VIBRATION SUPPRESSION OF CANTILEVER LAMINATED COMPOSITE PLATE WITH NONLINEAR GIANT MAGNETOSTRICTIVE MATERIAL LAYERS

In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials(GMM) is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in response to applied magnetic field under variable bias conditions(pre-stress and bias magnetic field).The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method(FEM) in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail.     

Features of plane wave propagation along the layers of a prestrained nanocomposite

Features of the propagation of longitudinal and transverse plane waves along the layers of nanocomposites with process-induced initial stresses are studied. The composite has a periodic structure: it is made by repeating two highly dissimilar layers. The layers exhibit nonlinear elastic behavior in the range of loads under consideration. A Murnaghan-type elastic potential dependent on the three invariants of the strain tensor is used to describe the mechanical behavior of the composite constituents. To simulate the propagation of waves, finite-strain theory is used for developing a problem statement within the framework of the three-dimensional linearized theory of elasticity assuming finite initial strains. The dependence of the relative velocities of longitudinal and transverse waves on two components of small initial stresses in each layer and on the volume fraction of the constituents is studied. It is established that there are thickness ratios of layers in some nanocomposites such that the wave velocities are independent of the initial stresses and equal to the respective wave velocities in composites without initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 3–26, April 2007.     

A theoretical analysis of piezoelectric/composite anisotropic laminate with larger-amplitude deflection effect,Part I: Fundamental equations

Considering the effects of both the different material properties of composite layers and the poling directions of piezoelectric layers, we utilized the assumption of the simple-higher-order shear deformation theory to model and analyze the laminated composite plate integrated with the random poled piezoelectric layers. Further, the generalized Hamilton’s variation principle for electro-elasticity was employed to deduce the fundamental equations of piezoelectric/composite anisotropic laminate, i.e. the governing equations and boundary conditions. For the special requirement of the larger-amplitude deflection of smart structures, the Von Karman strains were used to account for the geometric nonlinear effect of the practical larger-amplitude deflection on the electro-elastic behavior of smart composite structures. Moreover, the sensor equations were also carried out with considering the large-amplitude deflection effect of smart composite structures.     

摩擦温度对Ni—P基复合刷镀层摩擦学性能的影响

为了考察摩擦温度对Ni-P基复合镀层摩擦学性能的影响,作者按球-盘接触形式推导出了计算摩擦温度的数学表达式,其对Ni-P/WC和Ni-P/BN及Ni-P/MoS_2等几种复合镀层摩擦温度的计算结果与试样表面层的硬度分布显示了良好的对应性。磨损试验结果表明,特别在高PV值的情况下,Ni-P基复合镀层的摩擦学性能主要受摩擦温度的影响。这是因为Ni-P基复合镀层在镀态下呈非晶态组织,受热发生晶化反应后会使硬度上升,但温度过高时硬度却又下降。因此,镀层硬度是依摩擦温度的高低及其在镀层中的梯度分布而呈现出不同的分布特征,从而揭示了Ni-P/WC复合镀层在高PV值条件下显示良好固体润滑性能的原因。     

FRP strengthened walls with delaminated regions – Geometrically nonlinear response

The paper studies the geometrically nonlinear behavior of walls that are strengthened with fiber reinforced polymer (FRP) composite materials but include pre-existing delaminated regions. The paper uses an analytical–numerical methodology. Three specially tailored finite elements that correspond to perfectly bonded regions, to delaminated regions where the debonded layers are in contact, and to delaminated regions where the debonded layers are not in contact are presented. All finite elements are based on a high order multi layered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains whereas the contact nonlinearity is handled iteratively. The validity and convergence of the finite element models is demonstrated for each type of element through comparison with closed form analytical solutions available for specific cases. The unified model that combines the three types of finite element is then used for studying the nonlinear behavior of a locally delaminated FRP strengthened wall under in-plane normal and in-plane shear loads. Finally, conclusions regarding the effect of the delamination on the response of the strengthening system, on the conditions that evolve in the bonded region that surrounds the delamination, and on the global response of the multi-layered structure are drawn. Additional conclusions regarding the application of the modeling approach to other delamination sensitive layered structural systems close the paper.     

