Thermal buckling and postbuckling analysis of a laminated composite beam with embedded SMA actuators

In this paper, the thermal buckling and postbuckling behaviours of a composite beam with embedded shape memory alloy (SMA) wires are investigated analytically. For the purpose of enhancing the critical buckling temperature and reducing the lateral deflection for the thermal buckling, the characteristics of thermal buckling are investigated through the use of the shape recovery force associated with SMA wire actuators. The results of both thermal buckling and postbuckling behaviours present quantitatively how the shape recovery force affects the thermal buckling behaviour. The analytical results show that the shape recovery force reduces the thermal expansion of the composite laminated beam, which results in both an increment of the critical buckling temperature and also a reduction of the lateral deflection of postbuckling behaviours. A new formula is also proposed to describe the critical buckling temperature of the laminated composite beam with embedded SMA wire actuators.     

A simulation study on the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires

In this paper, numerical simulation analyses of the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires were performed to investigate the effect of embedded SMA wires on the characteristics of thermal buckling. In order to simulate the thermomechanical behavior of SMA wires, the constitutive equation of the SMA wires was formulated in the form of an ABAQUS user subroutine. The computational program was verified by showing the response of the pseudoelasticity and shape memory effect (SME) at various temperatures and stress levels. Modeling of the laminated composite shells with embedded SMA wires and thermal buckling analyses were performed with the use of the ABAQUS code linked with the subroutine of the formulated SMA constitutive equations. The thermal buckling analyses of the composite shells with embedded SMA wires show that the critical buckling temperature can be increased and the thermal buckling deformation can be decreased by using the activation force of embedded SMA wire actuators.     

热载荷作用下嵌入SMA丝复合材料梁的横向自由振动

基于形状记忆合金Brinson一维热力学本构方程,采用复合材料细观力学分析方法,建立了热载荷作用下嵌入SMA丝复合材料梁的一维热弹性本构关系。其次利用Euler-Bernoulli梁的轴线可伸长几何非线性理论和自由振动理论,建立了嵌入SMA丝复合材料梁在均匀升温场内自由振动的动力学控制方程,导出了热过屈曲构形附近嵌入SMA丝复合材料梁微幅横向自由振动的模型。最后通过打靶法求解了两端固定约束条件下嵌入形状记忆合金丝复合材料梁在加热过程中的振动响应,获得了梁的前四阶固有频率在不同SMA相对体积含量时随温度变化的特征关系曲线。数值结果表明,SMA丝相变过程中的回复应力和弹性模量变化对梁在过屈曲前后的各阶固有频率均有影响,是实现梁自振频率主动控制的一种有效方法。     

埋入形状记忆合金丝的复合材料圆柱壳壁板的热振动特性分析

采用有限元软件ABAQUS实现了埋入形状记忆合金（SMA）丝的复合材料圆柱壳壁板结构热振动特性分析．基于“ang-Rogers本构模型编写用户子程序（UMAT）模拟形状记忆合金材料的超弹性行为和形状记忆效应，并在不同温度和应力状态下验证了程序的正确性．基于此程序，计算了埋入SMA丝的复合材料圆柱壳壁板在温度和机械载荷作用下的一阶固有频率，分析了其热振动特性和屈曲特性．模拟结果表明：加热驱动SMA丝一般会提高结构的固有频率和屈曲临界，SMA丝的数量对结构的热振动和屈曲特性有显著影响。这些结论将对智能复合材料结构设计、抗热设计有一定的指导作用。     

Thermal post-buckling and flutter characteristics of composite plates embedded with shape memory alloy fibers

It is investigated that the composite plate embedded with shape memory alloy (SMA) fibers is subject to the aerodynamic and thermal loading in the supersonic region. The nonlinear finite element equations based on the first-order shear deformation plate theory (FSDT) are formulated for the laminated composite plate embedded with SMA fibers (SMA composite plate). The von Karman strain–displacement relation is used to account for the large deflection. The incremental method considering the influence of the initial deflections and initial stresses is adopted for the temperature-dependent material properties of SMA fibers and composite matrix. The first-order piston theory is used for modeling aerodynamic loads. This study shows the effect of the SMA on the critical temperature, thermal post-buckling deflection, natural frequency and critical dynamic pressure of the SMA composite plate.     

