点的复合运动的矩阵矢量法

利用线性代数中矩阵运算和矢量分析的方法,推导了作复合运动的点的绝对位置、速度和加速度计算公式,简化了具体的分析过程,且便于利用计算机求解较为复杂的空间运动.     

Free vibration analysis of composite beams with two non-overlapping delaminations

An analytical solution to the free vibration of composite beams with two non-overlapping delaminations is presented. The delaminated beam is modeled as seven interconnected Euler-Bernoulli beams using the delaminations as their boundaries. The continuity and the equilibrium conditions are satisfied between adjoining beams. The analysis includes the differential stretching between the delaminated layers and the bending-extension coupling. The results of the present model agree well with the analytical and experimental data reported in the literature. Parametric studies show that the sizes and locations of the delaminations have significant effect on the natural frequencies and mode shapes. These results provide useful information in the study of the free vibration of delaminated composite beams.     

Characteristics of thermo-acoustic emission from composite laminates during thermal load cycles

The thermo-acoustic emission (AE) technique has been applied for nondestructive characterization of composite laminates subjected to cryogenic cooling. Thermo-AE events during heating and cooling cycles showed a Kaiser effect. An analysis of the thermo-AE behavior obtained during the 1st heating period suggested a method for determining the stress-free temperature of the composite laminates. Three different thermo-AE types classified by a short-time Fourier transform of AE signals enabled to offer a nondestructive estimation of the cryogenic damages of the composites, in that the different thermo-AE types corresponded to secondary microfracturing in the matrix contacting between crack surfaces and some abrasive contact between broken fiber ends during thermal load cycles.     

Interlaminar stresses of a rectangular laminated plate with simply supported edges subject to free vibration

The interlaminar stresses in a laminated rectangular orthotropic plate with four sides simply supported edges during free vibration was determined by using the integration method involving the dynamic inertia terms and displacements. The approximate stresses solutions are obtained under the effect of frequencies of vibration for four-layer symmetric cross-ply laminates with the ply configurations [0°/90°]_s and [90°/0°]_s, angle-ply laminates with the ply configuration [45°/−45°]_s. Numerical results show that the natural frequency has significant effects on the dominant interlaminar stresses in the stacking sequences [0°/90°]_s, [90°/0°]_s and [45°/−45°]_s.     

A simple method to calculate mode components of strain energy release rate of free-edge delaminations in composite laminates

A simple method, which calculates the mode components of the strain energy release rate of free-edge delaminations in the laminates, is proposed. The interlaminar stresses are evaluated as an interface moment and interface shear forces that are obtained from the equilibrium equations at the interface between the adjacent layers. Deformation of an edge-delaminated laminate is calculated by using a generalized quasi-three dimensional classical lamination theory developed by the author. The analysis provides closed-form expressions for the three components of the strain energy release rale. The analyses are performed on [+30/−30/90]s laminates subjected to uniaxial extension, with free-edge delaminations located symmetrically and asymmetrically with respect to the laminate midplane. Comparison of the results with a finite element solution using the virtual crack closure technique shows good agreement. The simple nature of this method makes it suitable for primary design analysis for the delaminations of composite laminates.     

多切口层合曲梁分析

建立了多切口层合曲梁分析模型,根据切口的数目和位置梁被分成若干段,每段假设一层间非连续的剪应变为厚度方向坐标的二次多项式,进而根据层间连续条件和梁面剪应力为零的条件推出能反映横向剪切变形的位移场。各段的位移场形式相同,两个相邻段之间的连续条件可通过匹配位移变量来实现,该模型具有位移场变量少和精度高等优点,文中构造了其有限元模型,比较了本文模型及其简化模型的计算精度和适用范围。     

On the prediction improvement of transverse stress distributions in cross-ply laminated beams: advanced versus conventional beam modelling

This paper assesses the stress analysis performance of the most commonly used conventional, shear deformable beam theories as well as the advanced beam theories presented in references [Acta Mech. 1997;123:163; Math. Mech. Solids 1997;2:459; Int. J. Solids Struct. 1997;22:2857], by employing a predictor–corrector method. The assessment deals with the accuracy of the distribution of the interlaminar (transverse shear and transverse normal) stresses through the entire beam thickness. As far as simply supported, cross-ply laminated beams are concerned, it compares the corresponding stress analysis results obtained with their exact elasticity counterparts. The conclusions of this type of initial assessment are very much in favour of the advanced beam theories, which involve exponential shape functions of the transverse co-ordinate parameter. Hence, those advanced beam theories are employed for further applications that involve different sets of end boundary conditions for which explicit exact elasticity results are unavailable or very difficult to obtain.     

