Post-buckling analysis of slender elastic rods subjected to terminal forces

This paper presents formulation and solutions for the elastica of slender rods subjected to axial terminal forces and boundary conditions assumed hinged and elastically restrained with a rotational spring. The set of five first-order non-linear ordinary differential equations with boundary conditions specified at both ends constitutes a complex two-point boundary value problem. Solutions for buckling, initial post-buckling (perturbation), large loads (asymptotic) and numerical integration are developed. Results are presented in non-dimensional graphs for a range of rotational spring stiffness, tuning the analysis from double-hinged to hinged-built-in rods.     

Post-buckling analysis of slender elastic vertical rods subjected to terminal forces and self-weight

This article presents the behavior of slender elastic rods subjected to axial terminal forces and self-weight. The mathematical formulation is presented, a solution is sought for a double-hinged boundary condition and the analysis is carried out for different values of non-dimensional weight. The formulation derives from geometrical compatibility, equilibrium of forces and moments and constitutive relations yielding a set of six first order non-linear ordinary differential equations with boundary conditions specified at both ends, which characterizes a complex two-point boundary value problem. Furthermore, a perturbation method is used to find the critical buckling loads and initial post-buckling solutions. A numerical integration scheme based on a three parameter shooting method is employed in the post-buckling solutions.     

Plastic dynamic stability of a column under nonconservative forces

I.Introduction'Whenadeformableobjectmovinginamedium,thedirectionsofinteractiveforcessuchasfrictionalforceshouldvarywiththedeformationoftheobject.Thisisakindofnonconservativeforces.Forexample,thedirectionofgasfrictionalforceactingontherocketsandthefossiles…     

Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The nonlinear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge–Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance (10⁻⁵). The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.     

双向压弯钢筋混凝土柱的非线性分析

在指出现有多弹簧模型存在问题的前提下,结合现有分析剪力墙的多垂直杆单元模型,提出了一种拓展的多垂直杆单元模型,这种模型可适用于各种截面形式的柱、墙肢和梁。另外,本文也提出了考虑刚度下降段的简化方法,最后提供了一个算例,算例结果表明本文模型的合理性。     

A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.     

Thermal post-buckling of an elastic beams subjected to a transversely non-uniform temperature rising

IntroductionAxiallycompressedstresseswilloccurinaconstrainedelasticbeamsubjectedtoatemperaturerising .Ifthemagnitudeofthecompressedstressesexceedacertainlimit,thermalbucklingoftheheatedbeam ,whichisoutofitsinitialconfiguration ,willtakeplace .So ,investigationsonthermalbucklingofrodsandbeamsareverynecessaryandimportantforthedesignofstructuresworkinginhightemperatureenvironmentsandofsomethermalsensitiveelasticelements.Becausethermalelasticpost_bucklingofbeamsandrodsareinducedbythethermallyaxial…     

碳纤维约束高强混凝土圆柱压弯构件非线性全过程分析

为分析塑性铰区碳纤维约束高强混凝土圆柱的抗震性能,编制了可得到荷载-位移曲线软化段的非线性全过程分析程序,保护层和箍筋约束混凝土采用Mander本构模型,碳纤维约束混凝土采用ACI 440.2R-08给出的本构关系,将程序计算结果与试验结果进行比较,两者吻合较好;利用该程序分析了轴压比、混凝土强度、碳纤维包裹长度及层数、纵筋配筋率等参数对碳纤维约束混凝土圆柱荷载-位移关系的影响规律,结果表明:当轴压比超过0.55后,柱构件的水平承载力开始降低,柱的破坏形式由延性的受拉破坏向脆性的受压破坏转变;剪跨比大于3的圆柱,碳纤维在塑性铰区包裹长度大干1.2倍柱直径时,即可达到与全柱包裹基本一致的效果;对混凝土强度为50 MPa～80 MPa的高强混凝土圆柱,以包裹3～4层碳纤维为宜;随着纵筋配筋率的增加,柱的水平极限承载力及延性均有所提高.     

