the stiffening part.

The bolted-flange connection is a new application for mounting rectangular hollow section (RHS) columns in prefabricated multi-high-rise steel structures, which may bear the combination of bending moment and shear under permanent, live, wind loads or earthquake. The performance of the bolted-flange connection used in the structural column is different from that in its popular usage in the pipe because the subjected force is different. To investigate the bearing performance of a bolted-flange connection under the combination of bending moment and shear, this study conducted static tests and finite element analysis (FEA) of 12 column-to-column bolted-flange connections with different flange thicknesses, bolt edge distances, flange edge widths and bolt hole diameters, as well as one column without a connection. The test agreed well with the FEA, which verifies the FEA. The influences of the flange thickness, bolt edge distance, flange edge width and bolt hole diameter on the stiffness and strength of the connections, bolt tension and contact force were studied, and the failure mode and mechanism of the connection were obtained. A significant prying action occurred on the flange contact surface, increased the bolt tension in the tensile region, and caused the bolt shanks to experience tension and bending moment. The flange thickness had a large impact on the prying force, while other factors had less of an effect. Based on the yield line theory, the bearing mechanism of the connection was obtained. The formulas for the yield bearing capacity were proposed and were verified by the test and FEA.

The bolted-flange connection is used to connect rectangular HSS columns in prefabricated multi-story and high-rise steel structures. It may subject to coexisting axial compression, bending moments and shearing under the combination of dead, live, wind loads or earthquake action. The bearing performance is different from that of bolted-flange connections used in pipelines, towers and mast structures. To investigate the bearing performance of a connection subjected to coexisting compression, bending moments and shearing, static tests and a finite element analysis (FEA) were applied to 12 column-to-column bolted-flange connections with different flange thicknesses, bolt edge distances, flange edge widths and bolt hole diameters, as well as one column without connection. The effects of flange thickness, bolt edge distance, flange edge width, and bolt hole diameter on the stiffness and strength of connections, bolt tension levels, and contact forces between flanges were obtained as well as effects on the failure mode and mechanisms of the connections. Flange thickness was found to have a considerable impact on the performance of connections, while the bolt edge distance and flange edge width were found to have a lesser effect. The FEA results agree well with the test results, verifying the finite element model (FEM). Some performance results that could not be obtained through testing were obtained. Based on yield line theory and T-stub analogies, the load transfer mechanism of bolted-flange connections was obtained and formulas for yield-bearing capacity are proposed. The results obtained from the formulas agree well with the test and FEA results.

The vertical dynamic interaction between a railway vehicle and a slab track is simulated in the time domain using an extended state-space vector approach in combination with a complex-valued modal superposition technique for the linear, time-invariant and two-dimensional track model. Wheel–rail contact forces, bending moments in the concrete panel and load distributions on the supporting foundation are evaluated. Two generic slab track models including one or two layers of concrete slabs are presented. The upper layer containing the discrete slab panels is described by decoupled beams of finite length, while the lower layer is a continuous beam. Both the rail and concrete layers are modelled using Rayleigh–Timoshenko beam theory. Rail receptances for the two slab track models are compared with the receptance of a traditional ballasted track. The described procedure is demonstrated by two application examples involving: (i) the periodic response due to the rail seat passing frequency as influenced by the vehicle speed and a foundation stiffness gradient and (ii) the transient response due to a local rail irregularity (dipped welded joint).

Buckling of concentric tubular strings in pipe is an essential problem in the fields of medical, biological, and nanomaterials, especially in petroleum engineering. Completely different from the buckling of the classic Euler compression columns, the buckling of concentric tubular strings involves geometric nonlinearity and contact nonlinearity, and has more complicated geometric deformations and buckling configurations. In this paper, a finite element method combining the spatial beam element and the two-layer contact gap element is proposed, and a virtual transient dynamic method is introduced to solve the static buckling of concentric tubular strings. The internal concentric tubular strings are discretized into spatial beam elements, and the contact relationships between tubular strings are described by two-layer contact gap element. Meanwhile, the larger damping is used to attenuate the dynamic response of the system, so as to find the static part of the transient dynamic solution. Appropriate damping and element length are determined by numerical simulation. The structural characteristics and contact states of eight post-buckling configurations are studied. The helix pitch values of specific configurations are in good agreement with the theoretical solutions. In addition, the distribution of bending moment, shear force and contact force in various post-buckling configurations is studied. For the full helical buckling, it is found that there is only one non-contact section in the transition section of inner tube and two non-contact sections in the transition section of middle tube. The research results of this paper provide a theoretical basis and reference for further study on the buckling of multi-layer concentric tubular strings.

