Free vibration analysis of an elliptical plate with eccentric elliptical cut-outs

The elaborated collocation multipole method is employed to obtain a semi-analytical solution, involving proper products of angular and radial Mathieu functions, for the free flexural vibrations of a fully clamped thin elastic plate of elliptical planform containing multiple elliptical cutouts of arbitrary size, location, and orientation. The problem boundary conditions are satisfied by uniformly collocating points on the boundaries, and exactly calculating the normal derivative of plate displacement at the collocation points through use of appropriate directional derivative in each coordinate system. The multipole expansion is truncated to yield a coupled algebraic linear system of equations that is then solved for the nontrivial eigensolutions. Extensive numerical simulations present the first three calculated natural frequencies and the associated deformed mode shapes of an elliptical plate with elliptical/circular cutouts, for a wide range of plate/cutout aspect ratios, and cutout location/orientation parameters. The accuracy of solutions is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data available in the existing literature.     

Dynamic crushing characteristics of high strength steel cylinders with elliptical geometric discontinuities

Thin-walled members are commonly used as energy absorbers in engineering structures and often contain cutouts. This study performed numerical simulations of high strength steel cylindrical shells with elliptical cutouts subjected to dynamic axial impact. The LS-DYNA code was the primary analytical tool used to analyze the influence of cutout locations, cutout shapes and symmetry of cutout on the energy absorption capabilities and the crush characteristics of tubes with a cutout. For high strength steel tubes made from a rate sensitive material, the stress-strain curves of different strain rates were used to elucidate the effect of dynamic impact on the strain rate. Our results show that collapse crushing behavior is strongly influenced by the location and symmetry of cutouts and the variation of major axis influences the peak crush load.     

Free vibration of composite laminated plate with complicated cutout

Abstract

This paper presents the free vibration analysis of a composite laminated square plate with complicated cutout. The problem formulation is based on the higher order shear deformation plate theory HDST C⁰ coupled with a curved quadrilateral p-element. The elements of the stiffness and mass matrices are calculated analytically. The curved edges are accurately represented using the blending function method. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as the cutout shape, plate thickness, fiber orientation angle, and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New results for the fundamentals frequencies of a composite laminated plate with complicated cutout are presented.     

椭圆颗粒在剪切流中旋转特性的数值研究

研究颗粒在流体剪切作用下的运动特性是理解和预测颗粒悬浮流流动行为的关键.当流体的惯性不能忽略时,颗粒的运动往往变得非常复杂.本文采用格子Boltzmann方法对中等雷诺数下椭圆颗粒在剪切流中的旋转运动进行了模拟.首先,研究了雷诺数(0Re 170)的影响,结果表明当雷诺数低于临界值时,颗粒以周期性的方式旋转,角速度最小时对应的长轴方向随着雷诺数的增大而逐渐远离水平方向,而且这一倾角与雷诺数呈分段线性关系;当雷诺数大于临界值时,椭圆形颗粒最终保持静止状态,且静止时的转角与雷诺数呈幂函数关系,雷诺数越大,转角越小,椭圆的长轴越远离水平位置.其次,研究了椭圆颗粒的长短轴之比α(1α10)的影响,结果表明颗粒旋转的周期与α呈幂函数关系,α越大,颗粒旋转周期越小.此外,当α超过临界值时,颗粒也在水平位置附近保持静止状态,此时的转角与α也呈幂函数关系,α越大,转角越小.研究还发现,当雷诺数较大时椭圆颗粒在旋转过程中会产生过冲现象.     

Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout

The elastic buckling behavior of rectangular perforated plates was studied by using the finite element method in this study. Circular cutout was chosen at different locations along the principal x-axis of plates subjected to linearly varying loading in order to evaluate the effect of cutout location on the buckling behavior of plates. The results show that the center of a circular hole should not be placed at the end half of the outer panel for all loading patterns. Furthermore, the presence of a circular hole always causes a decrease in the elastic buckling load of plates subjected to bending, even if the circular hole is not in the outer panel.     

