The steady state response of a Mindlin annular plate of varying thickness

The steady state response of an internally damped Mindlin plate of radially varying thickness to sinusoidally varying force is determined by the transfer matrix approach. The method is applied to free-clamped annular plates of linearly, parabolically and exponentially varying thickness, which are driven around the free outer edge or driven around a concentric circle of any radius; the driving-point impedance, transfer impedance and force transmissibility of the plates are calculated numerically, and the effects of the varying thickness on them are studied.     

Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM

The critical compressive load in the buckling of circular and annular composite plates reinforced with carbon nanotubes (CNTs) is calculated using finite element method. The developed model is based on the third-order shear deformation theory for moderately thick laminated plates. Effects of CNTs orientation angles and thickness-to-inner radius ratio on the buckling of composite plates are discussed. The results are compared with those obtained by analytical method based on classical plate theory. The finite element method shows lower values for critical buckling load because of the elimination of shear strain in the classical plate theory.     

Bending of an annular plate in the presence of a concentrated, in-plane edge load

Bending behaviour of an annular plate with clamped inner boundary and a concentrated edge load at the outer boundary is studied using the semi-analytical finite element method. The annular plate elements developed by Pardoen are used for this purpose. Exact in-plane stress field is obtained for various harmonics. Geometric stiffness matrices are developed which are general and can handle any in-plane stress field once its Fourier expansion is known. Results are presented for two radii ratios and for chosen values of the in-plane load.     

Analysis on the thermal elastohydrodynamic lubrication of tapered rollers in opposite orientation

Faced to the lubrication of the meshing teeth of helical gears, thermal elastohydrodynamic lubrication (TEHL) of two tapered rollers located in opposite orientation was studied numerically. It has been found from the full numerical solution that the lubricating performances of two tapered rollers differ significantly from that of a finite line contact. For tapered rollers, the distributions of pressure and film thickness depend strongly on the distribution of the effective radius in the direction of the roller length, and the distribution of temperature rise depends strongly on the local slide-roll ratio in the direction of the roller length. Side-leakage is inevitable in the elastohydrodynamic lubrication (EHL) of two tapered rollers, and thin films are produced in the ends by side-leakage, but the high pressures in the ends could be decreased by the end-shape modification, which is beneficial to the end lubrication. The temperature distribution is interesting, and the lowest temperature in the high-pressure area is close to the ambient temperature, which occurs in a place where the local slid-roll ratio is zero.     

基于大挠度理论的减振器阀片精确变形模拟和研究

为获得筒式减振器环形阀片弯曲变形的大挠度表达式与半径的关系,基于圆薄板大挠度理论,提出了薄板变形问题表达式内在统一的表示,结合针对环板外边缘挠度的大挠曲变形解析式与小挠曲变形方程,推导出环形阀片大挠曲变形与半径相关的混合解法解析式与变形修正系数。利用ABAQUS有限元软件对环形阀片进行了仿真分析,验证了混合解法解析式的精确度。分析了基于混合解法的叠加阀片弯曲变形,对叠加阀片的等效厚度与弯曲变形刚度进行了研究,得出的解析式与结论可用于减振器阀片的设计、调校与仿真分析。     

Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers

This paper employs an analytical method to analyze vibration of piezoelectric coupled thick annular functionally graded plates (FGPs) subjected to different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Reddy's third-order shear deformation theory (TSDT). The properties of host plate are graded in the thickness direction according to a volume fraction power-law distribution. The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study closed-form expressions for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. The present analysis is validated by comparing results with those in the literature and then natural frequencies of the piezoelectric coupled annular FG plate are presented in tabular and graphical forms for different thickness-radius ratios, inner-outer radius ratios, thickness of piezoelectric, material of piezoelectric, power index and boundary conditions.     

Analysis of aerostatic porous annular thrust bearings with tilt

A theoretical analysis is presented in order to predict the static characteristics of an aerostatic porous annular thrust bearing with a tilted runner pad. The flow through the porous matrix is assumed to be axial because the thickness of the pad is small compared with its radius. After the pressure in the porous matrix is obtained, the modified Reynolds equation is solved numerically using a finite-difference technique for the pressure distribution in the bearing clearance. The theoretical results are computed numerically in dimensionless form for the load capacity, mass rate of flow and static stiffness for various bearing dimensions and supply conditions. The results are presented in the form of design charts as a function of the feeding parameter. The effect of tilt is to improve the load capacity and the mass rate of flow.     

