SNAP－THROUGH OF LAMINATED ORTHOTROPIC SHALLOW SPHERICAL IMPERFECT SHELLS WITH TRANSVERSE SHEAR

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均布载荷作用下正交各向异性圆锥扁薄壳的非线性稳定性问题

 本文研究了均布载荷作用下边缘可移夹支正交各向异性圆锥扁薄壳的轴对称屈曲问题。利用摄动法得到了临界载荷的近似解析表达式,对几种典型的纤维增强复合材料圆锥扁薄壳给出了数值结果和图表,可供工程应用参考。     

Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of function-ally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with functionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu-soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.     

Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel

In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG) spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the val-idation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.     

复合材料闭剖面加筋薄壁梁刚度系数计算分析

复合材料的可设计性为通过弹性剪裁来获得想要的变形模式带来了优势,其结构的耦合特性如拉扭耦合和弯扭耦合可以利用复合材料的各向异性来实现。以薄壁壳结构力学理论为基础,采用多种理论方法研究分析正交各向异性壳体本构关系,给出适合复合材料层压板矩形闭剖面薄壁梁截面的刚度系数解析表达;采用逐阶近似方法,完整设计复杂闭剖面的刚度系数数值算法;针对两种典型的复合材料铺层的矩形闭剖面梁截面布局构型,进行刚度特性的计算分析与讨论,获得铺层角度对复合材料薄壁梁弯曲、扭转及弯扭耦合刚度特性的定量结果。对分析设计闭剖面薄壁结构刚度条件具有应用价值。     

Plastic wrinkling model and characteristics of shear enforced Ti-alloy thin-walled tubes under combination die constraints and differential temperature fields

Plastic wrinkling predictions and shear enforced wrinkling characteristics of Ti-alloy thin-walled tubes under combination die constraints have become key problems urgently in need of solutions in order to improve forming quality in their shear bending processes under differential temperature fields. To address this, a wrinkling wave function was developed by considering their shear bend deformation characteristics. Based on this wave function and the thin shell theory, an energy prediction model for this type of wrinkling was established. This model enables considera-tion of the effects of shear deformation zone ranges, material parameters, loading modes, and fric-tion coefficients between tube and dies on the minimum wrinkling energy. Tube wrinkling sensitive zones (WSZs) can be revealed by combining this wrinkling prediction model with a thermal-mechanical coupled finite element model for simulating these bending processes. The reliability of this wrinkling prediction model was verified, and an investigation into the tube wrinkling char-acteristics was carried out based on the experimental conditions. This found that the WSZs are located on either a single side or both sides of the maximum shear stress zone. When the friction coefficients between the tube and the various dies coincide, the WSZs are located on both sides. The larger the value of the tube inner corner radius and/or the smaller the value of the outer corner radius, the smaller the wrinkling probability. With an increase in the value of the moving die dis-placement, the wrinkling probability increases at first, and then decreases.     

ON THE STABILITY OF ANISOTROPIC VISCOELASTIC THIN PLATES

Uptonow,someanalyses['~'Jhavebeendoneoncreepbucklingofviscoelasticstruc-tures.However,nomethodhaseverbeengiventodeterminethedurablecriticalloadofvis-coelasticstructuressubjectedtoadurableload.OnlyTroyanovskii['jsubmittedamethodtode-terminethedurablecriticalloadofisotropicviscoelasticthinplatesbutgavenoexample.Thededucingandcalculatingmethodinthispapercanbeusedtoresolvethecreepbucklingques-tionsofotheranisotropicviscoelasticplatesandshells.lAnalysisThecreepbucklingofanorthotropicviscoelastict…     

纤维增强复合材料圆柱壳的屈曲计算

本文利用各向异性多层扁壳的大挠度方程,探讨了正交各向异性多层圆柱壳,在考虑偶合效应和沿厚度方向剪切变形时的轴压,外压及其联合作用下的稳定性问题.用逆解法,给出正交各向异性多层圆柱壳在薄膜力作用下的临界载荷算式.进行了实例计算,并与国内、外实例的实验值比较,符合得相当好.     

