Computational modeling of spine and trunk muscles subjected to follower force

Recently, the follower force concept was introduced in the field of biomechanics to elucidate how the stability of the human spine could be maintained under substantial compressive loads. However, it has been controversial if the follower load concept is feasible to maintain the spinal stability by coordinating the appropriate trunk muscles. The purpose of this paper is to propose a computational model of the human spine and trunk muscles based on finite element method combining with an optimization formulation subjected to the follower force constraint in order to confirm that the follower force is related to the spinal stability and can be generated by the activation of trunk muscles. Spinal motion segments were modeled as linear elastic beam elements and trunk muscles were assumed to be static. In the optimization formulation, the muscle forces, the follower forces and shear forces, and the deformed shape of the spine model were investigated minimizing the sum of the magnitudes of follower forces under the constraints for the equilibrium equations, the directions of resultant forces, and the physiological bounds of muscle forces. Through a numerical example, it was confirmed that there was a combination of muscle activations transmitting external forces and moments along the follower force direction and the spinal stability was maintained with little change of spinal shape.     

Dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force

This paper presents the dynamic stability of a cantilevered Timoshenko beam with a concentrated mass, partially attached to elastic foundations, and subjected to a follower force. Governing equations are derived from the extended Hamilton’s principle, and FEM is applied to solve the discretized equation. The influence of some parameters such as the elastic foundation parameter, the positions of partial elastic foundations, shear deformations, the rotary inertia of the beam, and the mass and the rotary inertia of the concentrated mass on the critical flutter load is investigated. Finally, the optimal attachment ratio of partial elastic foundation that maximizes the critical flutter load is presented.     

Dynamic stability of a rotating asymmetric cross-section blade subjected to an axial periodic force

The finite element method is applied to study the static and dynamic stability of an aerofoil cross-section rotating blade subjected to an axial periodic force. The effects of coupling due to the center of flexure (shear center) distance from the centroid, rotational speed, stagger angle and disk radius on the stability are considered. Critical load parameters are calculated and dynamic instability regions of the blade with different reference values are illustrated graphically. The numerical results indicate that the coupling effect is very important in the third and fourth modes depending on d_Y distance. The increase in stagger angle makes the blade less stable. However, the increase in rotational speed and disk radius make the blade more stable.     

Effective elastic properties of randomly distributed void models for porous materials

Many 2D analytical models are available for estimating the effective elastic properties of porous materials. Most of these models adopt circular voids of a uniform diameter in superlattice arrays, such as unit void or periodically positioned models. There are two principal issues in a realistic representation of porous materials: the random distribution of a statistically sufficiently large number of voids in the model, and the random distribution of the size and position of the voids. Numerical schemes such as the FEM or the BEM have also been presented to cater for regular patterned circular voids. However, due to the large number of elements needed to produce sufficient accuracy for the curved boundary of circular voids or modelling a statistically sufficient number of voids with a random distribution in both the void size and the position, no such model has yet been produced.Modelling based on an FEM approach using a simplified approximation for void geometry is proposed here for the calculation of the effective elastic properties of porous solids. A plane strain model of a square geometry is adopted for a 2D array of voids. This simplified square shape allows a large number of voids to be simulated with a random distribution for both void sizes and their locations. The problem of anisotropy, which arises from the square shape, is discussed. It is verified that along the two principal directions (parallel to the sides of the square voids), the elastic properties remain the same as those predicted by using a circular void geometry. This square-shaped approximation, with its reduced requirement for FE analysis, has the potential to be extended to 3-dimensional modelling for a realistic simulation of engineering materials.     

Dynamic instability characteristics of laminated composite plates subjected to partial follower edge load with damping

The study of vibration and dynamic instability behaviour of laminated composite plates subjected to partially distributed non-conservative follower forces is presented by using the finite element technique. The first-order shear deformation theory is used to model the plate, considering the effects of shear deformation and rotary inertia. The modal transformation technique is employed to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping to study the significance of damping on stability characteristics. The effects of load width, boundary condition, aspect ratio, ply orientation, direction control of the load and damping parameters are considered for the stability behaviour of the plates. The results show that under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending on system parameters.     

Vibration and dynamic stability of pipes conveying fluid on elastic foundations

The paper deals with the vibration and dynamic stability of cantilevered pipes conveying fluid on elastic foundations. The relationship between the eigenvalue branches and corresponding unstable modes associated with the flutter of the pipe is thoroughly investigated. Governing equations of motion are derived from the extended Hamilton’s principle, and a numerical scheme using finite element methods is applied to obtain the discretized equations. The critical flow velocity and stability maps of the pipe are obtained for various elastic foundation para-meters, mass ratios of the pipe, and structural damping coefficients. Especially critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place, are precisely determined. Finally, the flutter configuration of the pipe at the critical flow velocities is drawn graphically at every twelfth period to define the order of the quasi-mode of flutter configuration.     

