Large deflection initial failure analysis of angle-ply laminated plates

A large deflection initial failure analysis of square angle-ply laminated plates subjected to uniform pressure loading is described. Approximate numerical solutions of the Mindlin laminated plate equations are derived using finite differences in conjunction with the Dynamic Relaxation (DR) technique. The solutions are scaled to satisfy the Tsai-Hill lamina failure criterion. The effects of plate slenderness, in-plane edge restraint and lay-up on the initial failure pressure and associated plate centre deflection are quantified for ±45° laminated plates with simply supported and clamped edges. It is shown, particularly for thin plates, that in-plane edge restraint increases the initial failure pressure substantially, though changing the plate edge conditions from simply supported to clamped does not always increase the initial failure pressure.     

A finite element for the linear analysis of laminated circular plates

A new finite element for modeling axiysymmetric circular plates is developed. The element is based upon Mindlin's shear-deformable plate theory, and elements may be stacked on top of one another to model laminated plate by the addition of only rotational degrees of freedom for each lamina. The elements assure continuity of the displacements between the layers, but not continuity of the traction vectors. Neither interlaminar slip nor debonding between the layers is considered.

The plate element is more efficient at modeling laminated structures than conventional plate elements or solid elements because it accurately models the structure while keeping the degrees of freedom per element to a minimum. If one were to use solid elements to model a laminated circular plate, many more elements would have to be used in the model to avoid loss of accuracy due to a large aspect ratio. Each layer in the laminated plate is allowed an independent rotation: hence, the model gives more accurate results than classical lamination theory models. The new element is also immune from shear locking at least for radius-to-thickness ratios up to 500 without having to incorporate reduced numerical integration schemes. In fact, the element's stiffness matrix may be integrated in closed form: this is not possible for most plate elements in the literature.     

Postbuckling analysis of unilaterally constrained laminated thin plates

Postbuckling responses of laminated thin plates supported by a tensionless foundation and subjected to in-plane compressive edge loads are investigated. The postbuckling analysis presented here is based on the classical laminated plate theory, and includes the plate-foundation interaction, for which the foundation reacts in compression only. The plate is assumed to be simply supported at four edges, while the two longitudinal unloaded edges may be either movable or immovable. The initial geometric imperfection of the plate is taken into account. The analysis uses a two step perturbation technique to determine the postbuckling response of the plate. An iterative scheme is developed to obtain numerical results without any prior assumption for the shape of the contact region. The numerical examples concern the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates with unilateral constraints, from which results for the same unconstrained plates are obtained as comparators. The numerical results show that the unilateral constraint has a significant effect on the postbuckling response of laminated thin plates.     

复合材料层合板的铺层几何对结构声传输的影响

采用基于复合材料一阶剪切理论－Mindilin理论的板单元和基于Rayleigh表面分方程的边界元,对嵌在无限障板上的复合材料层合板在低频简谐平面声波斜入射情况下,建立了考虑流体结构耦合的传声计算模型,并利用该模型计算研究了对称角铺设、反对称角铺设和正交铺设等不同铺设方式对层合板传声损失的影响以及在板侧流体介质分别为空气和水时层合板的传声特性,指出层合板的铺层几何对其传声损失有较大影响,应在设计中引起注意。     

界面过渡层对磁-电-弹性层合板多场耦合特征的影响

针对两种不同形式(压电-铁磁-压电,铁磁-压电-铁磁)的磁电层状复合材料,研究了热场环境下磁电层状复合材料的力、热、电以及磁的多场耦合特征,给出了磁电层状复合结构的位移、应力、电势以及磁势的变化规律,探讨了界面过渡层厚度变化及其不同界面过渡方式对磁电复合材料的位移、应力、电势和磁势的影响。研究结果表明,界面过渡层对应力特征、电势和磁势的分布具有非常重要的影响,尤其对磁势的分布特征影响尤为明显,这些结果可为磁电层合材料的结构设计和可靠性分析提供参考和依据。     

Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a laminated composite piezoelectric rectangular plate

The global bifurcations and multi-pulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations are investigated in this paper for the first time. The formulas of the laminated composite piezoelectric rectangular plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory and the Galerkin’s approach. The extended Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that multi-pulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the laminated composite piezoelectric rectangular thin plate.     

A model of composite laminated Reddy plate based on new modified couple stress theory

Based on new modified couple stress theory a model for composite laminated Reddy plate is developed in first time. In this theory a new curvature tensor is defined for establishing the constitutive relations of laminated plate. The characterization of anisotropy is incorporated into higher-order laminated plate theories based on the modified couple stress theory by Yang et al. in 2002. The form of new curvature tensor is asymmetric, however it can result in same as the symmetric curvature tensor in the isotropic elasticity. The present model of thick plate can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model for cross-ply composite laminated Reddy plate of couple stress theory with one material’s length constant is used to demonstrate the scale effects. Numerical results show that the present plate model can capture the scale effects of microstructure. Additionally, the present model of thick plate model can be degenerated to the model of composite cross-ply laminated Kirchhoff plate and Mindlin plate of couple stress theory.     

