复合材料层合板低速冲击后压缩的损伤累积模型

为了分析复合材料层合板低速冲击后的压缩性能,首先用三维动态有限元素法对两种层合板进行了低速冲击损伤模拟计算,以此作为冲击后压缩（CAI）层合板的初始损伤,然后用三维静态有限元对含损伤的层合板进行压缩破坏模拟和剩余强度计算,从而实现了层合板从冲击损伤到压缩破坏损伤全过程的模拟．结果表明,损伤投影面积和CAI强度的计算值与试验结果有较好的一致性．     

A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time

The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency domain, which is commonly used in harmonic expansion of disturbances, the approach advanced allows one to analyze the solution in the case of discontinuous first derivatives of displacements without calculating jumps in summing series. A generalized closed-form solution is obtained for stresses in an arbitrary cycle n(t), which is determined by the multiplicity of the time of wave travel across the double thickness of the plate. A method of recurrent solution based on calculating the convolution of repeated integrals of the initial form of disturbance at t = 0 is elaborated. The procedure can be used for evaluating the maximum stress and the contact time in a plane impact on the surface of a plate.     

Detection of matrix cracks in composite laminates by using the modal strain energy method

As the foremost mechanism of damage development, matrix cracking is the critical damage found in the early stage of structural failure of composites. This study aims to nondestructively detect matrix cracks in composite laminates by using an experimental modal analysis (EMA). An AS4/PEEK composite was used to fabricate cross-ply [0₂/90₁₂/0₂] and quasi-isotropic [(±45/0/90)₄] _s laminates. The damage in the form of a matrix crack in the laminates was created by using a tensile load. The EMA was conducted on the laminates to obtain the modal displacements before and after damage. The displacements were then employed to compute the modal strain energy and to define the damage index, which is used for detecting matrix cracks. Limited by the mesh points of measurements, we used the differential quadrature method to calculate the partial differentials in the strain energy formula. The results obtained were validated by using the X-ray radiography method and three-point bending tests. The experimental results showed that the damage index well identified the location of breadthwise matrix cracks inside the laminates. However, the resolution of the damage index became poor if the spans of matrix cracks were short or the matrix cracks were scattered over the laminates.     

On the extremal value of the thermoelastic energy of a material with an inclusion subject to mechanical and thermal action

Under prescribed thermoelastic stresses and known properties of the matrix and the inclusion in an elastic medium with an inhomogeneity, we find the shape of inhomogeneity that leads to an extremal value of the thermoelastic energy. From the necessary conditions for an extremum of the thermoelastic energy functional we find a condition for seeking the interface. For the case of isotropic cornponents and under loads of stretching (compression) type and uniform heating of the medium the shape of the inclusion can be found explicitly within a certain range of initial parameter values. The results of numerical study are presented and analyzed. One table. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 26–34.     

Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings

This work reports on a numerical investigation on the bifurcations of a flexible rotor response in active magnetic bearings taking into account the nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the actuator forces that are nonlinear function of the coil current and the air gap. For the values of design and operating parameters of the rotor-bearing system investigated in this work, numerical results showed that the response of the rotor was always synchronous when the values of the geometric coupling parameter α were small. For relatively larger values of α, however, the response of the rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of periods-2, -3, -6, -9, and -17, quasi-periodicity and chaos. Numerical results further revealed the co-existence of multiple attractors within certain ranges of the speed parameter Ω. In practical rotating machinery supported by active magnetic bearings, the possibility of synchronous rotor response to become non-synchronous or even chaotic cannot be ignored as preloads, fluid forces or other external excitation forces may cause the rotor’s initial conditions to move from one basin of attraction to another. Non-synchronous and chaotic vibrations should be avoided as they induce fluctuating stresses that may lead to premature failure of the machinery’s main components.     

On the influence of initial stresses on the velocities of the stoneley waves

Wave propagation along a plane boundary separating compressible, previously deformed bodies with elastic potential of arbitrary form, is studied. The linearized theory of wave propagation in bodies with finite initial deformation is used. A case in which one of the bodies is a liquid, is studied. It is shown that in the case of the Murnaghan and harmonic type potentials the wave velocities depend linearly on the initial stresses. In contrast with the case of an unbounded isotropic body /1/, here the character of the dependence is not influenced by the choice of the form of the potential. In the absence of the initial stresses the relations obtained coincide with the results of /2/.     