Performance evaluation of shape-memory-alloy superelastic behavior to control a stay cable in cable-stayed bridges

This paper focuses on introducing and investigating the performance of a new passive control device for stay cable in cable-stayed bridges made with shape-memory alloys (SMA). The superelasticity and damping capability of SMA is sought in this study to develop a supplementary energy dissipation device for stay cable. A linear model of a sag cable and a one-dimensional constitutive model for the SMA are used. The problem of the optimal design of the device is studied. In the optimization problem, an energy criterion associated with the concept of optimal performance of the hysteretic connection is used. The maximum dissipation energy depends on the cross-sectional area, the length, and the location of the SMA on the cable. The effectiveness of the SMA damper in controlling the cable displacement is assessed. Furthermore, a study is conducted to determine the sensitivity of the cable response to the properties of the SMA device. The comparison between the SMA damper and a more classical passive control energy dissipation device, i.e., the tuned mass damper (TMD), is carried out. The numerical results show the effectiveness of the SMA damper to damp the high free vibration and the harmonic vibration better than an optimal TMD.     

钢质套筒被动围压下混凝土材料的冲击动态力学性能

为了研究混凝土材料在钢质套筒侧限约束下的动态力学性能参数和破坏规律,采用分离式大直径（75 mm）SHPB实验技术,测试了钢质套筒侧限约束下不同混凝土试件在不同载荷作用下轴向或径向的应力、应变峰值,平均应变率,计算了混凝土材料的损伤值,描述了加载破坏现象,对实验结果进行了分析。结果表明:混凝土材料在被动围压下,延性、抗破坏能力得到加强,具有明显的增强效应。被动围压下SHPB实验中混凝土材料的破坏应变为典型SHPB实验中破坏应变的1.8～2.8倍;破坏应力达到150 MPa以上,为静力学无围压条件下的2～5倍。     

Vibration and stability of an elastic column subject to a generalized load

Summary The critical load of the divergence instability, eigenfrequency curves and the Rayleigh's quotient for a column with one clamped end, subject to a generalized load, have been established in the paper. In particular, it has been found that the way the external force is being applied results in the linear dependence of both the shearing force and the bending moment upon both the deflection and the deflection angle of the loaded end. Such a case of loading exists e.g. for a column which supports a transversally stabilized structure when the contact surfaces are cylindrical. Furthermore, it has been theoretically and experimentally proven, that the slope of some eigencurves can change from positive to negative with the increasing load value.This research has been supported by the State Committee for Scientific Research, Warsaw, Poland, 1995.     

Nonlinear mechanics of a ring structure subjected to multi-pairs of evenly distributed equal radial forces

Combining the elastica theory,finite element(FE) analysis,and a geometrical topological experiment,we stud-ied the mechanical behavior of a ring subjected to multi-pairs of evenly distributed equal radial forces by looking at its seven distinct states.The results showed that the theoretical predictions of the ring deformation and strain energy matched the FE results very well,and that the ring deformations were comparable to the topological experiment.Moreover,no mat-ter whether the ring was compressed or tensioned by N-pairs of forces,the ring always tended to be regular polygons with 2N sides as the force increased,and a proper compressive force deformed the ring into exquisite flower-like patterns. The present study solves a basic mechanical problem of a ring subjected to lateral forces,which can be useful for studying the relevant mechanical behavior of ring structures from the nano-to the macro-scale.     

Stochastic stability of a viscoelastic column axially loaded by a white noise force

This paper deals with the analysis of stability of a hinged-hinged viscoelastic column subjected to a non-zero mean stochastic axial force. The randomly variable part of this is described by a stationary Gaussian white noise process. The viscosity affects the curvature of the column, for which the classic Euler-Bernoulli's model is adopted. The viscosity is described by the linear Kelvin-Voigt's model. A dynamic stability analysis is performed. Normal modes are introduced in the integro-differential equation of motion so that uncoupled modal equations are retrieved. With reference to the first mode, by using an additional state variable, three Itô’s ODE are obtained, from which the differential equations ruling the response statistical moment evolution are written by means of Itô’s differential rule. The zero solution, that is undeformed straight column, corresponds to zero moments. If the column is perturbed, it is stable when the response moments tend to zero. A necessary and sufficient condition of stability in the moments of order r is that the matrix A_r of the coefficients of the ODE system ruling them has negative real eigenvalues and complex eigenvalues with negative real parts. Because of the linearity of the system the stability of the first two moments is the strongest condition of stability. If the mean axial force μ_P or the white noise intensity wP are increased, there exist critical values μ_Pcr, wPcr for which almost an eigenvalue is positive. The critical mean axial force is found to be inversely proportional to the parameter φ_∞, which measures the amount of viscous deformation. The search for the critical values of wP is made numerically, and several graphs are presented for a representative column.     