复合材料层板小挠度理论的改进

改进了复合材料层板高阶剪切变形理论。改进后的理论与一阶剪切变形理论同样只有5个独立变量,但考虑了横向剪切应变沿板厚呈二次曲线变化及满足了层间剪应力的连续性。该理论比简单高阶理论计算的位移和应力更为精确,且逼近三维弹性解。     

基于剖面翘曲修正理论的复合材料叠层梁动态特性分析

 利用复合材料叠层结构剖面翘曲修正理论和瑞利原理，导出了叠层梁的固有振动方程，然后利用升阶谱有限元法作数值计算，给出了叠层梁的动态特性及相应的动应力分布。与一阶剪切理论相比，指出一阶剪切理论在高频计算时有较大的误差     

Analysis of thin-walled stiffened rods using the beam theory

The stress-strain state of thin-walled aircraft structures such as a wing or fuselage made of composite materials is determined based on the beam theory. The laminated skin is orthotropic. The solution was obtained without using the centroidal principal section axes and subdividing the problem in shear and torsion. A calculation variant with skin discretization along the section contour was studied.     

一种半球谐振陀螺谐振子动力学建模方法

准确完备的半球谐振陀螺（HRG）谐振子动力学模型是陀螺误差分析的基础。为建立半球壳谐振子动力学模型,基于弹性力学薄壳理论,提出了一种谐振子动力学建模方法。首先,在薄壳的弹性力学几何方程基础上,推导了半球壳谐振子的变形几何方程。其次,在提高受力分析计算精度的基础上,推导了半球壳谐振子的物理方程。然后,分析了谐振子中面的受力平衡关系,推导了谐振子的平衡微分方程。最后,基于以上对整个谐振子的动力学分析,建立了谐振子动力学方程。根据谐振子的不同外载荷形式,利用布勃诺夫-伽辽金法求解得到谐振子2阶谐振状态动力学模型,并得到了谐振子比例系数和2阶谐振频率的表达式。通过对比验证可以看出,参数计算值与实测数据结果一致,证明了所建立的动力学模型的准确性。     

计及横向剪切效应的环形谐振子理论研究CSCD

经典环形谐振子理论是一种基于忽略横向剪切变形假设建立的环理论,因而无法准确求解高径比较大的环问题。为了克服上述不足,基于Timoshenko理论和哈密顿原理,建立考虑横向剪切效应的环形谐振子新理论,包括广义本构关系、平衡方程和周期性条件等。利用经典的布勃诺夫-伽辽金法,并结合有限元法,获得谐振子在缓慢、匀速转动过程中二阶弯曲角频率和进动系数的理论解。研究表明,横向剪切变形会在一定程度上影响环形结构二阶弯曲角频率和进动系数的计算结果;环形谐振子的进动系数不是恒定的,它会随着高径比h/r的增大而缓慢地减小。     

A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates

A refined trigonometric shear deformation theory (RTSDT) taking into account transverse shear deformation effects is presented for the thermoelastic bending analysis of functionally graded sandwich plates. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, the displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The sandwich with homogeneous facesheet and FGM core is considered. Material properties of the present FGM core are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The influences played by the transverse shear deformation, thermal load, plate aspect ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal–ceramic plates are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded plates.     

Parametric instability of twisted cross-ply laminated panels

The present paper deals with the study of the vibration, buckling and parametric instability characteristics of general laminated cross-ply pre-twisted cantilever flat and curved panels. The effects of angles of pre-twist, aspect ratio, static load factor, and the lamination parameters of the cross-ply twisted curved panels on the principal instability regions are studied using Bolotin?s approach. An eight-noded isoparametric quadratic shell element with five degrees of freedom per node is used to develop the finite element procedure. The first order shear deformation theory is used to model the twisted cross-ply curved panels considering the effects of transverse shear deformation and rotary inertia. The linear part of the strain is used to derive the elastic stiffness matrix and the non-linear part of the strain is used to derive the geometric stiffness matrix. The global matrices are obtained by assembling the corresponding element matrices using skyline technique. Subspace iteration method is used throughout to solve the eigenvalue problem. Reduced integration technique is adopted in order to avoid possible shear locking. Based on the parametric studies, it is found that the instability behavior of twisted cross-ply cantilever panels is greatly influenced by the geometry, material, angle of twist and lamination parameters. So, this can be used to advantage in tailoring during design of crossply twisted cantilever panels.     