REDUCTION OF MACHINING VIBRATION BY USE OF RUBBER LAYERED LAMINATES BETWEEN TOOL HOLDER AND INSERT

The aim of the present study is to investigate chatter when using carbide inserts by measuring surface roughness of the workpiece. Dimensional accuracy of the workpiece is affected by vibration. In order to suppress chatter, the tool was provided with an ultra thin metal rubber laminate between the tool holder and insert. An experimental investigation has been carried out in CNC lathe using a “design of experiments” approach. In this study, vibration of the tool and surface roughness of the workpiece were measured. It has been observed that the vibration of the tool, as well as the tool insert, has been reduced by using ultra thin rubber layered laminates, and the surface finish of the workpiece has been improved.     

A composite view on Windenburg's problem: Buckling and minimum stiffness requirements of compressively loaded orthotropic plates with edge reinforcements

This paper discusses the buckling behaviour of orthotropic composite plates under uniform uniaxial compression with one free reinforced unloaded edge. A typical application example for use of such a mechanical model is the web of stiffeners and frames attached to the fuselage skin of an aircraft. The considered plates are rectangular and simply supported at the loaded transverse edges. One of the longitudinal unloaded edges is also simply supported, while the second unloaded edge is not supported at all but is reinforced by a flange of arbitrary cross-section. At first, an exact solution for the elastic buckling problem is derived from the governing differential equation by imposing the underlying boundary conditions. Thereafter, two approximate closed-form solutions for the buckling load are derived, which can be conveniently used for practical application purposes. Generic buckling curves using characteristic non-dimensional quantities are also presented. Finally, the question of the required bending stiffness EI_min of the flange is treated, to ensure that the flange withstands buckling and provides simply supported boundary conditions to the free reinforced plate edge.     

Influence of invariant material parameters on the flexural optimal design of thin anisotropic laminates

A general discussion of the optimal solutions to the problems of maximum stiffness, buckling load and modal frequencies for rectangular laminates is proposed. The study is based upon some invariant dimensionless material parameters. The conditions giving rise to the same objective function for the three cases are discussed and a new physical meaning of the objective as a stiffness modulus is proposed. The geometrical and material conditions giving rise to non-trivial optimal solutions are also discussed.     

Modelling of cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip

An approximate theory for cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip is developed. This theory uses only 4 displacement and potential variables, the number of which is independent of the number of layers involved. The displacement and electric potential fields are depicted by the displacement and electric potential distribution functions through thickness, respectively. The two functions are formulated according to particular solutions to the three-dimensional elasticity equilibrium equations and electrostatics charge equation. In this shear slip modelling interfacial opening is neglected. The interfacial bonding conditions are characterised by a linear slip law and an electrically permeable assumption. A corresponding finite element is also developed to deal with piezoelectric laminates with local shear slip. The accuracy and effectiveness of the present theory are demonstrated in numerical examples.     

Free-edge effect in cross-ply laminated hollow cylinders subjected to axisymmetric transverse loads

On the basis of the theory of three-dimensional elasticity, free-edge stresses and displacements of axisymmetrically loaded laminated hollow cylinders are found by using the state space equation method. The study assumes three-dimensional variations of both stresses and displacements and takes into account material constants of all individual material layers. By this approach, composite cylinders may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thicknesses. The solution provides a continuous inter-laminar stress field across interfaces and a satisfactory approximation to the singularity occurring in the boundary layer region of a free-edge. Numerical solutions are compared with the results obtained from an alternative numerical method. New results are obtained and parametric studies are carried out.     

