大挠度后屈曲倾斜梁结构的非线性力学特性

基于弹性梁的几何非线性大挠度屈曲理论,建立两端固定对称倾斜支撑梁结构的大挠度后屈曲控制微分方程,采用几何非线性隐式变形协调关系来表达强非线性超静定边值问题,得到描述倾斜梁大挠度后屈曲行为的精确解析解.采用数值方法求解含有第一、二类椭圆积分的强非线性微分方程,给出不同倾角梁结构从初始屈曲到后屈曲并发生两态跳转过程中的位形曲线及非线性刚度.根据最小能量原理和挠曲线拐点个数,分析对称屈曲模态与非对称屈曲模态之间相互跳转的内在联系及其对结构非线性刚度突变的影响,得到了屈曲模态之间的转换条件.跳转过程的数值仿真表明,倾斜支撑梁结构发生大挠度后屈曲时具有明显的双稳态特性且只出现低阶(1、2阶)屈曲模态,仿真计算结果与试验结果相一致.     

Non-Newtonian couple stress poroelastic squeeze film

The aim of this paper is to develop a new model of the interaction of a fluid film with a porous medium. The model takes into account the fluid inertia in both the lubricant and the porous matrix. Non-Newtonian behavior of the fluid, viscous effects in the porous matrix, and poroelasticity of the matrix are also considered. The main concerns are modeling and simulation of the squeeze film lubrication between two discs when one has a porous facing. The fluid flow is described using a reduced version of the Navier–Stokes equations in the fluid film, and the Darcy–Brinkman–Forchheimer generalized model in the porous matrix.The present study focuses on the combined effects of the non-Newtonian fluid lubricant and porous matrix deformation. The non-Newtonian behavior of the lubricant is described by the so-called couple stress model. The porous interface deformation is obtained using the thin elastic layer approach. The partial differential equations established in this study are discretized by finite differences. The resulting algebraic equations are solved using the Gauss–Seidel relaxation method.The numerical results of the present simulations show that all these effects have a significant influence on the porous squeeze film performance.     

Buckling of poroelastic columns with axial diffusion

The buckling problem is investigated in this paper for fluid-saturated poroelastic beams consisting of materials for which the pore fluid flow is possible in the axial direction only. The beam material is assumed to be transversely isotropic with respect to the beam axis. The time dependent behaviours of the critical loads and deflections are considered for various diffusion and geometric boundaries.     

Maximum load factors corresponding to a slightly asymmetric bifurcation point

Explicit formulations are derived for quantitative evaluation of imperfection sensitivity of critical load factors corresponding to a slightly asymmetric bifurcation point; i.e. the perfect system itself has slight asymmetry. The load factor corresponding to local minimum or maximum along the fundamental equilibrium path and the complementary path are simultaneously obtained as functions of the imperfection parameter. The upper bound of the imperfection parameter is also derived for existence of critical points along the fundamental equilibrium path. This way, interpolation formulas are presented between symmetric and asymmetric systems. The accuracy of the proposed formulas is verified by the examples of rods supported by translational and rotational springs.     

Post-buckling behavior of carbon fiber epoxy composite plates

In this study, the pre-buckling and post-buckling behaviors of layered composite plates which were made of woven carbon fiber fabric with a circular hole in the middle were investigated experimentally and numerically. Firstly, load-displacement graphs of composite plates with different hole diameters were experimentally obtained under compressive load. Then the numerical load-displacement graphs of the plates were found with the ANSYS package program which used the finite element method. As a result, after linear buckling experimental and numerical results were found to be compatible with each other. In addition, damage behavior of plates after buckling with the aid of Tsai-Wu damage criterion was obtained similar to experimental results. The increase in hole diameter did not change the load-displacement behavior characteristics of the plates after buckling. However, it has reduced maximum damage load and maximum failure displacement. The stress at the perimeter of the hole increased significantly with the increase of the vertical displacement with immediately after the buckling but later was not significantly affected by this increase.