复合材料整体化加筋壁板高速冲击损伤数值模拟

 以复合材料结构抗弹性能分析与设计为目的,根据纤维的线弹性假设和基体的粘弹性假设,推导了复合材料单向板的粘弹性本构关系,导出了高应变率下复合材料层板的一阶剪切理论,建立了复合材料整体化加筋壁板高速冲击有限元分析模型.该模型引入界面单元模拟复合材料层间分层以及筋条与壁板间的脱粘损伤,结合Hashin失效准则进行筋条和单层板面内损伤识别,引入材料刚度退化,采用非线性有限元方法,研究了复合材料加筋结构高速冲击的破坏过程及损伤特性.数值分析结果与实验结果吻合良好,证明了该方法的合理有效性.探讨了筋条参数对高速冲击损伤的影响规律,获得了一些有价值的结论.     

梁壳组合结构的一种非线性有限元计算方法

提出了梁壳垂直组合结构在有限元计算中存在的问题,并以几何大变形问题为依托提供了解决该问题的计算原理和有限元方法。数值算例证明了该理论和方法的正确性。该法不仅适用于梁壳组合结构的大变形非线性计算,也适用于静动力小变形问题的线弹性分析计算。     

基于有限元方法的复合材料层合板自由振动分析

利用有限元分析方法分别研究了正交各向异性、对称角和反对称角铺设的正方形复合材料层合板的线性和非线性自由振动问题.结合一阶剪切变形理论推导出层合板自由振动的有限元方程,构造了三维有限元模型,并对其基频进行计算.数值结果与其他的文献的结果对照表明,用有限元方法求得的基频与用各阶剪切变形理论求得的结果非常接近,但对于厚板结果与经典Kirchhoff的结果有一些差距,对于其他理记是一致的.     

高精度数值方法在DNS中的应用

利用不同格式模拟扰动波在平板边界层中的传播,考察了格式对T-S波传播过程计算结果的影响。研究了不同计算格式对自由剪切层扰动波增长的影响,结果表明:对于二维扰动波模型,采用二阶精度格式,扰动波在平板边界层中只能出现衰减的结果;在自由剪切层中,虽然能模拟出扰动波在传播过程中幅值的增长,但却在相当长的计算范围内看不见三维波的出现。但对于同样的扰动模型,如果采用高精度格式,在边界层中能出现增长的T-S波,并与线性理论非常吻合;在自由剪切层中,扰动波不仅迅速增长,并能在不很长的距离内,明显的看到三维波的出现,并激发出了三维结构。      

微波在薄层等离子体中传输效应研究

为了准确预测再入飞行过程中等离子体对微波传输特性的影响,采用WKB方法、FDTD方法、平面波理论和薄层等离子体理论4种方法,结合粉末激波管上开展的试验研究了X波段和Ka波段微波在薄层等离子体中的传输效应。对于X波段,试验时激波马赫数为9.6、10.7和10.5;对于Ka波段,试验时激波马赫数为10.5。通过对比与分析获得的主要结论有：当等离子体厚度和入射波波长相近时,薄层等离子体理论计算结果比其它三种方法的计算结果更接近于试验结果;在碰撞频率接近并且电子密度小于临界电子密度的条件下,Ka波段微波信号穿过相同厚度的等离子体比X波段微波信号衰减小得多,具有更强的穿透性;如果等离子体碰撞频率和微波入射频率相同,随着电子密度的增加,微波信号穿过相同厚度的等离子体时衰减变大;当碰撞频率和入射波频率差不多时,共振吸收导致衰减达到最大值。