Elliptical crack normal to functionally graded interface of bonded solids

This paper presents an analysis of an elliptical crack that is perpendicular to a functionally graded interfacial zone between two fully bonded solids. The functionally graded interfacial zone is treated as a non-homogeneous solid layer with its elastic modulus varying in the thickness direction. A generalized Kelvin solution based boundary element method is employed for the calculation of the stress intensity factors associated with the three-dimensional crack problem. The elliptical crack surface is subject to either uniform normal traction or uniform shear traction. The stress intensity factors are examined by taking into account the effects of the non-homogeneity parameter and thickness of the functionally graded interfacial zone, as well as the crack distance to the zone. The SIF values are further incorporated into the S-criterion for prediction of crack growth. The paper presents the most possible direction and location of the elliptical crack growth under an inclined tensile (or compressive) load. The paper further presents results of the critical external loads that would cause the elliptical crack to grow at the most possible location and along the most possible direction. The paper also examines the effects of external load direction and material and geometrical parameters on the critical loads.     

大开口复合材料层合板强度破坏研究

复合材料层合板的各向异性及非均质,使得复合材料层合板内部的破坏形式非常复杂.在复合材料结构的设计中,为满足制造及使用功能上的需求,在复合材料层合板承力结构件上不可避免地需要设计各种开口.然而,含大开口复合材料层合板的强度破坏问题变得更为复杂,使得现有的强度理论面临新的挑战.针对碳纤维增强复合材料大开口层合板受单向拉伸载荷作用下的强度破坏问题进行了数值分析和实验研究.首先,根据Hashin准则和刚度退化模型,对含不同圆形开口尺寸的[0]_(10)单向铺层、[0/90]_5和[±45]_5正交铺层的层合板,进行了单向拉伸载荷作用下渐进失效的数值模拟分析,获得了对应结构的极限载荷和破坏模式.在此基础上,采用数字图像相关方法,进行复合材料大开口层合板强度破坏的实验研究.研究结果表明,大开口复合材料层合板在单向拉伸加载下主要呈现脆性破坏形式,破坏起始位置处于应力集中区.此外,破坏强度和失效模式与复合材料铺层方式和开口尺寸大小密切相关.其中[±45]_5铺层的开口层合板承载能力最弱,分层破坏最严重.开口尺寸越大,结构的极限载荷值越低.同实验测试结果相比,数值模拟对复合材料层合板的损伤失效分析略显不足,往往很难全面分析复合材料层合板破坏失效过程中的各种因素的影响.     

Buckling behavior of compression-loaded composite cylindrical shells with reinforced cutouts

Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the non-linear response of the shells are described. A high-fidelity non-linear analysis procedure has been used to predict the non-linear response of the shells. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate the complex non-linear response of a compression-loaded shell with an unreinforced cutout. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex non-linear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, results are presented that show how certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.     

PROGRESSIVE DAMAGE ARREST MECHANISM IN TAILORED LAMINATED PLATES WITH A CUTOUT

This study addresses the effectiveness of a simple stiffness tailoring concept to delay damage initiation, control damage progression, and improve residual strength in tensile-loaded composite plates with a central circular cutout. The tailoring concept is to simply reposit all axially oriented （0°） material into regions near the edge of the plate away from the cutout. This tailoring is done in a way so as not to affect the weight of the plate. This accomplishes several beneficial changes in the way that the plate resists loading with no increases in material cost or weight. Lowering the axial stiffness of the laminate surrounding the cutout lowers the stress concentration. Increasing the axial stiffness near edges of the plate attracts loading away from the vicinity of the cutout to further lower stresses in the critical cutout region. This study focuses on in-plane response including damage progression and residual strength as a function of the degree of tailoring and cutout size. Strength and stiffness properties typical of IM7/8551-7 preperg material were assumed and a modified version of the Hashin failure criteria was used to identify the local damage. Results show that tailoring can significantly increase the damage initiation load and the residual strength. In some cases, observed evidence shows that tailoring performs as a damage arrest mechanism.     