     

Micropolar fluid squeeze film lubrication between rough anisotropic poroelastic rectangular plates: special reference to synovial joint lubrication

Abstract

The effect of anisotropic permeability on micropolar squeeze film lubrication between poroelastic rectangular plates is studied. The non-Newtonian synovial fluid is modelled by Eringen’s micropolar fluid, and the poroelastic nature of cartilage is taken in to account. The stochastic modified Reynolds equation, which incorporates the elastic as well as randomised surface roughness structure of cartilage with micropolar fluid as lubricant, is derived. Modified equations for the mean fluid film pressure, mean load carrying capacity and squeeze film time are obtained using the Christensen’s stochastic theory for the study of roughness effects. The effects of surface roughness, micropolar fluid and anisotropic permeability on the squeeze film characteristics of synovial joint are discussed. It is found that the surface roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids, and the anisotropic nature of permeability of cartilage off-squares the plate size for optimum performance.     

Thermal post-buckling analysis of slender columns using the concept of coupled displacement field

Thermal post-buckling analysis of columns with an axially immovable ends is studied using the Rayleigh-Ritz (R-R) method, where the admissible displacement functions are chosen based on the concept of coupled displacement field (CDF) criteria. Geometric non-linearity is considered using the von-Karman strain displacement relations of the beam. Furthermore, the displacement fields derived from CDF criteria are used in an intuitive formulation, where the thermal post-buckling behavior can be predicted by using two parameters namely tension developed in the column and linear buckling load. An exhaustive set of column boundary conditions are considered namely classical such as hinged-hinged, clamped-clamped, clamped-hinged and non-classical such as clamped-guided and hinged-guided. Post-buckling analysis results are presented in the form of closed form expressions, where the ratio of post-buckling load to linear buckling load parameter is expressed as a function of central amplitude of the column for all the boundary conditions considered. The amount of non-linearity predicted using the present formulations (R-R method and intuitive method) based on the concept of coupled displacement field (CDF) criteria shows an excellent agreement with the available literature results for both classical and non-classical boundary conditions.     

Post-buckling and delamination propagation behavior of composite laminates with embedded delamination

Delamination occurred due to poor manufacturing process or in-service actions significantly affects the mechanical and failure behavior of laminated composite structures. In this study, the buckling and post-buckling delamination behavior of laminated composite with an embedded initial delamination under in-plane compression was studied experimentally and numerically. First, compression tests for laminated composite specimens with embeded initial delamination were performed and the buckling and delamination responses were obtained. Then the experimental test was numerically simulated using finite element methods with the progressive failure accounted for by using cohesive zone modeling. The load-displacement curve, strain behavior and delamination shapes of experimental specimens obtained from load cells, strain gages installed at different locations, and C scan images, respectively, were compared with the FEM results, and good agreements were attained. The effect of the buckling modes, laminate stacking sequence and shape of initial delamination on the buckling load and propagation behavior was studied by considering different ply stacking and shapes of initial delaminations. It was found that the buckling mode determined the growth direction of the delamination propagation, and the stacking sequence influenced the extent of the propagation area, while the orientation of the delamination affected the buckling loads.     

Strain rate dependent poroelastic behavior of bovine vertebral trabecular bone

It is widely accepted that the pressure variation of interstitial fluid is one of the most important factors in bone physiology. In order to understand the role of interstitial fluid on porous bony structure, a consideration for the biomechanical interactions between fluid and solid constituents within bone is required. In this study, a poroelastic theory was applied to investigate the elastic behavior of calf vertebral trabecular bone composed of the porous solid trabeculae and the viscous bone marrow. The poroelastic behavior of trabecular bone in a uniaxial stress condition was simulated using a commercial finite difference analysis software (FLAC, Itasca Consulting Group, USA), and tested for 5 different strain rates, i. e., 0.001, 0.01, 0.1, and 10 per second. The material properties of the calf vertebral trabecular bone were utilized from the previous experimental study. Two asymptotic poroelastic responses, the drained and undrained deformations, were predicted. From the predicted results for the simulated five strain rates, it was found that the pore pressure generation has a linearly increasing behavior when the strain rate is the highest at 10 per second, otherwise it showed a nonlinear behavior. The pore pressure generation with respect to the strain was found to be increased as the strain rate increased. The elastic moduli predicted at each strain were 208.3, 212.2, 337.6, 593.1, and 602.2 MPa, respectively. Based on the results of the present study, it was suggested that the calf vertebral trabecular bone could be modeled as a poroelastic material and its strain rate dependent material behavior could be predicted.     