Summary A new concept is proposed in the local tubular mechanical model, which provides a more-sophisticated description of tubular mechanical behaviors from a local perspective. The principles and assumptions for the local mechanical model are presented. Under these assumptions, the mechanical behaviors of tubular strings with connectors under nonbuckling/lateral-buckling, interhelical-buckling, and intrahelical-buckling modes in vertical and inclined wellbores are studied. The critical interhelical-buckling and intrahelical-buckling loads are deduced with the assumed load-displacement curve and potential-energy factor. The contact states under every buckling mode are divided into no contact, point contact, and wrap contact, and the critical contact loads are deduced with critical contact conditions. The results of critical buckling loads, critical contact loads, contact forces, and maximum bending moments are compared, and these results are given in explicit forms for the convenience of application. The results show that buckling mode transforms from nonbuckling/lateral buckling to interhelical buckling to intrahelical buckling, and contact state transforms from no contact to point contact to wrap contact with the increase of axial force. The effects of connectors on buckling behaviors are determined by both the geometric and mechanical parameters of tubular strings with connectors. Connectors can inhibit the buckling problem and increase the axial force and torque transfer, but may increase the possibility of tubular failure. Therefore, these two effects of connectors should be considered comprehensively in the optimal design of connectors on tubular strings.

Instability of structural members under axial compression probably leads to collapses of space grid structures. Therefore, a sleeved column has been to improve the stability of the axially compressed member. This paper presented a theoretical investigation of the behavior of the sleeved column considering the extension of the inner core, focusing on the deformation process of point contact and line contact between the inner core and the sleeve. Equilibrium differential equations were established for the cases when in the state of point contact and line contact, and the expressions were derived for responses such as deflection, shearing force, bending moment and contact force of the sleeved column. The two models considering the extension of the inner core could accurately predict the mechanical properties of the sleeved column. The most important factor on the end of the sleeved column was the length of the extension of the inner core with the parametric analysis. Empirical formulas of the force at the end of the sleeved column were obtained through regression analysis, providing a basis for the design of the end part of the sleeved column.

Helical buckling of tubular strings with connectors is divided into two sub-problems: inter-helical buckling and intra-helical buckling. The suspended section of the tubular string is depicted by beam-column model and the continuous contact section is depicted by helix. Further introducing the continuous conditions, boundary conditions and periodic conditions, the deflection curves of tubular strings can be determined. On the basis of energy stability condition, the critical helical buckling loads are deduced by introducing the potential energy factor. The contact forces on contact points and continuous contact sections and maximum bending moments on tubular strings are calculated. The above studied are further applied into a case study. At last, the supporting effect and boundary effect caused by connectors are introduced and the relationship between inter-helical buckling and intra-helical buckling modes is clarified. The results indicate that for connectors of smaller diameters, the supporting effect plays the most important role and inter-helical buckling is easier to initiate. However, for connectors of larger diameters, the constraint effect is dominant and intra-helical buckling is more likely to occur. Increasing connector diameter and decreasing the length between adjacent connectors can increase critical helical buckling loads. Both the contact forces and maximum bending moments in the intra-helical buckling mode are larger than that in the inter-helical buckling mode, so intra-helical buckling should be avoided in the optimal design of connectors on tubular strings.

When the sinusoidal buckling of suspended tubular strings is transforming to helical buckling, the deformation changes drastically, which makes the tubular strings extremely unstable. The quantitative description of this buckling configuration in previous theoretical studies is not precise enough. In our current study, dynamic relaxation method is applied to carry out numerical simulation of buckling transition of suspended tubular strings. To obtain stable buckling configurations, larger Rayleigh damping is used to attenuate the dynamic effect. With the increase of axial compression load, the lateral buckling of the suspended strings suddenly becomes spiral shape with two contact points. As the string length increases, the position of the lower contact point remains almost at the same position. While the upper contact point gradually moves upward, and the helix angle between the two points increases and gradually tends to be constant. The maximum contact force is located at the lower contact point, the maximum shear force is located at the bottom of the strings, and the dimensionless distance between the location of the maximum bending moment and the well bottom is about 1.0. These loads, including the maximum contact force, maximum shear force and maximum bending moment, gradually decrease with the increasing string length and tend to be constant. The dimensionless critical load is reduced from 4.41 to 3.81 with the effect of string length. The critical load calculated in this paper is the minimum value when helical buckling just occurs. The results obtained in the current study have wide engineering applications, particularly in failure analysis and prevention of helical buckling.

