Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory

This paper deals with elastic buckling analysis of stiffened and un-stiffened corrugated plates via a mesh-free Galerkin method based on the first-order shear deformation theory (FSDT). The corrugated plates are approximated by orthotropic plates of uniform thickness that have different elastic properties along the two perpendicular directions of the plates. The key to the approximation is that the equivalaent elastic properties of the orthotropic plates are derived by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates. The stiffeners are modelled as beams. The stiffness matrix of the stiffened corrugated plate is obtained by superimposing the strain energy of the equivalent orthotropic plate and the beams after implementing the displacement compatibility conditions between the plate and the beams. The mesh free characteristic of the proposed method guarantee that the stiffeners can be placed anywhere on the plate, and that remeshing is avoided when the stiffener positions change. A few selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results obtained for these examples, when possible, are compared with the ANSYS solutions or other available solutions in literature. Good agreement is evident for all cases. Some new results for both trapezoidally and sinusoidally corrugated plates are then reported.     

用耦合有限元／边界元方法研究加筋板的声传输

采用耦合的有限元／边界元方法,建立了考虑流体结构耦合的加筋板结构声传输计算模型,并利用该模型计算研究了加筋板的声传输特性。数值计算表明：结构的传声损失与结构的固有频率和激励频率密切相关,避免共振仍是产要的;改变板厚或肋骨惯性矩后,由于结构固有频率发生了变化会使得结构传声损失曲线上极小值的位置发生改变;当声波从空气经结构向空气中传递时,增大板厚或肋骨惯性矩可明显增大结构的传声损失;而当声波从空气经结构向水中传递时,增大板厚或肋骨惯性矩也增大了结构的传声损失,但效果明显不如当声波从空气经结构向空气中传递时显著。     

加强筋截面类型对轨道车辆板件结构隔声影响研究

针对轨道车辆轻量化设计后可能带来的隔声性能降低问题,研究不同截面加强筋铺设对板件隔声性能的改善效果。基于混合有限元-统计能量分析(Hybrid FE-SEA)方法建立轨道车辆加筋板结构隔声特性预测分析模型,系统分析T型、L型、I型和矩形加强筋截面类型对板件隔声性能的影响。研究结果表明,加筋板的刚度和1阶固有频率皆比均质板大,且随加强筋厚度的增大而增大;当加强筋厚度恒定时,T型加筋板的刚度和1阶固有频率最大,L型加筋板次之;敷设厚度15 mm的加强筋,板件的隔声性能最佳;当加强筋的质量、厚度、腹板面积及尺寸、翼板面积相等时,各类型加筋板的计权隔声量Rw差异不大;板件加筋后,刚度控制区的隔声量增幅3 dB~17 dB,1 250 Hz~4 000 Hz中高频段的隔声量增幅1 d B~6 d B。综合分析可知,以计权隔声量为评价标准时,在加强筋质量、腹板面积、翼板面积及尺寸相等时,敷设厚度15 mm加强筋,板件的隔声性能最佳,Rw较均质板可提高1.4 dB~1.5 dB,而加强筋厚度恒定时,T型和L型加筋板的刚度又最佳。相关研究成果可为轨道车辆板件结构加筋优化提供设计参考。     

U肋加劲板焊接残余应力的一种简化计算方法

基于焊接残余应力数值模拟方法, 分析了U 肋加劲板各组成板件的板宽、板厚对焊接残余应力分布的影响, 揭示了U 肋与母板残余应力合力的分配规律, 提出了针对不同构造尺寸的U 肋加劲板焊接残余应力分布简化计算方法。研究结果表明:各组成板件的板宽变化对焊接残余拉应力的分布影响较小, 但对焊接残余压应力的大小影响较大;U 肋与母板的板厚比对U 肋与母板残余应力的分配比例影响较大。U 肋加劲板受压承载力计算时, 焊接残余应力分布可以采用简化方法计算, 其结果与根据数值模拟得到的焊接残余应力分布计算的结果基本一致。     

Stiffened plate bending analysis in terms of refined triangular laminated plate element

Based on the higher-order global–local theories, a finite element model is proposed to study the bending behavior of stiffened laminated plates. The proposed model treats the embedded stiffeners as the part of laminated plate, so that the compatibility of displacements and stresses between the plate and the stiffeners can be automatically satisfied. Distributions of the displacements and stresses through the thickness of laminates were also given for the first time, which can serve as references for future investigations as such information is lacking in the published literature. In addition, the impact of the stiffeners on the bending response of the stiffened laminated plates is also studied in terms of the quantity, the collocation and the geometry of stiffeners. Numerical results showed that the higher-order global–local theories are more suitable for predicting the bending response of thick and moderately thick stiffened laminated plates compared to the first order theory commonly used in engineering. By varying the quantity, the collocation and the geometry of stiffeners, the stiffness and the strength of stiffened laminated plates can be remarkably improved.     