多墙翼面结构后屈曲强度试验和数值研究

采用静态试验和有限元分析相结合的方法研究了复合材料中厚蒙皮多墙翼面结构的后屈曲性态、强度和破坏过程。有限元分析取得的载荷-位移曲线和试验结果的一致性说明了有限元模型的正确性。在此模型基础上,采用非线性弧长法追踪外载-位移路径,研究了盒段在压缩和集中力两种不同载荷下的后屈曲行为。给出了屈曲临界载荷和屈曲变形性态,分析了后屈曲强度和破坏过程。     

Effect of an ultralight metal filler on the bending collapse behavior of thin-walled prismatic columns

The effect of low-density metal filler, such as aluminum foam or honeycomb, is studied on the bending collapse resistance of thin–walled prismatic columns. A combination of analytical and numerical results is used to predict the initial and post collapse response of empty and filled columns. Closed-formed solutions for the bending-rotation characteristics are constructed in terms of the geometrical parameters and the filler strength. The low-density metal core retards sectional collapse of the thin-wall column, and increases bending resistance for the same rotation angle. Numerical simulations show that, in terms of achieving the highest energy absorption to weight ratio, columns with aluminum honeycomb or foam core are preferable to thickening the column wall. Moreover, the presence of adhesive improved the specific energy absorption significantly.     

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.     

Analysis of the impact responses in a degenerated spinal motion segment FE model

A three-dimensional non-linear poroelastic finite element model of an L3/L4 motion segment was used to analyze the biomechanical effects of degeneration under impact loading on the spinal segment. A previously developed degeneration algorithm was applied to generate a degenerated disc model. Regional variation in intact vertebral body bone morphology was simulated by assigning different void ratios of 4.0–5.02, which were assessed for 27 regions of vertebral cancellous bone. For the osteoporotic structure of the vertebral body, the body was divided into 5 regions with 10–24 void ratios. Different material properties were assigned to the annulus fibers; hereupon our annulus model reflected variation in tensile behavior of multiple layer annulus samples. The impact load applied to the top of the L3 vertebral body was assumed to be a triangular impulsive force with a maximum compressive impact load of 3 kN and 20ms impact duration time. Calculated results indicated that the effect of the degeneration was predominant at the center of the vertebral body. The maximum von Mises stress was found at the region of near the endplate. The degeneration increased the averaged stress at the center of the vertebral body of L3 from 1.54 MPa to 1.69 MPa, the stress remaining relatively small at L4. Decreased fluid volume ratio of the degenerated nucleus tended to increase pressure slightly at the nucleus, and the averaged stress at the nucleus was almost doubled compared to the intact case. The innermost layers of the anterior annulus showed the highest stress concentration, followed by outermost anterior and posterior regions, for both the degenerated and the intact models. Despite an irregular stress distribution in the degenerated model, pore pressure showed relatively uniform distribution. This paper was recommended for publication in revised form by Associate Editor Young Eun Kim YoungEun Kim received a B.S. degree in Mechanics and Design from Seoul National University in 1978. He then went on to receive his M.S. from KAIST in 1986 and Ph.D. degrees from U. of Iowa 1988. Dr. Kim is currently a Professor at the Dept. of Mechanical Engineering at Dankook University in Yongin, Korea. He is currently serving as an Editor of the Open Orthopedic Research Journal. He was also served as a division chair of KSPE. Dr. Kim’s research interests are in the area of biomechanics, and occupant dynamics.     

On the vibration of imperfect circular disks

An analytical method is presented for vibration analysis of a rotating circular disk with distributed imperfections such as the nonuniform thickness, density. Young's modulus, Poisson's ratio and the odd distribution of internal stresses. In this paper, the linear governing equation of the disk is formulated, and then the relation between each imperfection and the split of degenerate modes is derived. In the derivation, the distributed imperfection, which is a periodic function of angular position, is expanded as a Fourier series. The derived simple relation suggests that the zeroth order imperfection causes the shift in the natural frequencies of all modes, whereas the 2m-th order harmonic imperfection results in the split of the natural frequencies, with the equal magnitudes but with different signs, for a pair of original degenerate modes with m nodal diameters.     