细丝对切刃口的设计

在某产品的生产制造过程中,需将一直径为0.051mm的不锈钢细丝通过火花放焊接在一铁镍合金弹簧片上。要获得良好的焊接效果,细丝的断口形貌尤为重要,锯齿状的断口能提高细丝焊接性能。分析了细丝剪切后的断口形貌及断口对焊接效果的影响,并通过正交试验法找出对切刃口的刃口半径与刃口角的最佳组合。     

Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method

In this paper, a finite element formulation is developed for analyzing the axisymmetric thermal buckling of FGM annular plates of variable thickness subjected to thermal loads generally distributed nonuniformly along the plate radial coordinate. The FGM assumed to be isotropic with material properties graded in the thickness direction according to a simple power-law in terms of the plate thickness coordinate, and has symmetry with respect to the plate midplane. At first, the pre-buckling plane elasticity problem is developed and solved using the finite element method, to determine the distribution of the pre-buckling in-plane forces in terms of the temperature rise distribution. Subsequently, based on Kierchhoff plate theory and using the principle of minimum total potential energy, the weak form of the differential equation governing the plate thermal stability is derived, then by employing the finite element method, the stability equations are solved numerically to evaluate the thermal buckling load factor. Convergence and validation of the presented finite element model are investigated by comparing the numerical results with those available in the literature. Parametric studies are carried out to cover the effects of parameters including thickness-to-radius ratio, taper parameter and boundary conditions on the thermal buckling load factor of the plates.     

Closed form solutions of axisymmetric bending of circular plates having non-linear variable thickness

A new analytical method for evaluation of elastic stresses and deformations in axisymmetric plates having variable thickness according to a power of a linear function, either solid or annular, subjected to symmetrical bending due to lateral loads either distributed on upper surface or distributed along the inner or the outer edges. The proposed procedure is based on two independent integrals of the hypergeometric differential equation describing the rotation field and constitutes the generalization of the one found in the literature. This method allows to study a wide range of plates, be they solid or annular, converging or diverging with linear or non-linear thickness function, convex, concave or linear tapered, without the restrictions of the known procedures. Analytical results obtained by using this method utterly match both theoretical results which may be obtained in the specific case known (constant-thickness circular plate, linear variable thickness annular circular plate) and numerical results obtained by using FEA.     

A6061薄壁圆锥管轴向压缩性能的数值分析和理论研究

采用LS-DYNA软件对锥倾角0°~40°、壁厚1 ~2.5 mm的A6061圆锥管进行轴向压缩仿真,研究锥倾角和壁厚对圆锥管吸能特性和变形规律的影响;基于Mamalis圆锥管瞬时载荷压溃模型,提出大范围锥倾角（15°~40°）瞬时载荷修正公式。研究结果表明：变形模式的临界角为15°,当锥倾角小于等于15°时,变形模式为堆叠模式,当锥倾角大于15°时,变形模式转变为嵌套模式;平均载荷与比吸能均随着锥倾角的增大缓慢减小,而初始峰值载荷则大幅度减小;随着壁厚增大,压溃模式由钻石模式转变为环形对称模式,平均载荷、初始峰值载荷和比吸能均增大。基于仿真结果,采用皮尔逊相关系数分析法修正了Mamalis瞬时载荷公式,修正值与仿真值的最大误差小于10%,通过试验验证了修正公式的准确性。修正公式为揭示大范围锥倾角薄壁管压溃机理提供了理论依据。     

A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates

An exact closed-form frequency equation is presented for free vibration analysis of circular and annular moderately thick FG plates based on the Mindlin's first-order shear deformation plate theory. The edges of plate may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson's ratio is set to be constant. The equilibrium equations which govern the dynamic stability of plate and its natural boundary conditions are derived by the Hamilton's principle. Several comparison studies with analytical and numerical techniques reported in literature and the finite element analysis are carried out to establish the high accuracy and superiority of the presented method. Also, these comparisons prove the numerical accuracy of solutions to calculate the in-plane and out-of-plane modes. The influences of the material property, graded index, thickness to outer radius ratios and boundary conditions on the in-plane and out-of-plane frequency parameters are also studied for different functionally graded circular and annular plates.     

气动高压激励的阵列式盘型压电俘能器

提出了利用气动高压激励的阵列式盘型压电俘能器实现气体能量的转化,以满足低功耗传感器的自供能需求。通过压电单晶片将气缸内部高压气体能量转化为电能,设计了阵列式盘型压电俘能器的样机结构;结合气缸的正常工作状态,分析了压电阵列的工作原理并进行了相应的实验。理论分析显示:盘型压电阵列具有较高的电荷量与良好的电容性,适合对具有交变载荷的高压气体能量进行收集。采用外径为12 mm、厚度为0.2 mm的压电单晶片及缸径为63mm、行程为150mm的气缸制作了实验样机,利用气动组件模拟气体环境搭建了测试系统。分别调节压力、周期、流量等参数进行了实验测试。结果表明:在交变的气动高压激励下,阵列式盘型压电俘能器可较好地收集交变高压气体载荷能量,其最佳匹配电阻为600kΩ,最大的瞬时功率为1 052μW,输出功率可满足低功耗传感器的能量需求。     

Free vibration of two span rectangular plates with some non-classical boundary conditions

This paper deals with the vibration of two span rectangular plates resting on linear and torsional springs. The two opposite continuous edges of the plate are considered as simple supports. The resulting equations are general. Numerical results have been obtained by varying spring stiffness and the aspect ratio. Some limiting cases of interest have also been developed.     