The Sensitivity of Residual Stresses of Cross-Ply Laminates to Manufacturing and Material Parameters

By using a finite-element model elaborated, the sensitivity of residual stresses of polyester/glass cross-ply laminates to manufacturing and material parameters is investigated. The development of residual stresses in the laminates and the significance of the parameters for the problem are discussed. It is found that the main attention in calculating residual stresses should be focused on the properties of resin, which must be measured with care. The most important parameters related to the resin are, of course, its stiffness, thermal expansion, and chemical shrinkage, while the properties of fibers can be obtained from material handbooks with a sufficient accuracy. In curing a thin laminate in an autoclave, the simulation of chemical reactions and the parameters needed in thermal analysis are quite insignificant, because, in practice, the autoclave temperature and the properties of the mold determine the laminate temperature history.     

Stress-dependent Failure Surface of Granular Materials

Numerical computations of geotechnical problems will become increasingly important because of the growing complexity of geotechnical applications. Therefore, a well-founded prediction of stability statements requires appropriate models, which are able to realistically depict the stress-strain behaviour of non-cohesive-frictional granular materials. On several stress paths, drained triaxial compression experiments on compact dense sand specimen exhibited that the size of the failure surface is not independent from the hydrostatic pressure. The failure surface and, thus, the maximal shear stresses at a specific confining pressure σ₃^exp can be increased by a compression preload at a level higher than σ₃^exp. This means that granular materials own several failure surfaces in dependence of the hydrostatic pressure. Consequently, the failure criteria based on the assumption of a compression stress-path-independent single-failure surface cannot recover the newly detected plastic yielding behaviour of granular materials. An improved approach for modelling the plastic hardening and softening behaviour coupled with the new yield properties at the limit state will be presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free-Edge Stresses around Holes in Laminates by the Boundary Finite-Element Method

In the present paper the boundary finite-element method is presented as a highly efficient technique for the numerical investigation of the free-edge stresses around a circular hole in laminates. In this method, as in the boundary element method, only the boundary needs to be discretized, whereas the element formulation in essence is finite-element based. The surface discretization provides a high numerical efficiency and requires less computation time compared to finite-element analyses. Numerical results for the concentration of interlaminar stresses at holes in composite laminates show a very good agreement with comparative finite-element calculations.     

Effects of initial stresses on guided wave propagation in multilayered PZT-4/PZT-5A composites: A polynomial expansion approach

Effects of initial stresses on the dispersion curves of Lamb and SH waves in multilayered PZT-4/PZT-5A composites are investigated using the polynomial expansion approach. The piezoelectric layers are considered with arbitrary crystal orientations with a result that only Lamb or SH waves may be transmitted. The problem is solved employing the Legendre polynomial approach that poses the advantages of numerically stability and effectiveness over conventional matrix method. The solution is validated by comparing the wave propagation behavior of piezoelectric materials with those reported in literature, and the convergence properties are examined. Numerical results demonstrate that initial stress has profound influences on the guided wave propagation in multilayered PZT-4/PZT-5A laminates. The phase velocity of Lamb and SH waves increases with initial tensile stresses. In addition, the effects of initial stresses rely on the wave mode and thickness of constituent layers and the stacking sequence of the constituent materials. The results are useful for understanding and optimization of new designs for actuator, electromechanical sensor and acoustic wave devices made of PZT-4/PZT-5A composites.     

Numerical investigation of residual thermal stresses in welded joints of heterogeneous steels with account of technological features of multi-pass welding

The paper describes a two-dimensional mathematical model to evaluate stresses in welded joints formed in multi-pass welding of multi-layered steels. The model is based on a system of equations that includes the Lagrange's variational equation of the incremental theory of plasticity and the Biot's variational principle for heat transfer simulation. In the constitutive equations, the changes in the volume which occur as a result of phase transitions can be taken into account. Therefore, the prehistory and impact of thermal processing of materials on macroscopic properties of the medium can be considered.The variational-difference method is used to solve both the heat transfer equation for calculation of the non stationary temperature field and the quasi-static problem of thermoplasticity at each time-step. The two-dimensional problems were solved to estimate the residual thermal stresses (for the case of plane stress or plane strain) during cooling of welds and assessing their impact on strain localization in the heat-affected zone under tensile and compressive loading considering differences in mechanical properties of welded materials.It is shown that at initial stages of the plastic flow, the residual stresses significantly affect the processes of stress concentration and localization of strains in welded joints. To estimate the model parameters and to verify the modeling results, the available experimental data from scientific literature obtained on the basis of the Satoh test for different welding alloys was used.     

Effect of low-speed impact damage on the buckling properties of E-glass/epoxy laminates

The postimpact buck ling loads of E-glass/epoxy laminates have been measured. Composite samples with the stacking sequence [+45/−45/90/0]_2s were subjected to low-speed impact loadings at various energy levels. The tests were conducted on a specially developed vertical drop-weight testing machine. The main impact parameters, such as the peak load, absorbed energy, deflection at the peak load, and damage area, were evaluated and com pared. The damaged specimens were subjected to compressive axial forces, and their buckling loads were determined. The relation between the level of impact energy and buck ling loads is investigated.     