加筋结构后屈曲有限元建模方法研究

预估加筋结构的承载能力对飞机设计极为重要,对整体加筋结构和铆接加筋结构分别拟定一系列不同的有限元模型化方法,考虑材料和几何非线性进行后屈曲分析。对比试验数据和分析结果可知,选取合适的离散化方法可以准确预估这两种结构形式的破坏载荷。对含有整体加筋板和铆钉连接的机翼盒段进行后屈曲分析验证,有限元预估值与试验数据吻合很好。     

光学元件的疵病检验与研究现状（续）

“光学零件表面疵病”曾在国家标准GB1031－68及GB1185－89中做过专门描述。研究发现,这些标准与国际上一些国家的相关标准及测试方法相差较大,而最近国际光学委员会推荐的一个不同用途光学元件的疵病指标值得注意[1]。本文在介绍了一些国外标准的基础上,侧重分类描述了当今世界上具有代表性的疵病检验方法、原理及各自的特点,旨在为我国光学界同行在应用、研究及制定相关标准时参考。文后作者提出了在光学元件的疵病检验和标准制定方面的一些粗浅看法。     

Analytical approximations to large post-buckling deformation of elastic rings under uniform hydrostatic pressure

This paper presents analytical approximations to large post-buckling deformation of a circular, elastic, and inextensional ring under uniform hydrostatic pressure. By combining the Newton's method with the method of harmonic balance, we establish analytical approximations to large deformation of the ring. Unlike the classical method of harmonic balance, the linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations. We are hence able to establish analytical approximate solutions. These approximate solutions show excellent agreement with the exact solution, and are valid for small as well as large difference of the curvatures of the undeformed and the deformed ring.     

应用ABAQUS的膜式空气弹簧弹性特性仿真研究

以某乘用车悬架膜式空气弹簧为研究对象,建立空气弹簧的有限元分析模型。应用有限元分析软件ABAQUS对其垂向静态力学特性进行仿真分析。有限元数值计算结果与空气弹簧的垂向静态力学特性试验结果吻合度较高,证明了有限元数值计算方法的正确性。对膜式空气弹簧结构设计参数进行灵敏度分析,得出的结论是:气囊内压与帘线角是膜式空气弹簧静态力学特性的最敏感参数。     

Investigation of couple stress effects on poroelastic squeeze film of parallel plates

The couple stress effects on hydrodynamic performances of poroelastic squeeze film in the case of infinitely long parallel plates are examined in this paper. The lower plate is a poroelastic matrix saturated by a Newtonian fluid. The poroelasticity is taken into account by the means of homogenisation method. The rheological behaviour of the lubricant is described by the Stokes couple stress fluid theory. The modified Reynolds equation accounting for the couple stress, the elasticity of the poroelastic plate and the slip velocity condition at the film–poroelastic plate interface is derived. The governing equations in the fluid film and poroelastic plate are discretised by finite difference method and solved iteratively by using Gauss–Seidel method. The fluid film and poroelastic plate coupling is managed by the iterative fixed point technique. A computer program is developed in this study. The result analysis shows that couple stress effects on poroelastic squeeze film performances are significant. Copyright © 2016 John Wiley & Sons, Ltd.     

Diffraction of sound by a poroelastic cylindrical absorber near an impedance plane

Acoustic scattering from an infinitely long fluid-saturated porous elastic circular cylinder located near a planar boundary with locally varying surface impedance is studied. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity, the appropriate wave field expansions, the classical method of images and the translational addition theorem for cylindrical wave functions along with a simple local surface reaction model involving a complex amplitude wave reflection coefficient applied to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which a cylindrical plastic foam absorber is located near a layer of foam material set on an impervious rigid wall. The numerical results reveal the important effects of incident wave frequency, angle of incidence, interface local surface reaction, cylinder poroelasticity and position on the acoustic field quantities. The proposed model can lead to a better understanding of acoustic scattering from two-dimensional near-interface porous absorbers or targets which are commonly encountered problems in outdoor acoustics, noise control engineering, and ocean engineering. The presented solution could eventually be used to validate those found by numerical approximation techniques.