Self-excited oscillations of a string on an elastic foundation subject to a nonlinear feed-forward force

We investigate the self-excited oscillations of a string on an elastic foundation that is subject to a nonlinear feed-forward force. The feed-forward follows that of a model first proposed by Steele and Baker [1] for an active cochlear, and is due to the gain factor profile which depends on the string displacement. In order to determine the bifurcation structure induced by the nonlinear feed-forward mechanism, we formulate a taut string initial-boundary-value problem with periodic boundary conditions which is reduced to a finite order modal dynamical system. We employ an asymptotic multiple-scales method to obtain slowly varying evolution equations that enable an analytical derivation of the periodic system response and analysis of its orbital stability. The resulting bifurcation structure includes multiple regions of both stable and unstable coexisting periodic solutions defined by primary and secondary Hopf stability thresholds. Numerical verification of the bifurcation structure determines the accuracy of the analytically predicted periodic self-excited response and reveals the existence of quasiperiodic combination-tone solutions and complex nonstationary solutions that emerge in a range of the asymptotically predicted unstable solutions. This analysis enables construction of a comprehensive analytical bifurcation structure and may shed light on mechanisms governing complex multi-component spectra that have been documented for spontaneous otoacoustic emissions in the mammalian inner ear.     

十字片簧弹性支承机构的设计

首先建立了接触式台阶测量仪中关键部件———十字片簧支承的杠杆机构的数学模型并对其进行初步设计。直片簧应力有限元分析表明 ,该结构应力分布很不均匀 ;经片簧参数的改进设计 ,得出变截面片簧的设计参数。 0 .2N外加载荷作用下 ,采用Algor有限元软件分别对变截面片簧进行仿真实验 ,最大、最小应力之比由直片簧的 3 1.4降低为7.7,扭转刚度为 0 .0 6N·m ,测量力变化率为 3 6.6N/m ,极大地改善了该机构的机械特性     

Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties

The present investigation is concerned with free vibration analysis of laminated composite plates resting on elastic foundation undergoing large amplitude oscillation with random system properties. The lamina material properties and foundation stiffness parameters are modeled as basic random variables for accurate prediction of the system behavior. The basic formulation of the problem is based on higher-order shear displacement theory including rotatory inertia effects and von Karman-type nonlinear strain displacement relations. A C⁰ finite element is used for descretization of the laminate. A direct iterative method in conjunction with first-order Taylor series based perturbation technique procedure is developed to solve random nonlinear generalized eigenvalue problem. The developed probabilistic procedure is successfully used for the nonlinear free vibration problem with a reasonable accuracy. Typical numerical results (second-order statistics) are obtained for the composite plates resting on Winkler and Pasternak elastic foundations with different support conditions, side-to-thickness ratio, aspect ratio, oscillation amplitude ratio, stacking sequences and foundation parameters for symmetric and anti-symmetric cross-ply and angle-ply laminates. The results are validated with existing available results and independent Monte Carlo simulation.     

Stability loss analyses of the elastic and viscoelastic composite rotating thick circular plate in the framework of the three-dimensional linearized theory of stability

In the present paper, in the framework of the three-dimensional linearized theory of stability the rotationally symmetric stability loss problems of the elastic and viscoelastic composite rotating thick circular and annular discs are investigated. The method for solution to these problems is developed by employing Laplace transform and finite element method. It is supposed that the disc and annular disc have an insignificant rotationally symmetric initial imperfection and as a stability loss criterion, the case where this imperfection starts to increase and grows indefinitely, is taken. Numerical results related to the critical angular velocity for elastic problems and to the critical time for viscoelastic problems are presented.     

应变式切削测力系统动态特性的研究

本文对应变式切削测力仪的动态性能进行了研究,比较测力仪弹性无件在粘贴应变片前后固有频率和阻尼比的变化。结论是：应变片的粘贴不会造成测力仪固有频率的损失;测力系统的通过频率取决于系统中固有频率最差的环节－动态应变仪。最后,用实验的方法验证了测力系统对动态力的测量结果。     

齿轮啮合弹性变形对齿轮基节的影响

针对渐开线直齿圆柱齿轮啮合时的弹性变形,采用了材料力学中的悬臂梁模型和赫兹接触应力理论的计算方法对齿轮啮合后在单位力作用下的轮齿的弯曲变形量与接触变形量进行了计算,并找出了该变形量与基节的关系。最后用有限元方法对轮齿的弯曲变形与接触变形及其对基节的影响进行了有效的验证。     

Vibration analysis of rolling element bearings with various defects under the action of an unbalanced force

In this paper, a method based on the finite element vibration analysis is presented for defect detection in rolling element bearings with single or multiple defects on different components of the bearing structure using the time and frequency domain parameters. A dynamic loading model is proposed in order to create the nodal excitation functions used in the finite element vibration analysis as external loading. A computer code written in Visual Basic programming language with a graphical user interface is developed to create the nodal excitations for different cases including the outer ring, inner ring or rolling element defects. Forced vibration analysis of a bearing structure is performed using the commercial finite element package I-DEAS under the action of an unbalanced force transferred to the structure via a ball bearing. Time and frequency domain parameters such as rms, crest factor, kurtosis and band energy ratio for the frequency spectrum of the enveloped signals are used to analyse the effect of the defect location and the number of defects on the time and frequency domain parameters. The role of the receiving point for vibration measurements is also investigated. The vibration data for various defect cases including the housing structure effect can be obtained using the finite element vibration analysis in order to develop an optimum monitoring method in condition monitoring studies.     