Large bending actuator made with SMA contractile wires: theory,numerical simulation and experiments

In this paper, the modeling, numerical simulation and experimental validation of the deformation of a composite cantilever beam actuated by shape memory alloy (SMA) wires are presented and discussed. The structural model incorporates a number of non-classical features such as laminated construction and anisotropy of constituent material layers, transverse shear deformability, distortion of the normals, and fulfillment of interfacial shear traction continuity requirement. Suitable for use in standard finite element codes, a numerical procedure is developed for solving the geometric non-linearity of the host structure and the hysteretic non-linearity of SMA wires, which is based upon the updated Lagrangian formulation. The application concerns an elastomeric beam with embedded and pre-stressed SMA wires at an offset from the neutral axis, which act as large bending actuators resulting from the thermally induced reversible transformation strains. The experiments and numerical simulation demonstrate the good predictive capability of the model proposed and the powerful role played by SMAs as large bending actuators.     

Dynamic instability response of smart composite material

Laminated composite is common to replace traditional metals in today's industries due to its high specific strength. Shape memory alloy has been used to improve structural behaviours such as buckling, vibration and fatigue through its well‐ known property of shape memory effect. This ability of shape memory alloy to improve the parametric instability behaviour of laminated composite plate has not been studied in the past and as such, this study is conducted. Here, shape memory alloy wires are embedded within the outer layers of the laminated composite plates. The Mathieu‐Hill equation for the parametric instability of the shape memory alloy composite plate has been developed using finite element method based on the first order shear deformation theory. The formulation is validated and parametric studies have been conducted to investigate the effect of shape memory alloy on the dynamic instability behaviour of the composite that corresponds to factors such as static load factor, thickness of the plate and boundary conditions. The study shows that shape memory alloy improves significantly the dynamic instability behaviour of the laminated composite plate by shifting the instability chart to the right. The effect of shape memory alloy can increase the frequency centre of the instability chart by more than 100 %.     

Adaptive post-buckling response of carbon fibre composite plates employing SMA actuators

Restoration forces, associated with embedded activated pre-strained SMA wires, have successfully been employed to enhance the post-buckling behaviour of laminated plate structures while under the influence of a uniaxial load. The results of which will be presented. The manufacturing methodology of the hybrid SMA-carbon-epoxy plates is outlined. Optical micrographs illustrate the effect of embedding diametrical inclusions within a host composite. Thermal and structural finite-element analysis have been employed to predict the non-uniform temperature profile within the laminates and to provide insight to the SMA-hybrid structure adaptive response. It is shown that by utilizing the considerable control authority generated, even for a small actuator volume fraction, the out-of-plane displacement of the post-buckled laminates can be significantly reduced. Such displacement alleviation allows for the load redistribution away from the plate's unloaded edges i.e. there is a tendency for the plate to conform to the optimal flat configuration beyond its critical buckling load. However, the stability of the adaptive response is very much dependent upon the laminate stacking sequence. It is envisaged that the range of operational performance for such an adaptive hybrid structure may be extended over conventional materials and structures.     

Vibration characteristics of SMA composite beams with different boundary conditions

Recently, the development of shape memory alloy (SMA) actuators, in the forms of wire, thin film and stent have been found increasingly in the fields of materials science and smart structures and engineering. The increase in attraction for using these materials is due to their many unique materials, mechanical, thermal and thermal-mechanical properties, which in turn, evolve their subsequent shape memory, pseudo-elasticity and super-elasticity properties. In this paper, a common type of SMA actuator, Nitinol wires, were embedded into advanced composite structures to modulate the structural dynamic responses, in terms of natural frequency and damping ratio by using its shape memory and pseudo-elastic properties. A simple theoretical model is introduced to estimate the natural frequency of the structures before and after actuating the embedded SMA wires. The damping ratios of different SMA composite beams were measured through experimental approaches. The natural frequencies changed slightly at a temperature above the austenite finish temperature of composite beams with embedded non-prestrained SMA wires. However, the increase of the natural frequencies of the beams with embedded prestrained SMA wires were found in both the theoretical prediction and experimental measurements. The damping ratios of SMA composite beams increased with increasing the temperature of the embedded wires with and without being pre-strained. Compressive and local failures of the beams with high wire content are a possible explanation.     