含椭圆孔的变角度复合材料层合板的屈曲性能研究

本文利用变角度复合材料的纤维方向角可沿平面位置任意连续变化的特点,提出在孔附近采用与孔同心的椭圆曲线作为纤维铺设路径的层合板铺层方案,以改善含椭圆孔的层合板的孔边应力集中,进而提高层合板的抗屈曲性能．主要研究内容有：利用ABAQUS软件分析本文提出的孔边特殊铺层方式下变角度复合材料层合板的面内应力分布及屈曲性能,通过与传统直线铺层方式以及线性变角度铺层方式进行比较,说明了本文提出的新铺层方式的优越性,并详细分析了椭圆孔的离心率、开孔尺寸及开孔方位对层合板的屈曲临界荷载的影响．研究结果可为含椭圆孔的变角度复合材料层合板的结构设计和优化提供一定的参考．     

About the Porous Media Flow Through Circular and Elliptical Anisotropic Inhomogeneities

In this article, we describe horizontal groundwater flow due to a uniform flow at infinity around a cylindrical or elliptical inhomogeneity, where the permeability inside the inhomogeneity is anisotropic and different from the isotropic domain outside the inhomogeneity. The orientation of the uniform flow with respect to the orientation of the ellipse is arbitrary as well as the orientation of the anisotropy inside the ellipse. We derive an expression for the ratio of the flow through the ellipse with respect to the flow in the homogeneous case.     

圆柱壳开孔的应力分析

本文研究圆柱壳开孔附近的应力分析问题。由于开孔问题的边界形状较为复杂,使用圆柱壳的 Morley 方程进行求解较为困难。本文在进行误差分析的基础上提出修正 Mo-rley 方程,并给出适合于开孔问题边界的一般解。以圆柱壳受轴向拉伸和内压为例分析了开孔附近的应力分布。给出了开孔率为 1/2以下的开孔解,并对 Donnell 方程解的适用范围给予了新的评价。     

THERMOELASTICITY ANALYSIS OF FINITE COMPOSITE LAMINATES WEAKENED BY MULTIPLE ELLIPTICAL HOLES

ＴＨＥＲＭＯＥＬＡＳＴＩＣＩＴＹＡＮＡＬＹＳＩＳＯＦＦＩＮＩＴＥＣＯＭＰＯＳＩＴＥＬＡＭＩＮＡＴＥＳＷＥＡＫＥＮＥＤＢＹＭＵＬＴＩＰＬＥＥＬＬＩＰＴＩＣＡＬＨＯＬＥＳＸｕＸｉ－ｗｕ（许希武）ＳｕｎＬｉａｎｇ－ｘｉｎ（孙良新）ＦａｎＸｕ－ｑｉ（范绪箕）...     

Analysis of crack extension in anisotropic materials based on local normal stress

The normal stress ratio theory is applied to predict crack extension behavior in center-notched unidirectional graphite-epoxy of arbitrary fiber axis orientation, subjected to arbitrary far-field planar loading. The theory is applied within analytical solutions for two infinite plate geometries: a plate with a sharp center crack, and a plate with an elliptical center flaw. A critical analytical case is identified suggesting that application of the theory within a stress solution modelling crack tip shape may increase the accuracy of crack growth direction predictions. Crack extension direction, location of crack extension, and critical stress predictions of the theory are compared to those obtained from experiments on specimens subjected to tensile, shear, and mixed-mode far-field loading. The comparison shows that, applied within each analytical solution, the normal stress ratio theory provides verifiable predictions of crack growth behavior. By modelling actual notch tip shape, the elliptical notch solution is able to provide accurate qualitative predictions of the origin of crack extension along the periphery of a cut notch tip in a way that the sharp crack analysis cannot. The sharp notch solution appears to provide slightly more accurate crack growth direction predictions, however. Also, in predicting critical applied far-field stresses, the sharp crack solution appears to exhibit a stronger ability to model subtle experimental trends.     