Temperature measurement during solidification of thin wall ductile cast iron. Part 1: Theory and experiment

Temperature measurement using thermocouples (TCs) influences solidification of the casting, especially in thin wall castings. The problems regarding acquisition of detailed cooling curves from thin walled castings are discussed.

Experiments were conducted where custom made TCs were used to acquire cooling curves in thin wall ductile iron castings. The experiments show how TCs of different designs interact with the melt and how TC design and surface quality affect the results of the data acquisition. It is discussed as to what precautions should be taken to ensure reliable acquisition of cooling curves. Measurement error depending on TC design and cooling conditions is shown.

A method is presented that allows acquisition of cooling curves in thin walled ductile iron castings down to a thickness of at least 2.8 mm. The obtained cooling curves can be used to compare nucleation and growth during solidification of castings with different plate thicknesses.     

高能激光反射镜热变形补偿

研制了一套由压电陶瓷驱动器、压力传感器、环状力施加机构和控制电路组成的反射镜动态热变形补偿系统用于补偿激光反射镜热变形球差。圆形反射镜在两个同轴不同半径的环形力作用下,其内环区域产生曲率可变的抛物面形变,由此补偿反射镜热变形带来的球差项。对镜体进行了有限元数值计算,建立了变形量与沉积热量与受力的关系。采用口径为100mm,厚度为8mm平面反射镜进行了受力-变形以及辐照-受力-变形实验,利用干涉仪对面型进行监测。研究表明,在不同推力作用下,有效区域内变形始终保持抛物面形。给出了推力-面型变化曲线,在225N推力下,中心最大变形超过3μm。在不同热沉积量下,镜体中心位移和受力保持线性关系,力-变形系数为0.013μm/N。     

Fracture prediction of thin plates under hemi-spherical punch with calibration and experimental verification

The response of thin clamped plates subjected to static punch indentation is investigated experimentally, analytically and numerically to determine the onset of fracture. The accumulated equivalent plastic strain with stress triaxiality as a weighing function is introduced as ductile fracture criterion in the finite-element simulation and analytical prediction. The fracture criterion was calibrated by finite-element simulations of uniaxial tensile tests. Based on the calibration, and calculated distributions and histories of stress and strain, the critical location, and penetration to fracture were predicted within 5–10% accuracy for three punch radii.The plots of force–penetration and locations of fracture initiation in the static punch indentation tests were compared with finite-element simulations and analytical approximations showing good agreement. The transverse deflection profiles of the plates at the point of fracture obtained numerically were shown to agree well with the closed-form solution derived by taking into account a variable stress ratio and varying stress triaxiality. The strain distribution along the plate radius is influenced by the friction between the interfaces of punch and plate. By changing the friction coefficient, the fracture-forming limit diagram was constructed numerically. The present procedure can replace the time-consuming experimental technique in which the strain path is controlled by changing the radius of a cut off.     

An exact solution for the bending of thin rectangular plates with uniform, linear, and quadratic thickness variations

In this paper, the analysis of the titled problem is based on classical thin-plate theory, and its numerical solution is carried out by using the small parameter method and Lévy-type approach. The thin rectangular plate considered herein is simply supported on two opposite edges. The boundary conditions at the other two edges may be quite general, and between these two edges the plate may have varying thickness. Closed-form solutions have been developed for the static response of isotropic rectangular plates with non-uniform thickness variation and subjected to arbitrary loading. The accuracy of the present model is demonstrated via problems for which the exact solutions and numerical results are available, and results are also compared with those obtained by using the finite-difference method.     

An elasto-plastic finite element analysis of the sheet metal stretch flanging process

The incremental updated Lagrangian elasto-plastic finite element method (FEM) was employed in this study to analyse the stretch flanging of circular plates with a pre-determined smaller hole at the centre of the sheet metal. An extended r _min technique was employed such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also by the change in the boundary condition along the tool-sheet interface. The experimental results, using a low-carbon (BA-CQ₂) sheet plate with a thickness of 1.0 mm, have been obtained and compared with the corresponding theoretical results. It was found that the flange thickness does not always decrease monotonically from the die shoulder to the flange edge. Reducing the punch diameter and increasing the flange height significantly reduced the flange thickness. Web width does not influence the thickness distribution of the flange. The tendency of flange thickness to thin decreases as punch diameter increases. The reduction of thickness at the die shoulder depends on the die shoulder radius. Simulation results of punch load of stretch flanging, the deformed geometry, and the distribution of thickness are compared with experimental data and found to satisfactorily agree.