Woven fabric composite material model with material nonlinearity for nonlinear finite element simulation

The objective of the current investigation is to develop a simple, yet generalized, model which considers the two-dimensional extent of woven fabric, and to have an interface with nonlinear finite element codes. A micromechanical composite material model for woven fabric with nonlinear stress-strain relations is developed and implemented in ABAQUS for nonlinear finite element structural analysis. Within the model a representative volume cell is assumed. Using the iso-stress and iso-strain assumptions the constitutive equations are averaged along the thickness direction. The cell is then divided into many subcells and an averaging is performed again by assuming uniform stress distribution in each subcell to obtain the effective stress–strain relations of the subcell. The stresses and strains within the subcells are combined to yield the effective stresses and strains in the representative cell. Then this information is passed to the finite element code at each material point of the shell element. In this manner structural analysis of woven composites can be performed. Also, at each load increment global stresses and strains are communicated to the representative cell and subsequently distributed to each subcell. Once stresses and strains are associated to a subcell they can be distributed to each constituent of the subcell i.e. fill, warp, and resin. Consequently micro-failure criteria (MFC) can be defined for each constituent of a subcell and the proper stiffness degradation can be modeled if desired. This material model is suitable for implicit and could be modified for explicit finite element codes to deal with problems such as crashworthiness, impact, and failure analysis under static loads.     

复合材料圆筒自由边效应的有限元分析

本文分析复合材料圆筒在内压作用下的自由边效应，讨论圆筒的叠层顺序对自由边应力的影响，预报最易发生边界脱层的界面．有限元分析结果表明：层间剪切破坏是该结构发生边界失效的主要原因，不同的叠层顺序可较大地影响自由边层间剪切应力，而大变形情况下线性有限元分析结果与非线性有限元数据相差较大，几何非线性的影响不容忽视．     

Strain and Fracture of Glass-Fiber Laminate Containing Metal Layers

This paper describes an experimental study on strain and fracture of plane samples made of glass-fiber laminate and fabric-based laminate with surface and inner aluminum layers. It is shown that the presence of these layers reduces the strength of glass-fiber laminate under static and low-cycle loading. This can be explained by the fact that the stretching of a hybrid composite along the layers is accompanied by the formation of localized tensile regions of glass-fiber laminate across the layers. As a result, both the hybrid composite and its glass-fiber laminate component are stratified.     

Study of the Nonlinearly Elastic State of an Orthotropic Cylindrical Shell with a Hole, Using Mixed Functionals

An analogy is established between some terms of the functionals under consideration and the formulas of the theory of random processes. On this basis, the efficiency of mixed functionals is attributed to a deeper minimum they help to reach by taking the energy of so-called false strains into consideration. We perform a numerical stress—strain analysis of an organoplastic cylindrical shell with a side circular hole and study how the orthotropy and nonlinear properties of the composite affect the stress distribution near the hole. The case is discovered where the orientation of the composite about the cylindrical shell changes so that a larger nonlinear effect corresponds to a smaller initial stress     

受热复合材料层合板的非线性静动态响应分析

基于高阶剪切变形理论，突出考虑横向正应变和横向剪切应变的影响，对受热和外力联合作用下复合材料层合板的非线性静、动态响应进行分析。动态分析时计及了转动惯量的影响，给出了Ｃ°类有限元公式。文中数值算例同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性。文中还对层合反的边界条件、纵厚比及铺设角度对非线性动态响应的影响进行了分析。     

一种求解层合圆柱壳的杂交应力单元

根据修正的余能原理，推导出一种求解复合材料层合圆柱壳的杂交应力单元。取用六面体等参单元，此单元反映了各层材料性质不同及应力分布沿整个厚度不连续现象，同时计入横向剪切变形和法向挤压变形，适用于厚层壳体。文章通过实例说明此单元能准确求出各层内的应力值，实用价值高。     

