Crack effect on dynamic stability of beams under conservative and nonconservative forces

The purpose of this paper is to investigate the dynamic stability of beams containing a single crack subjected to conservative and nonconservative forces.The governing equation of the system can be derived from the extended Hamilton’s principle in which the kinetic energy, the elastic potential energy, the conservative work and the nonconservative work must be taken into account.The local flexibility matrix of a beam of a rectangular cross-section with a single edge crack is employed in order to perform numerical analysis.The investigated cracked beams are subjected to triangularly distributed subtangential forces, which are the combination of axial and tangential forces.The studied cracked beams become unstable in the form of either flutter or divergence, depending on crack parameters and on the degree of nonconservativeness of the load, when boundary conditions are fixed.     

Linear and geometrically non-linear analysis of composite beams under transverse loading

The flexural analysis of fiber-reinforced composite beams based on a higher-order shear deformation theory is studied. The geometric non-linearity is incorporated in the formulation by considering the von Karman strains. The finite element method is used to solve the non-linear governing equations by direct iteration. Unlike conventional beam models, the present beam model accounts for y direction strains. It is observed that the solution obtained from the two approaches differ slightly in the case of cross-ply laminates, but there exists a considerable difference in the case of angle-ply laminates. The influence of boundary conditions, beam geometries, and ply orientations on the deflections and stresses of laminated beams is shown both in tabular and graphical form.     

Formation of multiple longitudinal high-absorption kinks under the action of collimated gaussian light beams

The possibility of formation of several longitudinal kinks under the action of a collimated Gaussian light beam in a medium with absorptive cavityless optical bistability is demonstrated to be possible. The beam is essentially affected by diffraction. The domain formation is caused by the focusing of an annular beam into which the Gaussian beam is transformed due to nonlinear light absorption at small depths.     

Numerical method for calculating the filling of a mold and heat transfer of a melt under the action of centrifugal forces

This paper presents an explicit difference method for solving the conjugate problem of pouring molten metal into a casting mold and its solidification under the action of centrifugal forces with allowance for the free surface.Notation r, z transverse and longitudinal coordinates - u, v horizontal and vertical velocity components - V velocity vector - angular velocity of rotation - P pressure - P normalized pressure - T temperature - time - g free fall acceleration - coefficient of volumetric expansion - C heat capacity - thermal conductivity - density - L crystallization heat - v viscosity - Re=|V|h/v Reynolds grid number - h grid spacing - l mixing length in a turbulent flow - relaxation parameter - coefficient of convective heat transfer - coefficient defining the boundary conditions at the solid wall - D flow divergence - volumetric velocity of filling - emissivity - ₀ Stefan-Boltzmann constant - thickness of a layer Indices r, z, I, j numbers of grid nodes - n number of the integration step with respect to time - L, S temperatures of the liquidus and solidus, respectively - s temperature on the surface - med temperature of the medium - 0 initial state of the system - m metal - mol molten state of the metal - red reduced emissivity in the gap - rad radiant component of the heat transfer coefficient; g, gas-air gap - coat heat-insulating coating - fil filling Dneprodzerzhinsk Industrial Institute. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 678–686, July–August, 1995.     

Enhanced transverse displacements analysis of transversely cracked beams with a linear variation of width due to axial tensile forces

This paper considers the analysis of slender single-sided transversely cracked beams with a linear variation of width where transverse displacements can occur exclusively due to axial tensile forces. The simplified model where the crack is represented through an internal hinge endowed with a rotational spring that takes into account the cracked cross section's residual stiffness has already established itself as a decent alternative to the detailed 2D or 3D finite element, offering a good ratio between the accuracy of its results against the computational efforts required. The first stage of the presented research proved that the solutions of the bending governing differential equations with directly included axial tensile force are not required. However, the need for enhancement of the model's governing parameters clearly emerged. Thus, the definitions of the moment lever arm and rotational spring stiffness were studied and fittingly updated. In the last stage, the modelling of the considered phenomenon by a newly derived one-dimensional beam finite element with closed-forms of the element's stiffness matrix and load vector was executed. At the end of the study, the performance and the quality of the newly obtained solutions were verified through several comparative case studies that complement the derivations.     