A new model depicting the buckling configuration of a tubular string in a three-dimensional curved wellbore is proposed. During modeling, the toolface angle is considered, and the sinusoidal buckling and helical buckling of the tubular string are considered on the basis of alignment with either the lower curved side or the outer curved side of the wellbore. After modeling, the energy method is used to solve the model, and the critical buckling load, which is related to the relationship between the buckling configuration and the axial load, can be obtained. The critical buckling loads calculated using the model presented in this paper are consistent with the measured data from published experiments and the trends of the He and Kyllingstad model. The results of the new model also show that with an increasing wellbore curvature, the influence of the toolface angle on the critical buckling load and the characteristic parameters of the buckling configuration (wavelength, amplitude, and pitch) decreases. Based on the expressions for the quantitative relationships between these characteristic parameters and the axial load, procedures for calculating the contact force and the bending moment are given. The results for the contact force show that the calculated values from the Johancsik et al. model and the Mitchell model are the average values calculated using the procedures presented in this paper for tubular strings under sinusoidal buckling and helical buckling, respectively. The calculation results show that the influence of the toolface angle on the bending moment of a tubular string under helical buckling is less than that under sinusoidal buckling. By using this model, not only can the critical buckling loads, contact forces and bending moments of tubular strings in three-dimensional curved wellbores be calculated, but the trends of these calculated values with the buckling configuration can also be identified to guide the selection of the control parameters for tubular strings in the field.

Aim of the present work is to build a link between a structural theory for large-scale analyses of three-dimensional cable structures undergoing, in general, large displacements and rotations, and a refined mechanical description of metallic strands, fully accounting for their composite nature and hysteretic bending behavior. A new formulation for metallic strands is presented. The strand overall mechanical behavior is modeled according to the Euler–Bernoulli beam theory. A constitutive law relating the cross sectional generalized stresses and strains of the adopted structural model is obtained by summing over the individual contributions of wires. Each wire in the strand is individually modeled as a curved thin rod. Kinematic equations are proposed to relate the wire generalized strain variables to those of the strand cross section. The equilibrium of the individual wires is analyzed under the hypothesis of radial contact between adjacent layers taking, most notably, also into account the effects due to the residual radial contact forces induced by the strand manufacturing process. Deformations of contact surfaces are neglected and friction is accounted for, through the Amontons–Coulomb law, in the study of the stick-slip conditions. The proposed sectional model accounts for some distinctive characteristic aspects of wire ropes, such as the coupling between axial force and torque and the non-linear, and non-holonomic, relation between bending moment and curvature, which is a consequence of sliding of wires. The performance of the proposed formulation is assessed with reference to well-documented physical tests and established analytical formulations. Moreover, the role of the residual contact forces due to the stranding process, on the bending behavior of a typical multi-layer strand is assessed.

This paper builds an analytical model to describe the comprehensive buckling behavior of CT (coiled tubing) with residual bending in a horizontal well. The new model is built on the basis of beam-column theory and solved by the Galerkin method of weighted residuals. The initial configuration of CT with residual bending are assumed to be in two typical trigonometric shapes, sine mode or cosine mode. By using the new buckling equations, critical buckling force and radial contact force are calculated accounting for the residual bending. Axial compressive displacement and maximum bending moment are also calculated. The calculation results show that a CT with residual bending behaves more easily to buckle than a straight CT, and the maximum contact force of CT with residual bending is larger than that of straight CT. As for the two initial trigonometric shapes, the sinusoidal critical buckling force of these two initial modes is almost the same, but CT with initial cosine mode tends to buckle easier than CT with initial sine mode in helical buckling. To verify the proposed model, the results of this paper are compared to Salies's experimental results, which support the proposed solutions. The comparison between buckling solutions of CT with residual bending and CT without residual bending show that the effect of residual bending on CT cannot be ignored in buckling analysis.

The paper deals with non-linear analysis of a telecommunication tower with circular flange-bolted connections (CFBCs). They are composed of two flanges, welded to the structural tubes, and then connected together with pre-tensioned bolts. A rigorous FEM analysis is performed for finding the connection stiffness in two cases. One deals with all bolts undamaged and the second one with one or more bolts broken. The analysis, which includes contact and friction forces, shows that when joints are under tension, the bolts are not only subjected to axial forces, but also to bending moments due the prying effect. The value of stresses caused by bending depends strongly on the bolt pre-tension and flange thickness. Removing one of the six connection bolts significantly increases stresses in the remaining bolts. Knowing the behaviour of the connection, it is possible to study the behaviour of the whole structure. This is achieved by applying the multilevel substructuring approach. The first levels is related to the flanges and bolts, whereby the connection model is simplified, and compared with the rigorous one, the second level is related to the assembly of the whole tower. The paper is illustrated with several examples of connections of different thicknesses, and different bolt pre-tensions. The considered tower comes from a real design.