Stability behaviour of arbitrarily laminated composite plates with free and elastically restrained unloaded edges

In this paper, the initial buckling loads and the corresponding buckling modes of symmetric rectangular laminated plates are investigated. The considered laminates are supposed to have a uniform thickness, are subjected to a linearly distributed inplane compressive normal load and are simply supported at the two loaded edges with one free unloaded plate edge and with one simply supported unloaded edge where elastic rotational restraints are considered. Unlike in many other investigations, the composite laminates presently under consideration may have arbitrary yet symmetric lamination schemes with bending–torsion coupling. The initial buckling loads of such plates are calculated using the RITZ-method for which some especially adjusted displacement shape functions are employed. Since a series expansion of the buckling shape is performed in the load direction only while in the perpendicular direction one single displacement function can be shown to be sufficient, the present approach is numerically very efficient when compared to approaches in which a series representation is chosen with respect to both inplane directions. Comparison with reference results and with finite element computations leads to an excellent agreement. Some new findings on the general stability behaviour of this class of laminated plates are presented as a closure.     

An accurate de-lamination model for weakly bonded laminates subjected to different sets of edge boundary conditions

This paper extends the applicability of a new method (Soldatos and Watson. Acta Mechanica 1997;123 (3): 163–86; Soldatos and Watson. International Journal of Solids and Structures 1997;34 (22):2857–85; Soldatos and Watson. Mathematics and Mechanics of Solids 1997;2(4):459–89; Shu and Soldatos. International Journal of Solids and Structures 2000;37:4289–307) towards the accurate stress analysis of weakly bonded laminates. The main advantage of the method stems from the fact that it is based on a suitable version of a generalised two-dimensional plate theory that makes use of a small number of degrees of freedom, which is not dependent on the number of the layers involved. Hence, although the method can accommodate with relative ease any set of boundary conditions imposed at the plate edges, it avoids the computationally expensive consequences of corresponding two-dimensional layer-wise plate models or relevant three-dimensional finite element considerations.     

单自由度双曲柄六杆压力机机构计算机建模与动态静力分析向量键合图法

针对单自由度双曲柄六杆压力机机构计算机建模与动态静力分析问题,提出了相应的向量键合图法。根据机构的结构及组成原理,建立其向量键合图模型;通过有效的方法,使机构向量键合图模型的贮能元件皆具有积分因果关系,解决了机构动态静力分析计算机建模的代数困难。应用相应的算法,实现了单自由度双曲柄六杆压力机机构计算机建模与动态静力分析,分析了脉冲形式的工作阻力对机构驱动力矩及运动副约束反力的影响,说明了所述方法的可靠性及有效性。     

Air damping influence on dynamic parameters of laminated composite plates

Damping performance of lightweight composite structures, like fibre reinforced plastics (FRPs) is more efficient than the conventional materials. This phenomena was found valuable in the aerospace and transport industries. For this reason accurate material properties of FRPs are required for precise prediction of dynamic response. However, the given properties are often burden with a significant uncertainty level due to environment influence which includes air damping, temperature changes, humidity, etc. The present study concerns with the air damping influence on the dynamic behaviour of laminated composites plates with moderate damping level. The effect on dynamic characteristics is evaluated experimentally using a vacuum chamber and a laser vibrometer. Resonant frequencies and modal loss factors changes are investigated in terms of material type, sample size and excitation amplitude. A semi-automatic and time efficient two-step testing procedure is developed for a precise measurement of loss factors of laminated composite plates.     

Hygrothermal effects on the postbuckling of shear deformable laminated plates

The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.     

An analytical study on prediction of effective properties in porous and non-porous piezoelectric composites

Eshelby type micromechanics model with a newly developed piezoelectric Eshelby tensor is proposed for predicting the effective electroelastic properties of the piezoelectric composite. The model is applied for piezoelectric solids containing both porosities and metal inhomogeneities. The effective electroelastic moduli of the composites such as stiffness, piezoelectric constants, and dielectric constants are predicted by the present model, which are extensively compared with the existing experimental results from the literatures. The validity of Eshelby type model for predicting the effective properties of the composite is thoroughly examined. It can be concluded from this study that a new mechanism is needed to compute correctly the dielectric constants among the effective properties of the composites.     

一种单芯片多轴运动控制器设计

设计了一种以现场可编程门阵列(FPGA)为核心模块的多轴运动控制器.该运动控制器具有开放式、可重构及模块化的特点,并且能够方便地运用到各种应用场合.