Shear design of reinforced concrete beams with FRP longitudinal and transverse reinforcement

The shear resisting mechanisms of reinforced concrete (RC) beams with longitudinal and transverse FRP reinforcement can be affected by the mechanical properties of the FRP rebars. This paper presents a mechanical model for the prediction of the shear strength of FRP RC beams that takes into account its particularities. The model assumes that the shear force is taken by the un-cracked concrete chord, by the residual tensile stresses along the crack length and by the FRP stirrups. Failure is considered to occur when the principal tensile stress at the concrete chord reaches the concrete tensile strength, assuming that the contribution of the FRP stirrups is limited by a possible brittle failure in the bent zone. The accuracy of the proposed method has been verified by comparing the model predictions with the results of 112 tests. The application of the model provides better statistical results (mean value V_test/V_pred equal to 1.08 and COV of 19.5%) than those obtained using the design equations of other current models or guidelines. Due to the simplicity, accuracy and mechanical derivation of the model it results suitable for design and verification in engineering practice.     

Deformation of composite beams and plates under transverse impact

A theoretical and experimental approach to an investigation of transient loading and deformation of composite beams and plates was developed for the purpose of creating structures best resisting impact loading. The problem of transverse impact on beams and plates is formulated and solved on the basis of the finite-element method with the use of Timoshenko's shear theory and finite-difference method for orthotropic composite plates. The experimental investigations were conducted by means of a strain-gauge complex. It is shown experimentally and by calculations that minimum deformations under transverse impact are realized for reinforcement angles approaching the transversal isotropic scheme of placing fibers in layers of the composite, and fracture should be expected in the form of delaminations near the impact site and near the support fastenings.Translated from Problemy Prochnosti, No. 1, pp. 42–47, January, 1992.     

Approximate analysis of a conveyor system

An approximate method for the performance analysis of a particular flexible manufacturing system with unreliable machines and a circular conveyor consisting of a fixed number of cells is presented. Workpieces are transported among the machines on the conveyor. We assume that the time to failure and the time to repair are exponentially distributed. Our analysis is based on the service completion time of the workstations, which leads us to find the system time. We have developed a decomposition method that analyses each workstation in isolation. The performance measures of our interest include the mean system time, the mean number of workpieces in the system, the probability that a cell is occupied by a workpiece and the conveyor's throughput. Experimental results show that the approximate method is highly accurate.     

Deformation of composite beams under transverse impact loading

Results of experiments on determining the contact force with transverse impact on carbon-filled plastic beams are presented. The problem of transverse impact on beams is stated and solved based on the finite-element method using the Timoshenko shear theory. The Runge-Kutta-Felberg method is used for integrating the main equation of the finite-element method. Analysis of the results of experiments and calculations shows that the form, magnitude, and duration of the contact force of impact depend on elastic and strength characteristics of the contact surface and are determined by the spectrum of natural frequencies of vibrations. Maximum nonsteady deformations in bending and shear are realized for beams, the first natural frequencies of which are comparable with the impact pulse duration. The existence of time-intermediate peaks of nonsteady bending and shear deformations in various sections of the beam, as well as span-intermediate maxima of bending and shear deformations, makes it possible to state and solve the problem of optimizing the structure and form of composite beams in relation to the external nonsteady action.Translated from Problemy Prochnosti, No. 2, pp. 114–119, February, 1990.     

Approximate analysis of forming forces in woven preforms

In this paper, an approximate analysis has been developed for rapid computation of forming forces. The orientation of yarns in a deformed woven fabric on a surface is obtained using a differential geometry based draping algorithm. The fabric is assumed to behave like a membrane with very small strain along the principal yarn directions. This assumption allows computation of the tension along the yarns and the pressure on the surface. This methodology can also identify areas of wrinkling, which is a function of shear stiffness and applied forces.     