In this study, finite element analyses of masonry infilled frames using a general purpose FE program, ABAQUS, were conducted. Analysis models consisted of the bare frame, infilled frames with masonry wall thickness of 0.5B and 1.0B, respectively. The masonry walls were constructed using the concrete bricks which were generally used in Korea as infilled wall. The material properties of frames and masonry for the analysis were obtained from material tests. However, four times increased the tensile strength was used for 1.0B wall, which is seemingly due to the differences in locating the bricks. The force-displacement relation and development of crack from the FE analysis were very similar to those from the experiments. From the FEA results, contact force between the frame and masonry, distribution of shear force and bending moments in frame members were analyzed. Obtained contact stress shows a trianglur distribution, and the contact length for 0.5B speciment and 1.0B specimen were close to the value estimated using ASCE 41-06 equation and ASCE 41-13 equation, respectively. Obtained shear force and bending moment distribution seems to replicate actual behavior which originates from the contact stress and gap between the frame and masonry.

This paper addresses the formulation and implementation of a contact algorithm for circular pipes within elliptic and spiralled wellbores using nonlinear finite element analysis. The need for such a capability originates from drilling applications in oil industry. Normally, the drilling bits have circular cross sections and the intention is to drill perfectly circular holes. However, it is quite common that the drilled wellbores show irregularities. This study derives the formulations to calculate the clearances between the pipes and such boreholes, which are essential to detect contact and calculate the associated contact forces. The formulations are described in detail and the implementations and flowcharts are provided as well. A case study is presented to reveal the implications to have such capabilities within a finite element engine, such as capturing the damage on the drillpipes in terms of bending moments.

The piles of channel bridges generally exist in the form of steel casing composite piles (SCC pile, namely, the reinforced concrete pile wrapped by steel casing) owing to construction factors, such as drilling and temporary platforms. To investigate the effect of steel casings on the behaviors of the original reinforced concrete (RC) piles, and to clarify the reasons for this effect, we conducted a lateral loading experiment on three sets of piles. The three sets of piles included a set of RC piles, a set of SCC piles with partially set steel casings, and a set of piles with fully set steel casings. Each set comprised two identical specimens. In addition, to provide a theoretical basis for determining appropriate parameters for steel casings in practice, parameter analysis was conducted by numerical modeling. The results indicated that the contact force between the steel casing and the RC shaft directly caused the transformation of failure mode of the pile. When the length of steel casing was insufficient, the accumulated contact force resulted in great shear force and bending moment in the uncased RC shaft, and the failure mode of the pile would transform from bending to bending-shear failure. The mechanical behaviors and failure modes of SCC piles were significantly affected by the relative position between the steel casing and the equivalent plastic zone of the original RC shaft. Only if the equivalent plastic zone of the original RC shaft was wrapped by the steel casing, the critical state would be governed by the steel casing, and the bearing capacity and toughness of SCC pile would be significantly improved. Moreover, a fitting formula of the optimum length-to-diameter ratio for a steel casing was proposed, and the most unfavorable length-to-diameter ratio was discussed.

The contact force distribution between the core member and the external member of a buckling-restrained brace (BRB) is closely related to its deformation mode, and it directly affects the working state of the extended core and external restraining member. This study focuses on a pinned BRB with extended core as a research object and investigates the stress state of a BRB. Based on the specified core deformation modes and contact force distributions, the contact force and the bending moment distribution in the external member are deduced. Lastly, by considering the mechanical characteristics of the external member and extended strengthened core region (ESCR), their strength design criteria are established. In the theoretical derivation of the design method, the influence of some parameters is considered, including the initial geometrical imperfection of the external member, the gap between the core and the external member, the rigidity reduction of the restrained strengthened core region (RSCR), and the change of contact position. Finite element numerical verification of the corresponding theoretical derivation is discussed in detail in another paper as Part II (Jiang et al., 2015).

The theoretical derivation from Part I (Jiang et al., 2015) has obtained the core contact force and the bending moment distribution of the external member in the single-wave core deformation mode. In addition, the design criteria of the external member and the strengthened core region (SCR) have also been obtained based on the understanding of the mechanical characteristics of the buckling-restrained brace (BRB). Based on the theoretical results from Part I, this study conducts the corresponding finite element (FE) numerical verification, and the BRB parameter analysis is also performed when the core deforms as a single-wave deformation. The influence of nine parameters on the core contact force and the external member stress is investigated. These parameters include the flexural rigidity of external member, the initial imperfection of external member, the core thickness and its width-to-thickness ratio, the pinned connector length, the external member length, the length of restrained strengthened core region with uniform section and the height of the wing-plate of the SCR, as well as the gap between the core and the external member. Lastly, the 12 examples of BRBs that are designed according to the proposed design criteria are analyzed using FE simulation, and the reliability of the theoretical derivation is also verified.