Frequency dependence of elastic (SH-) wave velocity and attenuation in anisotropic two phase media

The propagation and attenuation of elastic waves in a random anisotropic two-phase medium is studied using statistical averaging procedures and a self-consistent multiple scattering theory. The specific geometry and orientation of the inhomogeneities (second phase) are incorporated into the formulation via the scattering matrix of each inhomogeneity. The anisotropy of the composite medium is due to the specific orientation of the non-symmetric inclusions. At low frequencies, analytical expressions are derived for the effective wave number in the average medium as a function of the geometry and the material properties and the angle of orientation of the inclusions. The results for the special cases of oriented cracks may find applications in geophysics and material science. The formulation is ideally suited for numerical computation at higher frequencies as evidenced by the results presented for composites reinforced by fibers of elliptical cross section.     

Dynamics of two elliptical particles sedimentation in a vertical channel: chaotic state

The LB-DF/FD method derived from the Lattice Boltzmann Method and direct forcing/fictitious domain method is used to numerically investigate the dynamics and interaction of two elliptical particles settling in an infinitely long channel. One particle (EP0) is initially kept horizontal (major axis perpendicular to sedimentation) for all simulations while the other's (EP1) orientation is varied. It is found that if EP1strays away from horizontality, the particles undergo transitions from a steady state to reach a chaotic state. Furthermore, there are two distinct chaotic states for the particle motion when EP1 orientation is varied, in which a turning point is observed to distinguish the two states.     

Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression

This study investigates the elasto-plastic buckling behaviour of simply supported square and rectangular thin steel plates having elliptic cut-outs by means of finite element method. Plates with simply supported in the out-of-plane direction are applied uniform compression in long-edge direction. A50 steel was used in the analysis and the focus was on the effect of plate aspect ratio, elliptical hole size, elliptical hole angle, elliptical hole location and slenderness ratio on buckling behaviour. It was found in the study that as the plate slenderness ratio increases, the critical buckling stress decreases for all the perforated plates.     

基于平板振动精确化方程求解动应力集中问题

基于文献[8]给出的平板弯曲振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究.文中给出了分别基于Mindlin板与精确化板方程在不同参数下圆孔动弯矩集中系数的数值结果,并对结果进行了对比分析和讨论.结果表明:在较低频率和薄板情况下,基于文献[8]的方程与基于Mindlin板理论得到的动弯矩结果是基本一致的;在较高频率和厚板情况下,基于文献[8]的方程与基于Mindlin板理论的动弯矩结果相差较大,最大值超出可达16%.由于文献[8]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此其分析计算结果更精确一些.      

Relative orientation constraints in the nonlinear large displacement analysis: application to soft materials

This study dealt with the dynamic stability and geometrical nonlinear problems of carbon nanotube/fiber/polymer composite (CNTFPC) cylindrical panels without or with delamination around a central cutout. A multiscale analysis using the Hewitt and Malherbe model was performed to determine the carbon nanotube (CNT) weight ratios, thickness–radius ratios, thickness–length ratios, and delamination area ratios around a cutout. A delamination around a central cutout was modeled in two dimensions by introducing continuity conditions of displacements at the delamination boundaries. The proposed approach in this study has been verified by previous studies. Parametric results showed the significance of a proper CNT ratio and curvature for better structural performance on the dynamic instability and nonlinearity of delaminated CNTFPC cylindrical panels.

     

Multiple scattering of flexural waves in a semi-infinite thin plate with a cutout

The multiple scattering of flexural waves and dynamic stress concentration in a semi-infinite thin plate with a cutout are investigated, and the expressions of this problem are obtained. The analytical solutions of wave fields are expressed by employing the wave function expansion method and the expanded mode coefficients are solved by satisfying the boundary condition of the cutout. The image method is used to satisfy the traction free boundary condition of the plate. As an example, the numerical results of dynamic stress concentration factors are graphically presented and discussed. Numerical results show that the analytical results of the scattered waves and dynamic stress in semi-infinite plates are significantly different from those in infinite plates when the ratio of distance b/a is relatively little. In the region of low frequency and long wavelength, the maximum dynamic stress concentration factors occur on the illuminated side of the scattering body with θ = π, but not at the edge of the cutout with θ = π/2. As the incidence frequency increases (the wavelength becomes short), the dynamic stress on the illuminated side of the cutout decreases, however, the dynamic stress on the shadow side increases.