槽道板结构的应力分析方法

分析板翅式换热器和微换热器的基本结构,通过引入小挠度薄板理论和弹性支承结构模型,解析计算槽道板结构的弯曲变形和弯曲应力,然后将这种分析法拓展到多层槽道板结构,进而利用有限元方法对其进行对比验证分析.结果表明,应用小挠度薄板理论和弹性支承结构模型分析槽道板结构的变形和应力具有较好的精度,为微小型装置或具有槽道结构设备的应力分析提供一种有效的方法和依据.     

弹性基础梁弯曲问题有限元解析与直接边界元法解析的研究

对有限元解析方法和直接边界元解析方法开展了相关研究工作,基于弹性基础梁弯曲问题的静态特性的解析公式,通过ANSYS程序验证实例正确性。     

旋转膨胀系统膨胀力和液压力的研究

为了推广旋转膨胀技术在国内大范围内得到应用,采用非线性大塑性变形有限元分析技术着重研究了不同的工艺参数(膨胀锥角、摩擦系数、定径区长度)对膨胀过程中膨胀力的影响,得到了相关膨胀参数与膨胀力之间的关系曲线,从关系曲线中得到了降低膨胀力的最佳膨胀参数值.并且进一步对液压力进行了分析,得出旋转角速度、膨胀速度对液压力的影响,通过关系曲线得到了最佳的膨胀参数值.这为膨胀工具的设计及膨胀方案的优化提供了理论依据.     

Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation

An asymptotic solution is formulated for non-linear buckling of elastically restrained imperfect shallow spherical shells continuously supported on a non-linear elastic foundation. The asymptotic iteration method is introduced to result in a cubic non-linear analytical relation between the external load and central transverse displacement (deflection) of the structures incorporating the effects of geometrical imperfection, edge-restraint coefficients, moduli of foundation and characteristic geometrical parameter. The resulting expression can be used easily to evaluate the effects of these factors on buckling behaviors. Numerical examples are given, and comparisons of the available results show validity of the method suggested in the present work.     

A numerical study on an infinite linear elastic Bernoulli-Euler beam on a viscoelastic foundation subjected to harmonic line loads

Journal of Mechanical Science and Technology - This paper presents a numerical study on the low-amplitude responses of an infinite Bernoulli-Euler beam resting on a viscoelastic foundation...     

Optimum design of structures with stress and displacement constraints using the force method

A new structural analysis and optimization algorithm is developed to determine the minimum weight of structures with the truss and beam-type members under displacement and stress constraints. The algorithm combines the mathematical programming based on the sequential quadratic programming (SQP) technique and the finite element technique based on the integrated force method. The equilibrium matrix is generated automatically through the finite element analysis while the compatibility matrix is obtained directly using the displacement–deformation relations and the single value decomposition (SVD) technique. By combining the equilibrium and compatibility matrices with the force–displacement relations, the equations of equilibrium with the element forces as variables are obtained. The proposed method is extremely efficient to analyze and optimize the truss and beam structures under stress and displacement constraints. The computational effort required by the force method is found to be significantly lower than that of the displacement method. The effect of the geometric nonlinearity in the structural optimization problems under the stress and displacement constraints were also investigated and it is illustrated that the geometric nonlinearity is not an important issue in these types of problems and hence, it does not affect the final optimum solution significantly. Four examples illustrate the procedure and allow the results to be compared with those reported in the literatures.     

Influence of elastic effects on the performance of slot-entry journal bearings

Modern high-performance machines require bearings to operate under stringent conditions. For bearings operating under heavy loads, the bearing deformations can no longer be neglected as they are comparable to the order of magnitude of the fluid film thickness. This paper describes the performance of slot-entry hydrostatic/hybrid journal bearings by considering bearing shell flexibility in the analysis. The relevant governing equations have been solved by the finite element method. Slot-entry journal bearings of two separate configurations have been studied over a wide range of bearing operating and geometric parameters. Elastic effects are found to significantly affect the static and dynamic performance characteristics of the bearing studied. The study indicates that, for given operating conditions, to get optimum performance of a bearing proper selection of the bearing flexibility parameter (), the concentric design pressure ratio () and the type of bearing configuration (symmetric/asymmetric) are essential.