爆炸加载下金属柱壳破片软回收技术研究

针对爆炸加载下金属柱壳膨胀断裂破片软回收的研究需求,本文通过理论分析和初步的数值模拟设计了由低密度聚氨酯泡沫与水介质为主体的回收装置。与传统单一材料为主的回收装置相比,该回收装置既能在破片高速阶段将低阻抗聚氨酯泡沫对破片的冲击压力减小到约为水对破片冲击压力的1/3,又使破片速度全程持续地较大幅度衰减,还能在破片低速阶段又能充分利用水介质密度大的优势,减小以聚氨酯泡沫单一材料为主的回收装置尺寸。依托该装置开展了炸药加载下304不锈钢柱壳膨胀断裂回收实验。通过测量回收池外壁速度、检查实验后的回收池外观,发现回收池池壁和底部完好,可以重复使用;通过对回收破片称重统计,破片回收率超过85%,破片内外界面辨识度高,破片表面车刀纹清晰可见,内部可见多条未贯穿的裂纹。表明该回收装置对破片的冲击损伤显著降低。根据破片断口和表面信息,推测了破片在金属柱壳的大致位置。本文最后初步给出了回收破片的平均厚度及质量分布等相关信息的统计结果。

     

The regions of flutter and divergence instability of a column subjected to Beck's generalized load, taking into account the torsional flexibility of the loaded end of the column

Investigations into a slender system subjected to Beck's generalized load taking into account two rotational springs situated at each end of the system are presented in the paper. One spring models the finite rigidity of the mounting, while the second restricts the rotation of the loaded end of the system. The regions of divergence and flutter instability of the considered system were determined using the kinetic criterion of the stability. The boundary value of the rigidity of the spring situated at the loaded end of the column was also determined. The boundary value of the rigidity separates the regions of divergence and flutter instability. In respect of the problem of vibrations, the characteristic curves in the plane: load - natural frequency were presented. All computations were carried out using the parameters of the considered system, including the rigidity of the springs and the follower coefficient of the load.     

Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading

The behaviour of a bi-piezoelectric ceramic layer with a centre interfacial crack subjected to anti-plane shear and in-plane electric loading has been studied. The dislocation density functions and the Fourier integral transform method have been employed to eliminate the problem of singular integral equations. The normalized energy release rate, stress and electrical displacement intensity factors, G/G₀,K_III/K_III0 and K_D/K_D0, respectively, were determined for different geometric and property parameters by use of two different crack surface electric boundary conditions, i.e. impermeable and permeable. It has been shown that the effects of the thickness and material constants of the piezoelectric layer on all the three parameters, i.e. G/G₀,K_III/K_III0 and K_D/K_D0 were significant.     

Nonlinear flutter of a two-dimension thin plate subjected to aerodynamic heating by differential quadrature method

The problem of nonlinear aerothermoelasticity of a two-dimension thin plate in supersonic airflow is examined. The strain-displacement relation of the von Karman＇s large deflection theory is employed to describe the geometric non-linearity and the aerodynamic piston theory is employed to account for the effects of the aerodynamic force. A new method, the differential quadrature method （DQM）, is used to obtain the discrete form of the motion equations. Then the Runge-Kutta numerical method is applied to solve the nonlinear equations and the nonlinear response of the plate is obtained numerically. The results indicate that due to the aerodynamic heating, the plate stability is degenerated, and in a specific region of system parameters the chaos motion occurs, and the route to chaos motion is via doubling-period bifurcations.     

Buckling of a beam subjected to electromagnetic force and its stabilization by controlling the perturbation of the bifurcation

For a beam subjected to electromagnetic force, magnetoelastic buckling due to the increase of such force is theoretically investigated by taking account of the nonlinearity of the electromagnetic force and the elastic force of the beam. Using Liapunov-Schmidt method and center manifold theory, the equilibrium space, the bifurcation set and the bifurcation diagram are theoretically derived. Also, the effect of the higher modes other than the buckling mode on the mode shape of the postbuckling state is discussed. Furthermore, a control method to stabilize the magnetoelastic buckling is proposed, and the unstable equilibrium state of the beam in the postbuckling state, i.e., the straight position of the beam, is stabilized by controlling the perturbation of the bifurcation.     

Elastic–plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic–plastic impact–contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic–plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results. The project supported by the National Natural Science Foundation of China (10532020).