Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.

Finite element analysis of spatial curved beam in large deformation

For the purpose of carrying out the large deformation finite element analysis of spatial curved beams,the total Lagrangian（TL）and the updated Lagrangian（UL）incremental formulations for arbitrary spatial curved beam elements are established with displacement vector interpolation,which is improved from component interpolation of the straight beam displacement.A strategy of replacing the actual curve with the isoparametric curve is used to expand the applications of the UL formulation.The examples indicate that the process of establishing the curved beam element is correct,and the accuracy with the curved beam element is obviously higher than that with the straight beam element.Generally,the same level of computational accuracy can be achieved with 1/5 as many curved beam elements as otherwise with straight beam elements.

Analysis of plane strain bending of a strain hardening curved beam based on unified yield criterion

The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. The solutions for the mechanical properties of plane strain bending are derived, which are adapted for various kinds of non-strength differential materials and can be degenerated to those based on the Tresca, von Mises, and twin-shear yield criteria. The dependences of the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane on different yield criteria and Poisson’s ratios are discussed. The results show that the influences of different yield criteria and Poisson’s ratio on the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane of the curved beam are significant. Once the value of bis obtained by experiments, the yield criterion and the corresponding solution for the materials of interest are then determined.

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Large deflection of curved elastic beams made of Ludwick type material

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlin- earities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

Exact solution for warping of spatial curved beams in natural coordinates

The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present theory are demonstrated by comparing its numerical results with Heins＇ solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

Dynamic Response of Curved Beam under Moving Load

In this paper an integral transform method is used to analyze the dynamic response of simple supported curved beam under single moving load with constant speed, and some parameters are defined. These parameters, such as radius of curvature, ratio of stiffness, velocity, warping stiffness, which may influence the response, are also discussed.

Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section

A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of fiexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.

The solution of minimum reliability index for modified weak point of arbitrary curved beam under pure bending

This paper is based on the fundamental loading model of pure bending and the analytical model of a circular beam element with arbitrary initial deflection. The L.W. Guo solution is modified and generalized according to the elastic theory, and the analytical solution for the stress of the beam element with arbitrary initial deflection under pure bending is derived. Using yield theory of edge strength, an expression for the safety margin of one point in the arbitrary curved beam under pure bending （ACPB） is built. This paper modifies the model for weak points of service structures and establishes a foundation for safe design and inspection of imperfect structures. Also, according to the theory of the method of advanced first-order second-moment（AFOSM） , this paper derives an expression for the reliability index of one point in ACPB. Lastly, it modifies the solution for weak points by solving the minimal reliability index.

THE CURVED BEAM ELEMENT AND ITS CONVERGENCE RATE

The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam clement. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approxtmately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l2) and when regular elements are used. I is the element length.

Geometric nonlinear formulation for curved beams with varying curvature

Based on exact Green strain of spatial curved beam, the relation for plane curved beam with varying curvature is derived nonlinear strain-displacement Instead of using the previous straight beam elements, curved beam elements are used to approximate the curved beam with varying curvature. Based on virtual work principle, rigid-flexible coupling dynamic equations are obtained. Physical experiments were carried out to capture the large overall motion and the strain of curved beam to verify the present rigid-flexible coupling formulation for curved beam based on curved beam element. Numerical results obtained from simulations were compared with those results from the physical experiments. In order to illustrate the effectiveness of the curved beam element methodology, the simulation results of present curved beam elements are compared with those obtained by previous straight beam elements. The dynamic behavior of a slider-crank mechanism with an initially curved elastic connecting rod is investigated. The advantage of employing generalized-or method is pointed out and the special nonlinear dynamic characteristics of the curved beam are concluded.

Enabling the transfer matrix method to model serial-parallel compliant mechanisms including curved flexure beams

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.

Dynamic Performance of Straddle Monorail Curved Girder Bridge

In this work,a monorail vehicle-bridge coupling(VBC)model capable of accurately considering curve alignment and superelevation is established based on curvilinear moving coordinate system,to study the VBC vibration of straddlemonorail curved girder bridge and the relevant factors influencing VBC.While taking Chongqing Jiao Xin line as an example,the VBC program is compiled using Fortran,where the reliability of algorithm and program is verified by the results of Chongqing monorail test.Moreover,the effects of curve radius,vehicle speed,and track irregularity on the corresponding vehicle and bridge vibrations are compared and analyzed.It is observed that the test results of lateral vibration acceleration(LVA)and vertical vibration acceleration(VVA)of track beam,and LVA of vehicle,are consistent with the simulation results.Owing to the track irregularity,vibration of track beam and vehicle increases significantly.Besides,an increase in vehicle speed gradually increases the vibration of track beam and vehicle.For the curve radius(R)≤200 m,lateral and vertical vibrations of the track beam and vehicle decrease significantly with an increasing curve radius.Alternatively,when 200 m<R<600 m,the lateral vibration of the track beamand vehicle decreases slowly with an increasing curve radius,while the relevant vertical vibration remains stable.Similarly,when R≥600 m,the lateral and vertical vibrations of the track beam and vehicle tend to be stable.Accordingly,the results presented here can provide a strong reference for the design,construction,and safety assessment of existing bridges.