Nonlinear low-velocity impact on damped and matrix-cracked hybrid laminated beams containing carbon nanotube reinforced composite layers

This paper investigates the low-velocity impact response of a shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and carbon fiber reinforced composite (CFRC) layers. The effect of matrix cracks is considered, and a refined self-consistent model is selected to describe the degraded stiffness caused by the damage. The beam including damping effects rests on a two-parameter elastic foundation in thermal environments. Based on a higher-order shear deformation theory and von Kármán nonlinear strain–displacement relationships, the motion equations of the beam and impactor are established and solved by means of a two-step perturbation approach. The material properties of both CFRC layers and CNTRC layers are assumed to be temperature-dependent. To assess engineering application of this hybrid structure, two conditions for outer CNTRC layers and outer CFRC layers are compared. Besides, the effects of the crack density, volume fraction of carbon nanotube, temperature variation, the foundation stiffness and damping on the nonlinear low-velocity impact behavior of hybrid laminated beams are also discussed in detail.

     

Mechanical Performance of a Recycled Carbon Fibre/PP Composite

A composite made of recycled carbon fibres in recycled polypropylene matrix is studied experimentally to describe the features of the elastic and time dependent nonlinear mechanical behaviour. The properties of the developed material have a large variability to be addressed and understood. It was found that the stress-strain curves in tension are rather nonlinear at low strain rate and the strength is sensitive to strain rate. The elastic properties’ reduction for this composite after loading to high strains is rather limited. More important is that even in the “elastic region” due to viscoelastic effects the slope of loading–unloading curve is not the same and that at higher stress large viscoplastic strains develop and creep rupture is typical. The time and stress dependence of viscoplastic strains was analysed and described theoretically. The viscoelastic response of the composite was analysed using creep compliance, which was found to be slightly nonlinear.     

Moderately large flexural vibrations of composite plates with thick layers

In this paper moderately large amplitude vibrations of a polygonally shaped composite plate with thick layers are analyzed. Three homogeneous and isotropic layers with a common Poisson’s ratio are perfectly bonded and their arbitrary thickness and material properties are symmetrically disposed about the middle plane. Mindlin–Reissner kinematic assumptions are implemented layerwise, and as such model both the global and local response. Geometric nonlinear effects arising from longitudinally constrained supports are taken into account by Berger’s approximation of nonlinear strain–displacement relations. Overall cross-sectional rotations are defined and subsequently a correspondence of this complex problem to the simpler case of a homogenized shear-deformable nonlinear plate with effective stiffness and hard hinged boundary conditions is found. The nonlinear steady-state response of composite plates subjected to a time-harmonic lateral excitation is investigated and the phenomena of nonlinear resonance are studied and evaluated.     

Thermal stress analysis of a silicon carbide/aluminum composite

Thermal deformations and stresses were studied in a silicon-carbide/aluminum filamentary composite at temperatures up to 370°C (700°F). Longitudinal and transverse thermal strains were measured with strain gages and a dilatometer. An elastoplastic micromechanical analysis based on a one-dimensional rule-of-mixtures model and an axisymmetric two-material composite cylinder model was performed. It was established that beyond a critical temperature thermal strains become nonlinear with decreasing longitudinal and increasing transverse thermal-expansion coefficients. This behavior was attributed to the plastic stresses in the aluminum matrix above the critical temperature. An elastoplastic analysis of both micromechanical models was performed to determine the stress distributions and thermal deformation in the fiber and matrix of the composite. While only axial stresses can be determined by the rule-of-mixtures model, the complete triaxial state of stress is established by the composite cylinder model. Theoretical predictions for the two thermal-expansion coefficients were in satisfactory agreement with experimental results.     