Kinds of tubular strings are widely applied to oil exploration & development. In the preceding studies, theses tubular strings are usually taken as homogeneous thin rods without connectors constrained in a straight cylinder or torus. Recent studies have indicated that the effect of connectors on the tubular strings is ignorable. On the basis of the previous studies, the paper provides an analytical model describing the helical buckling behaviors of a rod with connectors constrained in a torus. The new model is solved based on beam-column model and minimum potential energy theory. There are three contact cases between the rod and the torus, namely no contact, point contact and wrap contact. The deflections of the rod and critical conditions between different contact cases are calculated. The results show that the deflections and critical conditions are quite different when the equivalent torus curvature radius changes. The effects of equivalent torus curvature radius, rod buckling and connectors on bending moment and contact force are analyzed. The results show that connector is an important factor which should not be neglected.

The force affect factors of anchor anti-slide pile in slope reinforcement under seismic load are studied in this paper. First of all, the method of dynamic analysis is introduced in FLAC3D. At the same time, seismic wave is selected in seismic dynamic analysis. Then, the sensitivity influence of anti-slide pile design parameters on dynamic contact stress, shear force and dynamic bending moment is analyzed by applying the seismic wave, giving the most significant effect factors of the dynamic contact stress and dynamic moment. In the end, the distribution regular of the contact force and the pile body stress under earthquake action is analyzed by selecting a case, laying a theoretical foundation for the further study of the dynamic performance of the reinforced slope.

Kinds of tubular strings are widely applied to the development of oil and gas fields. Most of these tubular strings constrained in straight or curved wellbores can be taken as homogeneous thin elastic rods constrained in straight cylinders or tori. Recent studies have shown that connectors on the tubular strings play an important role on the tubular string deflection problem. On the basis of previous studies, this paper provides a new model to describe the deflection behaviors of a tubular string with connectors constrained in a curved wellbore. The axial force on the ends of the tubular string is divided into axial tension and axial compression. The deflection state is divided into no contact, point contact and wrap contact according to the radial displacement of the tubular string or divided into initial configuration, sinusoidal buckling and helical buckling configurations according to the angular displacement of the tubular string. The critical conditions between no contact and point contact, between point contact and wrap contact in the initial configuration are studied. The deflection curves under the three contact cases in the initial configuration are obtained. These results show that the deflections curves and critical conditions are closely related to the tubular string weight and wellbore curvature. The effects of tubular string weight, wellbore curvature, connectors and axial force on bending moment and contact force are also analyzed at last.

This paper investigates the buckling mechanism of the steel core of buckling-restrained braces. The development of buckling mode is revealed with increasing axial load. The formulae of the maximum contact force and the maximum bending moment of the restraining member are obtained. The analytical results are validated by the finite element analysis. Compared to the results by conventional analysis, the number of contact points or buckling waves is much less; for hinged ends, the contact force for the lower mode is the identical while the contact force for higher modes is 1/4 lower; for fixed ends, the contact force is half of the conventional method.

Many coiled tubing(CT) operations involve passage through the production tubing. However, due to the adverse wellbore trajectory or tubing geometries, especially in helically buckled tubing, the CT operations are still encountering various bottlenecks when it is pulled or lowered through the tubing. In this paper, a new concept "local model", which provides a sophisticated description of CT deflection in buckled tubing from local perspective, is proposed to help supplement the integral torque-drag model. Firstly, the CT can pass through the buckled tubing freely without any deformations. According to the constrained geometric relationship between the tubing and CT, the maximum CT length and maximum outside diameter can be calculated. Secondly, when the CT dimension parameters are beyond the scope of the above rigid dimension, the CT can pass through the tubing flexibly with deformations. So a beam-column model is established to analyze the CT deflection and bending behavior in snaky and helically buckled tubing. The results show that the buckled tubing configurations have significant effects on the CT passage dimension. Once the CT dimension parameters are out of the range of rigid dimension, it would contact the tubing at some points with large buckled tubing amplitude. Moreover, the contact forces and bending moments are influenced by the axial force and buckled tubing amplitude. This "local model" analysis results can be implemented in the torque-drag modeling to optimize the CT extended reach and axial force transfer.