A condensed microelectromechanical constitutive and damage model for tetragonal ferroelectrics

A condensed model for ferroelectric solids with tetragonal unit cells is presented. The approach is microelectromechanically and physically motivated, considering discrete switching processes on the level of unit cells and quasi-continuous evolution of inelastic fields on the domain wall level. To calculate multiple grain interactions an interaction tensor is introduced. Hysteresis loops are simulated for pure electric and electromechanical loading, demonstrating e.g. the influence of a compressive preload on the poling process and interaction between statistically arranged crystallits. The residual stresses and the corresponding principle stresses are used to simulate fatigue damage in ferroelectric materials. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A phenomenological method of calculating the residual stresses and plastic deformations in a hollow surface-hardened cylindrical sample

A phenomenological method is proposed for calculating the residual stress and plastic deformation fields in a hollow surface-hardened cylindrical sample. Versions of the hardening are considered that lead to isotropy and anisotropy in the plastic deformations in the surface layer. A hardening anisotropy parameter is introduced that relates the axial and circumferential components of the residual plastic deformation tensor. The experimentally determined axial and/or circumferential components of the residual plastic stress tensor are used as the initial information. The tensor fields of the residual stresses and deformations are constructed assuming the hypothesis of surface hardening anisotropy and the absence of secondary plastic compression deformations and that the tangential components of the residual stress tensor and the plastic incompressibility of the material are small. A technique is developed for identifying the parameters of the proposed method. The adequacy is checked using experimental data for test pieces of type 45 and 12X18H10T steels hardened by hydro-shot blasting treatment and of type 45 steel hardened by treatment with a roller. Good agreement is observed between the calculated and experimental results. It is noted that the anisotropic hardening procedure leads to a substantial difference between the circumferential and axial components of the residual stresses in the hardened layer, unlike the case of isotropic hardening where they are practically identical.     

Theory of the biomechanism of fractures of the diaphysis of long tubular bones

A new theoretical basis is proposed for the biomechanism of fractures of the diaphysis of long tubular bones resulting from bending deformation. Bone damage is shown to result from the concentration of maximum tensile stresses on the tension side and shear stresses in the compression zone. The origin of fan-shaped cracks and oblique fractures, occurring individually or in combination, is explained in these terms.Altai State Medical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 318–322, March–April, 1971.     

A comparative study for the calculation of the temperature dependent shapes of unsymmetric laminates based on finite element analysis and extended classical lamination theory

It is well known that the room-temperature shapes of unsymmetric laminates do not always conform to the predictions of classical lamination theory. Instead of being saddle shaped, as classical lamination theory predicts, the room-temperature shapes of unsymmetrically laminated composites are often cylindrical in nature. In addition, a second cylindrical shape can sometimes be obtained from the first by a simple snap-through action. Hyer examined the class of all square unsymmetric cross-ply laminates which can be fabricated from four layers, i.e., [0/0/0/90], [0/0/90/0], [0/90/0/90], [0/0/90/90], and developed an extended classical lamination theory to predict whether these laminates have a saddle shape or one or two cylindrical shapes. Finite element analysis (FEA) has just recently been used for the calculation of the room-temperature shapes of unsymmetric laminates because more sophisticated finite element codes are now available and the calculations can be made in an acceptable time. The hope is to get more accurate results for the shape and the stresses and forces that occur during the snap-through action. These results are needed for the development of active deformable composite structures based on unsymmetric laminates and incorporated shape memory alloy wires [1]. Results for different lay-ups are presented and compared.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 341–350, May–June, 1995.     

Mechanical properties of polyester polymer-concrete

The properties of a polymer-concrete composed of polyester matrix and locally available rock aggregate are investigated. The formula of the concrete is found by an experimental-calculation approach in such a way as to attain a closer packing of the aggregate particles on the one hand, and to ensure the needed processing characteristics (placeability) of the mix on the other. It is shown experimentally that the material obtained has a rather high compression strength. Under prolonged compression loads, the polymer-concrete exhibits a noticeable creep behavior with a linear relation between the creep strains and stresses. After the action of half the ultimate load over 3000 h, the total strains exceed the instantaneous ones by 2.0 to 2.2 times. The accumulation of irreversible strains is also observed; however, their contribution to the total strain is small. It is found that the stress-strain relation can be represented by the equation of linear hereditary creep theory.