Determination of longitudinal and transverse shifts of three-dimensional Gaussian beams reflected at a grating near an anomaly

Spatial displacements of three-dimensional Gaussian beams diffracted at a reflection grating are studied theoretically and numerically. The complex diffraction coefficients (amplitudes and phases) of the grating diffracted plane waves calculated by a rigorous method for conical diffraction are the basis for this investigation. The classical analytical formula for the longitudinal shift depending on the gradient of the reflection phase is generalized to the simultaneous analytical treatment of the longitudinal Goos—Hänchen like shift as well as a transverse shift. A second method uses the full integration on the whole spectrum of plane waves of the diffracted beam.     

横向稳态磁场作用下微束等离子电弧数值分析

为分析外加横向稳态磁场作用下电弧特性与电弧对工件热、力输入的变化规律,本文建立了微束等离子电弧三维模型,将外加磁场简化为背景场添加至模型,使用有限元分析软件COMSOL进行求解计算.结果表明:外加横向稳态磁场作用下,喷嘴内部各项特性均未发生较大变化,喷嘴下方电弧等离子体在洛伦兹力的作用下向x负方向移动,电弧温度、等离子...     

输电塔线体系的风(雨)致振动响应与稳定性研究

为准确模拟输电塔构件的屈曲特征,该文提出了一种组合式屈曲单元。该单元基于有限元基本理论,用宏观塑性铰来实现构件材料的非线性,采用拉压弹簧模拟轴向塑性伸长,采用转动弹簧模拟塑性弯曲。基于MATLAB程序编写了该单元的静动力仿真程序,并应用于输电塔结构的静力推覆分析和倒塌仿真。通过对比自编程序和ABAQUS软件的仿真结果,验证了自编程序在几何非线性和动力求解方面的正确性;同时与钢支撑实验数据对比,验证了该组合式屈曲单元对非线性行为模拟的精确性和适用性;采用该单元对输电塔足尺实验进行了模拟,结果表明,该组合式屈曲单元可以有效地预测输电塔的极限承载力、失效位置及倒塌过程。     

Bending and transverse shear stresses in fiber-composite beams by the transformed-section method

A method to determine bending and transverse shear stress distributions in beams composed of fiber-composite layers is presented. The method is based on the transformed-section concept and takes into account the effects of Poisson's ratios and in-plane shear coupling. To demonstrate the feasibility of the transformed-section model, numerical solutions are presented for three rectangular and I-shaped cross-sections. It is shown that for bending moments the transformed-section model presented herein is entirely consistent with the lamination theory. The model can also be used to determine the transverse shear stresses, and it is shown that the accuracy of the results may be significantly affected when the effects of Poisson's ratios and in-plane shear are neglected in the analysis.     

Stochastic stability of a thick beams using contact transformation method

Stochastic stability of a high-order shear deformable beam is studied in this paper. Contact transformation method is used for decoupling the equations of motion of the gyroscopic system with two degrees-of-freedom. Method of regular perturbation is used to determine the asymptotic expressions for these exponents in the presence of small intensity noises. Analytical results are presented for the moment stability of a stochastic dynamical system.     

On deformation of functionally graded narrow beams under transverse loads

Solution is obtained for functionally graded (FG) narrow beams under plane stress condition of elasticity by using the mixed semi analytical model developed by Kant et al. (Int J Comput Methods Eng Sci Mech 8(3): 165–177, 2007a). The mathematical model consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) in the beam thickness direction. Analytical solutions based on two dimensional (2D) elasticity, one dimensional (1D) first order shear deformation theory (FOST) and a new 1D higher order shear-normal deformation theory (HOSNT) are also established to show the accuracy, simplicity and effectiveness of the developed mixed semi analytical model. It is observed from the numerical investigation that the present mixed semi analytical model predicts structural response as good as the one given by the elasticity analytical solution which in turn proves the robustness of the present development.     

Relative motion of drops under the action of variable forces

The boundary between moderate and large drops, which is fixed for each drop-medium system in gravitational conditions, shifts toward smaller drops with increase in the forces applied to the drop.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 5, pp. 750–756, November, 1989.