A theoretical analysis of piezoelectric/composite laminate with larger-amplitude deflection effect,Part II: Hermite differential quadrature method and application

Incorporating the effects of larger-amplitude deflection and electro-elastical properties of piezoelectric lamina, the Hamilton’s variation principle was used to deduce the fundamental formulations of smart anisotropic composite plate in Part I in terms of Reddy’s simple higher-order theory. In order to solve the five highly coupled nonlinear partial differential equations with complicated overlapping boundary conditions, a novel numerical method-Hermite differential quadrature (HDQ) method was developed to implement the differential equations with complicated overlapping boundary conditions. Based on the presently developed HDQ method, any orders derivatives of the unknown functions or any boundary conditions can be point-collocation-based discretized by a set of point-values along x- and y-direction. Then, a system of complete algebraic nonlinear equations can be constructed to calculate out the final point-values of the mid-plane displacements by using the governing equations and relative boundary conditions with HDQ method. Finally, some detailed numerical examples for the anisotropic piezoelectric/composite laminate with the distributed poling directions of piezoelectric layer and fiber orientations of composite layers were studied to validate the developed theoretical analysis model and HDQ numerical method.     

Geometrically nonlinear large deformation analysis of triangular CNT-reinforced composite plates

A first known investigation on the geometrically nonlinear large deformation behavior of triangular carbon nanotube (CNT) reinforced functionally graded composite plates under transversely distributed loads is investigated. The analysis is carried out using the element-free IMLS-Ritz method. In this study, the first-order shear deformation theory (FSDT) and von Kármán assumption are employed to account for transverse shear strains, rotary inertia and moderate rotations. A convergence study is conducted by varying the supporting size and number of nodes. The effects of transverse shear deformation, CNT distribution and CNT volume fraction on the nonlinear bending characteristics under different boundary conditions are examined.     

Application of fractional exponential hereditary kernels in the nonlinear theory of viscoelasticity

It is proved that fractional exponential hereditary kernels of nonlinear viscoelasticity can be used to evaluate creep strains and stress relaxation. A nonlinear theory of viscoelasticity with time-independent nonlinearity described as a nonlinear curve of instantaneous elastoplastic deformation is used. The calculated results are validated against experimental data on the viscoelastic deformation of laminated and unidirectional fibrous composites and their components under the conditions of constant stresses, complete unloading, incremental loading, pure torsion, and constant strains     

Compound Bifurcations in the Buckling of a Delaminated Composite Strut

An analysis of the buckling and post-buckling of a delaminated composite strut is presented using a simple 4 degree of freedom nonlinear Rayleigh–Ritz formulation. Bifurcation analysis indicates that instability occurs in general at an asymmetric point of bifurcation. Depending on the depth of delamination both thin-film and overall buckling can occur in the post-buckling range, the transition being seen at a point of secondary bifurcation. For certain combinations of parameters this becomes a stellar bifurcation, associated with a double eigenvalue, where there are three possible subsequent routes for the post-buckling. The method used is fast and reliable and can be readily extended to modelling a composite with several layers.     

Design of patterned multilayer films with eigenstrains by topology optimization

We develop a formal approach to design shaped microstructures from multilayer films with eigenstrains in the layers. The eigenstrains are inelastic strains that vary from layer to layer resulting in elastic misfit between the layers. Examples include thermal expansion mismatch between the layers, piezoelectric strains, and strains in shape memory alloys. In our approach, the eigenstrains are manipulated by spatially patterning the films to generate structures that, although fabricated by a conventional, planar thin film technology, deform into desired three-dimensional shaped surfaces. The material patterns in the individual layers are determined by topology optimization allowing the creation of arbitrarily complex, geometric layouts. In contrast to existing topology optimization methods for patterning plate structures, the goal of the proposed approach is to generate large deformations via eigenstrains, rather than to increase the stiffness of plate via reinforcement patterns. The optimization methodology is demonstrated by the design of two- and three-layer thin film structures. The performance of the optimized designs is verified by experiments showing the importance of accounting for a nonlinear kinematics in order to obtain the desired shape in the deformed configuration. While our approach is demonstrated in the context of the design of three-dimensional microstructures, it can be easily applied to a variety of problems where it is desired to control the complex shape of plate-like structures by spatial actuation—the spatial actuators are represented by eigenstrains.