International audience; The transient dynamic response of a steel beam-column subjected to impact loading is a complex phenomenon involving large localized plastic deformations and non-smooth contact interactions. Exposed to high intensity of the contact force generated from impact, the beam-column may undergo large displacement and inelastic deformation. Previous research has shown that a calibrated elasto-plastic single degree of freedom system is able to reproduce both the displacement and the force time-history of a steel beam subjected to non-impulsive loading or low-velocity impact. In these models, the static force-displacement curve is derived from either experiments or detailed 3D nonlinear analysis. Tri-linear resistance function has been extensively used to reproduce the different stages of the response including catenary effects. A rigorous treatment of such a complex problem calls for the use of non-smooth analysis tools to handle the impulsive nature of the impact force, the unilateral constraint, the impenetrability condition and the discontinuity of the velocity in a rigorous manner. In this paper, we present a non-smooth elasto-plastic single degree of freedom model under impact loading that permits the use of arbitrary resistance function. Adopting the non-smooth framework offers tools such as differential measures and convex analysis concepts to deal with unilateral contact incorporating Newton's impact law. The mid-point scheme is adopted to avoid numerical unrealistic energy decay or blowup. Furthermore, the non-penetration condition is numerically satisfied by imposing the constraint at only the velocity level to guarantee energy momentum conservation [1]. The explicit expression of resistance functions of the beam that are used in the SDOF model are obtained from a simplified nonlinear static analysis of two beam-column models. In the analysis, a linear relation between normal force and bending moment is assumed for the plastification of the hinges. Two proposals to simplify the explicit expressions of the model's response behavior are given. Performing an energy-based analysis, we predict maximum displacement that is needed to absorb the kinetic energy arising from the impact for different coefficient of restitution. The numerical examples underline the validity of the model by showing good agreement with the predictions of reference models. (C) 2017 Published by Elsevier Ltd.

This paper presents a refined analytical solution for pipe-laying on an elasto-plastic seabed. The solution builds on previous work, extending it to include elastic rebound of the pipe. The approach simplifies the pipeline as the combination of four segments: a natural catenary through most of the water column; a boundary-layer segment in the water close to the seabed where the bending stiffness of the pipe modifies the shape of the catenary; a beam under uniform tension through the touch down zone up to the point where maximum pipe–soil load concentration occurs, within which the soil responds plastically; and finally a rebound segment, also modelled as a beam under uniform tension, where the soil rebounds elastically as the pipe–soil contact force reduces back to the submerged pipe weight. Continuity of displacement, gradient, bending moment, shear and deduced tension along the pipeline are preserved. In comparison with previous models, such as a rigid-plastic seabed model, the distribution of seabed resistance is continuous. Results from the solution are presented for the case of seabed resistance to pipe penetration increasingly proportionally with depth, as is approximately the case at very shallow depths within the seabed. The lower the gradient of seabed resistance, the greater is the pipe embedment, but the maximum contact force and curvature of the pipe both reduce. Analyses also show that the rebound stiffness can have a marked effect on pipeline embedment, which increases with increasing rebound stiffness. However, the effect on pipe embedment becomes small beyond a certain ratio of rebound stiffness to shear strength.

Kinds of tubular strings with connectors are widely used in petroleum exploration and development field. In previous research, tubular strings are usually treated as homogeneous thin elastic rods constrained in a cylinder and few studies have been made on the effect of connectors. This paper builds a model to describe the sinusoidal buckling behaviors of a rod with connectors. The three-dimensional buckling problem is divided into two lateral buckling problems in two mutual-perpendicular planes and the buckling solutions are obtained by solving the two lateral buckling equations. There are two buckling states for the rod, including initial plane configuration and sinusoidal configuration. And there are three contact cases between the rod and the cylinder, including no contact, point contact and wrap contact. The critical condition from initial plane configuration to sinusoidal configuration is approximately obtained from the results of no connector rod, and the critical conditions between different contact states are obtained by solving the model numerically. The effects of geometric parameters of the connectors and weight of the rod on critical conditions are analyzed. For the no contact and point contact cases, the deflection curves of a rod in the initial plane configuration and sinusoidal configuration are calculated in this paper. The effects of connectors on bending stress and contact force of the rod are analyzed. The results indicate that buckling states and contact states depend on the combination of the dimensionless axial compression K u , the ratio of rod/cylinder radial clearance to connector/cylinder radial clearance K r and the dimensionless weight per unit length of the rod μ . Compared with the no connector case, connectors have a great influence on the deflection curve, bending moment and contact force of the rod. All the results from the model indicate that the effects of connectors cannot be ignored in sinusoidal buckling analyses.