具有初始几何缺陷加劲板的动态屈曲

针对工程中常用的加劲板,研究了动态屈曲的求解方法。将加劲板分为母板与加劲肋两个部分考虑,其中母板按经典薄板理论计算,加劲肋视为Euler梁。假定加劲板的位移,利用Hamilton原理结合系统能量和振型叠加法建立了加劲板的动态屈曲特征方程。最后,选择四边简支加劲板进行数值分析,分析中考虑初始几何缺陷的影响,并讨论了初始几何缺陷、加劲肋的数量及其刚度的变化对动态屈曲临界荷载的影响。结果表明：一阶模态的初始几何缺陷对加劲板的临界荷载影响很大,而增加加劲肋的数量及其刚度可以提高加劲板的抗动态屈曲能力。研究结果也为加劲板的结构设计方法提供一定的参考。     

Vibration of stiffened skew Mindlin plates

Summary This paper presents a formulation for the free vibration analysis of skew Mindlin plates with intermediate parallel stiffeners attached in two directions. The Mindlin theory is used to account for the effects of transverse shear deformations and rotary inertia of the plate while the Engesser theory associated with the consideration of torsion is employed for stiffeners. Based on these two theories, the energy functionals for the plate system have been derived. To obtain the vibration frequencies, these energy functionals are minimized with the shape functions assumed in a set of two-dimensional mathematically complete polynomials. This procedure has been implemented numerically to compute the vibration solutions. Convergence studies have been performed to verify the accuracy of this method. Sets of first known results have been presented for several stiffened plate structures.     

联肢加劲钢板剪力墙滞回性能试验研究与数值分析

完成了3个1/3比例的3层联肢钢板剪力墙试件的低周反复加载试验。3个试件的钢板剪力墙分别采用非加劲、槽钢竖向加劲和井字加劲的形式,钢板剪力墙的竖向边缘构件采用方钢管混凝土。得到了联肢钢板剪力墙试件的荷载-位移滞回曲线和破坏形态,对试件的骨架曲线、应力发展、延性及耗能能力等进行了分析。采用有限元软件ABAQUS对试件进行了数值模拟。结果表明:非加劲和槽钢竖向加劲墙板先屈曲后屈服,井字加劲墙板先屈服后屈曲,墙板屈服后连梁与钢板剪力墙边框梁相继屈服。方钢管混凝土柱脚屈服较早,屈服后仍具有良好的承载力和弹塑性变形能力。采用非加劲墙板的试件承载力最低,滞回环捏缩效应最严重,其次是采用槽钢竖向加劲墙板的试件。采用井字加劲墙板的试件滞回环较饱满。井字加劲和槽钢竖向加劲试件的峰值荷载分别比非加劲试件的峰值荷载提高了11.7%和6.9%,井字加劲和槽钢竖向加劲试件的等效黏滞阻尼系数分别比非加劲试件的等效黏滞阻尼系数提高了65.9%和19.9%。各试件的延性系数均大于4.5,表明不同加劲形式的联肢钢板剪力墙均具有良好的延性。数值分析与试验结果吻合较好,可充分地反映试件的滞回性能和破坏过程。加劲肋对连梁和边缘构件的内力影响较小,但可显著提高剪力墙板的抗剪承载力。相较于两片单肢钢板剪力墙,联肢钢板剪力墙的承载力和耗能能力均有大于20%的提高。     

穿芯高强螺栓-端板节点方钢管混凝土框架抗震性能数值分析

为研究采用穿芯高强螺栓-端板节点的方钢管混凝土框架的抗震性能,基于一榀两层两跨方钢管混凝土框架的拟静力试验研究结果,利用有限元软件ABAQUS对试验试件进行了非线性数值分析。研究框架的破坏机制、延性、耗能能力及节点性能。在峰值荷载前,数值分析结果与试验结果吻合较好。对轴压比、节点端板厚度、加劲肋厚度以及高强螺栓预拉力等因素进行了分析。结果表明,框架滞回曲线饱满,具有良好的延性和耗能能力,节点在加载过程中未产生塑性变形。当框架柱的轴压比较小时,可形成理想的梁铰破坏机制。增大端板厚度和设置梁端加劲肋可提高结构的刚度与承载力,使框架刚度的退化趋于平缓。高强螺栓预拉力对框架性能无显著影响。     

Effective behaviour of elastic heterogeneous thin structures at finite deformations

In this contribution the effective material behaviour of thin structures like membranes and plates consisting of heterogeneities is investigated. The diameter of typical inclusions can be in the order of magnitude of the thickness of the membrane or plate. Thus, the prerequisite for a standard homogenization procedure using representative volume elements is not fulfilled anymore, since the required size of an RVE would be larger than the thickness of the structure itself. Additionally the assumption of uniformity of the boundary conditions on the RVE would be violated especially for plates since in general the predominant deformation of such structures is bending. However, it can be shown that the effective behaviour of such heterogeneous thin structures subjected to finite deformations is still in good agreement to the results obtained for homogenized materials.     