Analytical layerwise solution of nonlinear thermal instability of SMA hybrid composite beam under nonuniform temperature condition

Abstract

Thermal buckling and post-buckling behavior of composite beam reinforced with shape memory alloy (SMA) wires under nonuniform temperature distribution is explored. Thermo-mechanical behavior of SMA wires is formulated by using the one-dimensional Brinson SMA model. Considering von Karman strain–displacement relation, corresponding nonlinear governing equations are obtained and solved analytically. Heat conduction equation is employed and through-the-thickness temperature distribution is obtained by discretization scheme of layerwise method. Influence of SMA-wire positioning across the thickness, temperature distribution, SMA wire pre-straining level and volume fraction of SMAs upon the thermal buckling and post buckling of reinforced beam are examined and discussed in detail.     

Vibration characteristics of laminated composite plates with embedded shape memory alloys

Shape memory alloy (SMA) is commercially available for a variety of actuator and damping materials. Recently, SMA wires have also become commercially available for the design of smart composite structures because SMA wires with a small diameter can be easily produced. In this work, two types of SMA-based composites are presented for investigating the vibration characteristics. First, laminated composite plates containing unidirectional fine SMA wires are fabricated. By measuring the vibration mode of a clamped cantilever, the influence of both SMA arrangement and temperature on the vibration characteristics is made clear. Next, laminated composite plates with embedded woven SMA layer are fabricated. The stiffness tuning capability is evaluated by impact vibration tests with different temperatures. It is found that the stiffness tuning capability may be improved by increasing the volume fraction of SMAs and by controlling accurately the internal stress according to the phase transformation temperature of SMAs from martensite to austenite. The theoretical prediction on the natural frequency considering the SMAs behavior and laminated structures is proposed and their results agree reasonably with experimental ones.     

Post-buckling analysis of composite beams: A simple intuitive formulation

Post-buckling analysis of composite beams with axially immovable ends is investigated using an Intuitive formulation. Intuitive formulation uses two parameters namely critical buckling load and axial stretching force developed in the post-buckled domain of composite beam. Geometric nonlinearity of von-Karman type is taken into consideration which accounts for membrane stretching action of the beam. Axial stretching force developed in post-buckled domain of composite beam is evaluated by using an axial governing equation and is expressed either in terms of lateral displacement function as an integrated value, or as a function of both axial and lateral displacement functions at any discrete location of the beam. The available expressions of critical buckling load and derived expressions of axial stretching force developed in the beam are used for obtaining an approximate closed-form expressions for the post-buckling loads of various beam boundary conditions. Numerical accuracy of the proposed analytical closed-form expressions obtained from the intuitive formulation are compared to the available finite element solutions for symmetric and asymmetric lay-up schemes of laminated composite beam. Effect of central amplitude ratio and lay-up orientation on post-buckling load variation is briefly discussed for various beam boundary conditions considered in this study.     

Lateral buckling analysis of thin-walled laminated channel-section beams

The lateral buckling of a laminated composite beam with channel section is studied. A general analytical model applicable to the lateral buckling of a channel-section composite beam subjected to various types of loadings is derived. This model is based on the classical lamination theory, and accounts for the material coupling for arbitrary laminate stacking sequence configuration and various boundary conditions. The effects of the location of applied loading on the buckling capacity are also included in the analysis. A displacement-based one-dimensional finite element model is developed to predict critical loads and corresponding buckling modes for a thin-walled composite beam with arbitrary boundary conditions. Numerical results are obtained for thin-walled composites under central point load, uniformly distributed load, and pure bending with angle-ply and laminates. The effects of fiber orientation, location of applied load, and types of loads on the critical buckling loads are parametrically studied.     