A T-stub is a component comprising a T-section with two bolts attached to its flange. It can be used to analyze the mechanical behavior of high-strength bolts in tension. In this study, the mechanical behavior of bolts was assessed via six static tests and 17 finite element analysis models. The effects of the thickness of the flange, the length of the inner and outer flange, and the diameter of the bolt were studied. With the exception of outer flange length, the parameters significantly affected the bolt bending moment, yielding load, and T-stub failure mode. Both the tests and the finite element analyses indicated that when the bolts yielded, the bending stress could reach 13% to 45% of the total tensile stress in the samples. It is not advisable to design bolts without considering the effect of the bending moment. A stable bending moment distribution relationship was also found between the bolt and the outer flange. The bending moment of the joint, the bending moment ratio of the bolt to the joint, and the distance from the contact force center to the bolt center are also discussed. Lastly, a new T-stub connector model and calculation method were proposed and proven to be reliable. This method is based on the theory of moment distribution and does not require the prying force to be calculated.

With the hypotheses of small deformation and Bernoulli-Euler beam, a gap element is introduced to describe the contact between the circular column and the external cylinder. The dynamic relaxation method is used to calculate the static equilibrium of the twisted column constrained by the cylinder. The post-buckling modes of a torsional column in a cylinder are investigated for the deformation configurations of one-point, two-point, three-point, and point-line-point contact. It is found that the end constraint has an effect on the length of the two suspended sections of helical buckling mode, but has no effect on the length of the continuous contact section in the middle. The relations have been derived among critical torque, post-buckling modes, lengths of each section, and loads (including shear, bending moment, and contact force). Finally, the torsional buckling has been investigated for sucker rods and drill pipes with lengths of 1 km. It is found that the helical buckling of multiple pitches occurs. The results of the current study provide theoretical guidance for the design of centralizer spacing in oil and gas engineering applications.

The mechanism of vertebral shear failure is likely a bending moment generated about the pars interarticularis by facet contact, and the moment arm length (MAL) between the centroid of facet contact and the location of pars interarticularis failure has been hypothesised to be an influential modulator of shear failure force. To quantitatively evaluate this hypothesis, anterior shear of C3 over C4 was simulated in a finite element model of the porcine C3-C4 vertebral joint with each combination of five compressive force magnitudes (0-60% of estimated compressive failure force) and three postures (flexed, neutral and extended). Bilateral locations of peak stress within C3's pars interarticularis were identified along with the centroids of contact force on the inferior facets. These measurements were used to calculate the MAL of facet contact force. Changes in MAL were also related to shear failure forces measured from similar in vitro tests. Flexed and extended vertebral postures respectively increased and decreased the MAL by 6.6% and 4.8%. The MAL decreased by only 2.6% from the smallest to the largest compressive force. Furthermore, altered MAL explained 70% of the variance in measured shear failure force from comparable in vitro testing with larger MALs being associated with lower shear failure forces. Our results confirmed that the MAL is indeed a significant modulator of vertebral shear failure force. Considering spine flexion is necessary when assessing low-back shear injury potential because of the association between altered facet articulation and lower vertebral shear failure tolerance.

Pebble bed reactors (PBR) are graphite-moderated, gas-cooled nuclear reactors. PBR reactors use a large number of spherical fuel elements called pebbles. From mechanical point of view, the arrangement of “small” spherical fuel elements in a container poses the same problem, as the so-called silo problem in powder technology and agricultural engineering. To get more exact information about the contact forces arising between the fuel elements in static and dynamic case, we simulated the static case and the effects of an earthquake on a model reactor by using discrete element method. We determined the maximal contact forces acting between the individual fuel elements. We found that the value of the maximal bending moment in the central reflector beam has a high deviation from the average value even in static case, and it can significantly increase in case of an earthquake. Our results can help the engineers working on the design of such types of reactors to get information about the contact forces, to determine the dust production and the crush probability of fuel elements within the reactor, and to model different accident scenarios.

We investigate the stress-strain state of an infinite isotropic plate with a crack the faces of which are free of external loading. The plate is under the action of concentrated bending moments. It is assumed that the crack faces are in a smooth contact along the entire length of the crack in the two-dimensional zone of constant width near the upper base of the plate. As a result of the contact of the crack faces, a solution of the problem is presented in the form of solutions of two related problems: a plane problem of the theory of elasticity and a problem of bending of plates using the Reissner theory. Using methods of the theory of functions of complex variable and complex potentials, we obtain a system of singular integral equations and numerically solved this system by the method of mechanical quadratures. In the case of geometric and physical symmetry of the problem with respect to the crack, we perform the numerical analysis of a solution of the problem and plot graphic dependences of the contact force between the faces of the crack and moment intensity factors for different parameters of the problem.