Behavior of laminated sandwich plates having interfacial imperfections by a new refined element

The static response of laminated sandwich plates having imperfections at the layer interfaces is investigated by a refined plate theory. The plate theory represents parabolic through thickness variation of transverse shear stresses, which are continuous at the layer interfaces and become zero at the plate top and bottom surfaces. In this plate model the interfacial imperfection is represented by a linear spring-layer. Moreover, with all these features of an accurate modeling, it involves unknowns only at the reference plane of the plate. To have generality in the analysis, finite element method is adopted. But any existing plate element cannot be used, as the plate theory demands certain inter-elemental continuity. Thus an attempt has also been made to develop a new triangular element. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and ordinary laminated plate with inter-laminar imperfection are used for validation.     

Buckling analysis of partially corroded steel plates with irregular surfaces

Corrosion is a long-term, inevitable process, lessens the thickness and load carrying capacity of structures. Old steel structures are more vulnerable to buckling, yielding and fracture due to corrosion. In lieu of a detailed analysis, average thickness assumption is employed for general type of corrosion. However, the estimation of load carrying capacity reduction of corroded structures typically need a much higher level of accuracy, since the actual corroded plates would have irregular surfaces. The objective of this article is to determine the effect of general corrosion on reduction of elastic buckling strength of both-sided partially corroded plates with irregular surfaces. Eigenvalue analysis using finite element method is employed for Euler stress calculation of corroded plates. The effects of different influential parameters are investigated and it is found that, aspect ratio of plate, location of corroded area, standard deviation of thickness diminution and concentration of corrosion have influence on reduction of elastic buckling strength. Reduction of elastic buckling strength is very sensitive to the amount of corrosion loss. The higher the amount of corrosion loss, the more reduction of elastic buckling strength.     

A geometry projection method for the topology optimization of curved plate structures with placement bounds

Single‐curvature plates are commonly encountered in mechanical and civil structures. In this paper, we introduce a topology optimization method for the stiffness‐based design of structures made of curved plates with fixed thickness. The geometry of each curved plate is analytically and explicitly represented by its location, orientation, dimension, and curvature radius, and therefore, our method renders designs that are distinctly made of curved plates. To perform the primal and sensitivity analyses, we use the geometry projection method, which smoothly maps the analytical geometry of the curved plates onto a continuous density field defined over a fixed uniform finite element grid. A size variable is ascribed to each plate and penalized in the spirit of solid isotropic material with penalization, which allows the optimizer to remove a plate from the design. We also introduce in our method a constraint that ensures that no portion of a plate lies outside the design envelope. This prevents designs that would otherwise require cuts to the plates that may be very difficult to manufacture. We present numerical examples to demonstrate the validity and applicability of the proposed method.     

加纵肋平底圆柱壳振动和声辐射的FEM/BEM研究

建立了两端带平底板的加纵肋圆柱壳水中声辐射计算的FEM／BEM三维模型，探究了加肋的高度、宽度、数目对平底圆柱壳表面平均速度、辐射功率、辐射效率、声场指向性的影响规律。计算方法是在有限元软件ANSYS中做加肋平底圆柱壳建模、模态分析基础上，将有关数据（网格、模态）导入边界元软件SYSNOISE中计算流体-结构耦合状态下的辐射声场特性。结果表明：（1）纵肋的高度、宽度以及数目增大都可以引起平底圆柱壳的表面平均速度、辐射功率、辐射效率随频率变化曲线峰的移动，同时使声辐射效率增大，但使表面平均速度、辐射功率变化不明显。（2）纵肋的高度、宽度增大都使低频声辐射中两端平底板的贡献量增大，而使研究频域内的高频声辐射在激励力的反方向上增强。当径向激励力作用在纵肋上时适当调整均布纵肋的数目可以改变平底圆柱壳辐射声场的指向性。这对于水下结构辐射噪声预报以及噪声抑制具有重要意义。     

Experimental Investigation Into the Fatigue of Welded Stiffened 350WT Steel Plates Using Neutron Diffraction Method

Abstract: The propagation of fatigue cracks under constant amplitude cyclic loading was studied in welded stiffened steel plates. The residual stresses in the stiffened plates were measured using the neutron diffraction strain‐scanning technique. The neutron diffraction measurements indicated that, in general, the residual stresses were tensile near the welded stiffeners and compressive between the stiffeners and ahead of the starter notch tips. Fatigue testing indicated that the fatigue crack growth rates of the stiffened plates were, in general, lower than that of a corresponding unstiffened plate, especially near the notch tips, where compressive residual stresses existed. An analytical method, using Green's function, was developed to predict the fatigue crack growth rates. Reasonable accuracy was obtained.     