具有形状记忆合金丝的复合材料轴转子系统的振动与稳定性

提出具有SMA丝的复合材料轴-盘-刚性支承转子系统的数学模型,研究转子系统的振动与稳定性。将轴视为一个平行于轴线方向埋入SMA丝的薄壁复合材料空心梁,盘为各向同性刚性圆盘,轴位于刚性轴承上。基于变分渐进法(VAM)描述复合材料薄壁梁的变形,基于Brinson热力学本构方程计算SMA丝的回复应力,采用Hamilton原理推导出系统的运动方程,采用Galerkin法进行模型离散化和近似数值计算。着重分析SMA丝含量和初始应变对复合材料轴振动固有频率和转子系统临界转速的影响。研究结果表明,所建立的动力学模型能够用于揭示SMA对转子系统的振动与稳定性的影响机理。     

Hole effects on lateral buckling of laminated cantilever beams

In this study, the effects of hole diameter and hole location on the lateral buckling behaviour of woven fabric laminated composite cantilever beams have been investigated. In the experimental studies, two different groups of samples were used; samples with a single circular hole and samples with no hole. The critical buckling load for each sample was then determined experimentally. For the numerical analyses, ANSYS 10.0 finite element program was utilized. It has been noted that there is a good agreement between experimental results and those of finite element analyses. On the basis of this harmony, the numerical analyses of some models having different dimensions and fiber orientations have been done by changing length and width of the beam, diameter and location of the hole. It has been concluded that the effects of the hole diameter and hole location on the lateral buckling behaviours is very important, especially for the short beams.     

SMA纤维复合材料变截面板簧的固有频率特性研究

摘 要:研究了形状记忆合金（SMA）纤维混杂复合材料变截面板簧的固有频率特性。基于Brinson本构模型,讨论了SMA的受限回复特性。在建立具有SMA纤维的各向异性层合梁本构方程的基础上,利用瑞利-里兹能量法求板簧的固有频率,并给出板簧固有频率的表达式。应用MATLAB进行数值计算,得到板簧固有频率与温度、铺层角、SMA含量的关系曲线,揭示了形状记忆合金纤维复合材料变截面板簧的固有频率可调节机理。     

基于弹性基础梁理论的复合材料薄壁圆柱壳屈曲承载力模型

提出一种复合材料薄壁圆柱壳轴压局部屈曲承载力计算模型。在梁弯曲变形平截面假定和小变形假定的基础上,提出复合材料层合梁抗弯刚度的计算方法;根据轴压下圆柱壳的几何对称性及受力对称性,将圆柱壳局部屈曲问题转化为轴向和环向壳带的弯曲变形问题。依据薄壳稳定理论,建立弹性基础上纵向壳带局部屈曲模型,得到了复合材料圆柱壳屈曲承载力解析公式。理论计算公式与经验工程计算公式相比,具有形式上的相似性,且得到的计算系数可直接求出,而非经验范围选取。对三种铺层的复合材料薄壁圆柱壳进行了轴压试验,结合文献试验数据对比,试验结果与理论预测值基本一致,满足工程精度要求,验证了模型的正确性。     

On a moderate rotation theory of thin-walled composite beams

A small strain and moderate rotation theory of laminated composite thin-walled beams is formulated by generalizing the classical Vlasov theory of sectorial areas. The proposed beam model accounts for axial, bending, torsion and warping deformations and allows one to predict critical loads and initial post-buckling behaviour. A finite element approximation of the theory is also carried out and several numerical applications are developed with reference to lateral buckling of composite thin-walled members. The sensitivity of critical load to second-order effects in the pre-buckling range is pointed out.     

Effect of superelastic shape memory alloy wires on the impact behavior of carbon fiber reinforced in situ polymerized poly(butylene terephthalate) composites

Low-velocity impact properties of shape memory alloy (SMA) wires and carbon fiber reinforced poly(butylene terephthalate) obtained by resin transfer molding were characterized. At the subcritical regime the dissipated energy is not affected by the presence of the wires. However SMA has a positive effect on the maximum absorbed energy, since the maximum allowable load is higher. The contribution of the SMA wires to the higher impact performance of the hybrid composite is suggested to be due to their energy absorbing capability, and also to the high reversible force that acts as a healing force.     

A study on thermomechanical deformation of elastic beam with embedded shape memory alloy wires

The bending deformation of an elastic beam with eccentrically embedded shape memory alloy (SMA) wires under the activation of electrical current has been investigated. A procedure, which accounts for the effect of transient heat transfer and gives rise to the beam bending responding to prescribed input electrical current profile is used for analysis. It is found that influences of ambient temperature, electric current intensity and prestrain of SMA on the bending deformation of beam are significant.