Pedestrian upper leg impact protection is a challenging requirement in the Euro NCAP assessment. In upper legform to bonnet leading edge tests, the legform impact force, the legform intrusion and the injury parameters (impact force and bending moment measured on the upper legform) are highly related to design of vehicle front-end styling and structure, as well as clearance underneath bonnet leading edge. In the course of impact, the contact area variation has significant influence on the stress distribution and consequently the force and the bending moment on the upper legform. Using finite element simulations of upper legform impact with a typical sedan, the deformation of the legform and the vehicle structure, and the variation of the contact force distribution are characterized and analyzed. Based on the study, a method for calculating the contact force is put forward by assuming a shape of the contact zone on the upper legform and a stress distribution function within the contact zone. The calculation method is verified using a simplified model of vehicle front-end structure developed in a previous study. Then a parametric study is conducted using the simplified vehicle front-end model to study influence of key design variables. The results of the parametric study, to some extent, have revealed relationship among vehicle front-end design parameters such as styling, geometry and stiffness, contact characteristics such as the maximum stress on outer foam, and the injury parameters (mainly the impact force). Language: en

During the cold rolling forming of non-symmetric Z-section steel, the twist will appear because two sides of the blank suffering bending moments of the same direction. In this paper, simplified FE model was used to simulate the closing process of the rolls. The contact forces of the rollers on blank, and the stress and strain of the blank was obtained by FE analysis, and relations between section torque and the position angle θ as studied and the result that when θ=100 the torque is minimum was discovered. The further detailed calculations showed that angle θ was only correlative with the geometry of the product section and didn’t change with the altering of material properties.

Interaction of a moving nanoparticle with a single-walled carbon nanotube (SWCNT) is of concern. The SWCNT is simulated by an equivalent continuum structure (ECS) under simply supported boundary conditions. The moving nanoparticle is modeled by a moving point load by considering its full inertial effects and Coulomb friction with the inner surface of the ECS. The ECS under the moving nanoparticle is modeled based on the Rayleigh, Timoshenko, and higher-order beam theories in the context of the nonlocal continuum theory of Eringen. The dimensionless discrete equations of motion associated with the nonlocal beam models are then obtained by using Galerkin method. The effects of slenderness ratio of the ECS, ratio of mean radius to thickness of the ECS, mass weight and velocity of the moving nanoparticle, and small scale parameter on the dynamic response of the SWCNT are explored. The capabilities of various nonlocal beam theories in capturing the longitudinal and transverse displacements as well as the nonlocal axial force and bending moment are also scrutinized in some detail. The possibility of moving nanoparticle separation from the inner surface of the SWCNT is examined by monitoring the sign of the contact force. Subsequently, the role of important parameters on the possibility of this phenomenon is explored using various nonlocal beam theories.

Different modes of load applications are used to simulate flexion and extension of the upper body. It is not clear which loading modes deliver realistic results and allow the comparison of different studies. In a numerical study, a validated finite element model of the lumbar spine, ranging from the vertebra L1 to the disc L5-S1 was employed. Each of six different loading modes was studied for simulating flexion and extension, including pure moments, an eccentric axial force, using a wedged fixture, and applying upper body weight plus follower load plus muscle forces. Intersegmental rotations, intradiscal pressures and facet joint contact forces were calculated. Where possible, results were compared to data measured in vivo. The results of the loading modes studied show a large variance for some values. Outcome measures such as flexion angle and intradiscal pressure differed at a segment by up to 44% and 88%, respectively, related to their maximum values. Intradiscal pressure is mainly determined by the magnitude of the applied compressive force. For flexion maximum contact forces between 0 and 69 N are predicted in each facet joint for different loading modes. For both flexion and extension, applying upper body weight plus follower load plus muscle forces as well as a follower load together with a bending moment delivers results which agreed well with in vivo data from the literature. Choosing an adequate loading mode is important in spine biomechanics when realistic results are required for intersegmental rotations, intradiscal pressure and facet joint contact forces. Only then will results of different studies be comparable.

The influence of under sleeper pads (USP) on dynamic train–track interaction is investigated in a parameter study. Two numerical models that are valid in different frequency intervals are used. The time-domain model DIFF is used to study wheel–rail contact forces, rail bending moments, rail vibrations (displacements, velocities and accelerations), sleeper vibrations and loads on sleepers at high frequencies, here 50–3000 Hz. The frequency-domain model GroundVib is adopted to calculate sleeper vibrations at low frequencies. Frequency-dependent material properties of rail pads, USP and ballast/subgrade are accounted for by viscoelastic spring–damper models that are calibrated with respect to measured data. It is found that USP influence dynamic train–track interaction mainly in the frequency range 0–250 Hz. Similar sleeper responses are calculated by the two models, although some differences in magnitudes are present.