On the plastic buckling of curved carbon nanotubes

This research,for the first time,predicts theoretically static stability response of a curved carbon nanotube(CCNT)under an elastoplastic behavior with several boundary conditions.The CCNT is exposed to axial compressive loads.The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy.The elastoplastic stress-strain is concerned with Ramberg–Osgood law on the basis of deformation and flow theories of plasticity.To seize the nano-mechanical behavior of the CCNT,the nonlocal strain gradient elasticity theory is taken into account.The obtained differential equations are solved using the Rayleigh–Ritz method based on a new admissible shape function which is able to analyze stability problems.To authorize the solution,some comparisons are illustrated which show a very good agreement with the published works.Conclusively,the best findings confirm that a plastic analysis is crucial in predicting the mechanical strength of CCNTs.

Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam

Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling.The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points,and to get high-quality parametric model for isogeometric analysis.ATimoshenko beam element is established for an initially curved spacial beam with arbitrary curvature.The approximation and interpolation methods to get parametric models of curves from given points are examined,and three strategies of parameterization,meaning the equally spaced method,the chord length method and the centripetal method are considered.The influences of the different geometric approximation algorithms on the precision of isogeometric analysis are examined.The static analysis and the modal analysis with the established parametric models are carried out.Three examples with different complexities,the quarter arc curved beam,the Tschirnhausen beam and the Archimedes spiral beam are examined.The results show that for the geometric approximation the interpolation method performs good and maintains high precision.The fitting algorithms are able to provide parametric models for isogeometric analysis of spacial beam with Timoshenko model.The equally spaced method and centripetal method perform better than the chord length method for the algorithm to carry out the parameterization for the sampling points.

Behaviour and Analysis of Horizontally Curved Steel Box-Girder Bridges

Various theories and analytical formulations were implemented and exploited in the 1980s and 1990s for the design of bridge beams or decks curved in the horizontal plane and subjected to out-of-plane loads. Nowadays, the Finite Element Method (FEM) is a valid tool for the analysis of structures with complex geometries and, therefore, the development of sophisticated analytical formulations is not needed anymore. However, they are still useful for the validation of FE models. This paper presents the case study of an existing viaduct built in North Italy, aiming to compare analytical approaches and numerical modelling. The bridge is characterized by an axis curved in two directions and a rectilinear segment. The global analysis of the viaduct is carried out with special attention to the attributes that cause torque action and bending moment. The theoretical developments focus on a deeper understanding of the torsional response under different constraint and loading conditions and aspire to raise awareness of the mutual interaction of flexural and torsional behaviour, that are always present in these complex curved systems. The examination of the case study is also obtained by comparing the response of isostatic and hyperstatic curvilinear steel box-girders.

保守开髓洞型及One Curve根管预备对下颌第一磨牙近中根管危险区的影响

目的研究使用One Curve预备系统时,保守开髓洞型对下颌第一磨牙近中根管危险区的侧穿风险的影响,为临床选择更优的髓腔入路提供依据。方法选择符合纳入标准的20颗因严重牙周病拔除冠根完整、近中根具有近颊根管与近舌根管2个独立根管,弯曲度为0°~20°的下颌第一磨牙,根据髓腔通路设计随机分为2组:传统开髓洞型组与保守开髓洞型组。传统开髓洞型髓室顶完全去除,保守开髓洞型尽可能多地保留髓室顶及颈周牙本质,使用One Curve单支锉行根管预备。对预备前后的离体牙进行锥形束CT扫描,定位近中根根分叉下方0~7.0 mm位置,以1 mm为间隔确定测量截面。测量各截面中根管近远中侧最小根管壁厚度。结果①20颗下颌第一磨牙近中根预备前CT测量结果示:危险区位于根分叉下0~4 mm,近颊根管近中侧平均厚度为1.18 mm,远中侧为1.08 mm。近舌根管近中侧平均厚度为1.28 mm,远中侧为1.07 mm。②传统开髓洞型组与保守开髓洞型组的下颌第一磨牙的近中根管的危险区的根管壁厚度减少量比较无显著差异(t=1.319,P=0.19)。③传统开髓洞型的近颊根管根尖偏移更偏向近中,保守开髓洞型更趋向于远中侧。而两组在近舌根管的偏移趋势均偏向远中。结论使用One Curve预备系统时,临床上使用基于微创理念的保守开髓洞型不会增加下颌第一磨牙近中根管危险区的穿通风险。