Boundary element analysis of shear deformable stiffened plates

In this paper a boundary element formulation for analysis of shear deformable stiffened plates is presented. The formulation is derived by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Both concentric and eccentric stiffeners have been considered. The interaction forces between stiffeners and the plate are treated as either line distribution or area distribution of body forces along the attachment. A rectangular stiffened plate and a circular stiffened plate under uniform load are analysed by the proposed method. Good agreement has been achieved compared with other published results.     

Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method

Based on the first-order shear deformation theory, a mesh-free Galerkin method for free vibration analysis of stiffened and un-stiffened folded plates and plate structures is presented in this paper. The folded plate or plate structure is modelled as a composite structure that consists of flat plates. The stiffness and mass matrices of the flat plates are derived based on the mesh-free formulation. To avoid the failure of direct superposition, a treatment is introduced to modify the stiffness and mass matrices. The global stiffness and mass matrices of the entire folded plate or plate structure are then obtained by superposing the modified stiffness and mass matrices of the flat plates. The analysis of the stiffened folded plates or plate structures proceeds in a similar fashion, as they are regarded as composite structures of stiffened and un-stiffened flat plates. The stiffness and mass matrices of the stiffened flat plates are also given by the mesh-free method. As no meshes are used in deriving the stiffness and mass matrices, the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. Several numerical examples are computed with the proposed method to demonstrate its accuracy and convergence. The results show good agreement with the solutions that have been given by other researchers and ANSYS.     

SiCP/Al功能梯度装甲板抗侵彻性能的试验与数值模拟

采用粉末冶金方法制备碳化硅陶瓷颗粒(SiC_P)增强金属铝基复合材料板(MMCs), 并采用热压扩散法制备功能梯度装甲板(FGM)。利用高速冲击空气炮系统, 对纯铝靶板和两种不同铺层结构的功能梯度装甲靶板进行侵彻试验, 并利用LS-DYNA软件对侵彻试验过程进行数值模拟分析, 同时考察等厚、 等面密度下SiC颗粒分布对抗侵彻性能的影响。研究结果表明, 功能梯度板的抗侵彻性能比纯铝板好, 而两种不同铺层结构功能梯度板的抗侵彻性能相差不大。数值计算结果与现有试验结果取得了较好的一致, 说明了数值模拟的有效性。从数值计算结果可以看出, 层状功能梯度板比等厚、 等面密度均质复合材料靶板的抗侵彻能力好, 并可近似地认为等厚、 等面密度下多层功能梯度板的抗侵彻性能对颗粒分布不敏感。     

Optimum distribution of smart stiffeners in sandwich plates subjected to bending or forced vibrations

The problems of optimum distribution of active stiffeners manufactured from piezoelectric or shape memory alloy materials and bonded to or embedded within the facings of a sandwich plate are considered. The sandwich plate consists of thin composite or isotropic facings which are in the state of plane stress and a thick shear deformable core. The amplitude of forced vibrations of the plate is reduced using symmetric couples of piezoelectric stiffeners subjected to out-of-phase dynamic voltages. Shape memory alloy stiffeners are used to reduce bending deformations. In the latter case, a desirable effect is achieved by activating the stiffeners on one side of the middle surface. Optimum design is considered based on the requirement of minimal transverse static or dynamic deflections subject to a constraint on the volume of smart stiffeners. The variables employed in the process of optimization are the ratios of the cross-sectional areas of the stiffeners in each direction to their respective spacings. It is shown, that, dependent on the load, materials, and geometry, optimum design can significantly reduce deflections, i.e. enhance the strength, of sandwich plates.     

Model-based characterization of homogeneous metal plates by four-point alternating current potential drop measurements

We determined the conductivity, relative permeability, and thickness of homogeneous metal plates from four-point measurements of alternating current potential drop (ACPD) over the frequency range 1 Hz to 10 kHz. We developed simple analytical expressions from which these parameters can be calculated. In the low-frequency regime, in which the measured voltage tends to a constant, real value, the relative permeability of the plate does not influence the ACPD voltage. For known plate thickness, conductivity can be easily determined, even for ferrous metals. For known conductivity, plate thickness can be determined. Relative permeability can be obtained from measurements at higher frequency, for known conductivity and thickness. The inductance of the pickup circuit can also be determined from higher frequency measurements. This practical technique is especially useful for conductivity or plate thickness measurements in configurations where access is restricted to one side of the plate. We studied brass, aluminum, stainless steel, spring steel, and carbon steel plates. Our results agree with available independent measurements.