Estimating the depth and width of arbitrarily-oriented disbonds in laminates using shearography

Disbonds in a laminated plate are readily revealed from anomalies in the fringe pattern of a shearogram. The shearographic fringes represent loci of constant displacement derivatives of the deformed surface of the plate when subjected to a load increment such as vacuum stressing. In this investigation, a simple method is developed for easy estimation of the size and depth of arbitrarily-oriented square disbonds in laminated plates from a shearogram. The theory and experimental method presented may also be extended to the assessment of disbonds of arbitrary shapes.     

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论,用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值,推导了复合材料层合板刚度阵,质量阵列式,阻尼阵列式,并由Lagrange方程导出了层合板的动力学方程,通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性,在Kirchhoff假设的基础上,对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计,数值算列验证了算法的有效性。     

A finite element for the nonlinear analysis of laminated circular plates

Recently, a new finite element for modelling axisymmetric circular plates was developed.¹ The elements were based on Mindlin's shear-deformable plate theory, and unlike most conventional plate elements, these new elements could be stacked on top of one another to model laminated plates. The elements assured continuity of the displacements between the layers, but not continuity of the traction vectors. Neither interlaminar slip nor debonding between the layers was considered.

In this paper, these new plate elements are incorporated into a Von Karman-type plate theory. The elements may be used to model problems where the membrane stresses play an important role in determining the plate's deflection. For example, it is well-known that for a homogeneous, isotropic plate the membrane stresses begin to affect the deflections when the deflections reach about half the thickness of the plate. For laminated plates, regardless of the magnitude of the deflections, the membrane stresses are present in each layer to balance the interlaminar shear stresses. In this paper, the behavior of these membrane stresses and their influence on the deflections of laminated circular plates are investigated.     

传递矩阵法分析复合材料层合板的传声损失

为了得到不同频率下正交各向异性复合材料层合板的传声损失,基于传递矩阵的方法,推导出层合板的传声损失计算公式。通过建立复合材料层合板的传声计算模型,研究了层合板铺设角度、板厚度和板密度等结构参数对层合板的传声损失影响。计算结果表明：复合材料的密度与传声损失之间没有明显的线性关系,而是随着频率的增加而上升;层合板的总厚度越大,传声损失也越大,而且各层之间厚度不同,也会引起传声损失的较大改变;层合板铺层角度越大,传声损失也越大。采用传递矩阵法能充分考虑复合材料层合板的铺设方式和铺层角度等因素的影响,利用层合板层间的速度和应力连续边界条件,准确的反应复合材料层合板隔声性能。     

Initial and progressive failure analysis of laminated composite structures under dynamic loading

The problem of theoretical prediction of the initial failure and ply-by-ply failure processes in laminated composite structures under dynamic loading is under consideration. A history of deformation can be predicted at any point of a structure using the proposed analytical techniques. The phenometological. second-order tensor-polynomial and maximum stress failure criteria are used to calculate the lower bound of an applied dynamic load. This lower bound corresponds to a start of failure in a structural part. A ply-by-ply failure model is then developed. Using the model, some higher bound for a critical dynamic load impulse value, corresponding to the total exhaustion of a load-bearing capacity by all of the layers in a laminated structure can be predicted. The analysis is applied to thin-walled imperfect laminated graphite/epoxy cylindrical shells, loaded with a short-time impulse of axial compression or external pressure. A general approach to the 3D dynamic deformation analysis of a brick-type mosaic plate and its interaction with a rigid impactor is proposed The approach allows one to model both the initial and damage induced inhomogeneities in a composite structure under dynamic impulsive or impact loading cases.     

Buckling behavior of standing laminated Mindlin plates subjected to body force and vertical loading

In this article, an exact analytical solution for stability analysis of vertical moderately thick laminated rectangular plates subjected to selfweight and top load on the basis of the first-order shear deformation plate theory is presented. It is assumed that the symmetric laminated rectangular plate is composed of transversely isotropic layers. Employing an analytical approach, the coupled governing stability equations of the laminated plate are converted into two uncoupled partial differential equations in terms of transverse displacement and an auxiliary function. It is considered that the vertical sides of the laminated plate are simply supported. Using Levy-type solution, the decoupled equations are reduced to two ordinary differential equations. One of these equations has variable coefficients, for which an exact analytical solution is obtained in the form of power series method of Frobenius. After appropriate convergence study, the present analysis is validated by comparing the results with the existing data reported in the literature. Furthermore, the effects of aspect ratio, plate thickness, boundary conditions, weight of plate and top load on the stability of laminated rectangular plates are investigated and discussed in details. The presented formulations and results can be used as benchmark for future research studies.     

A correspondence principle for laminated plates

The problem of determining the stress distribution within a plate laminated of any number of isotropic plies is considered. The general method of approach is via the three-dimensional theory of elasticity. The laminated plate is regarded as a material continuum characterized by material property functions which possess finite jumps across material interfaces. The stress field is supposed to be induced by boundary tractions applied to the edges and to one lateral face, and by temperature, the plate being stress-free in the reference state. The continuity conditions across material interfaces are automatically satisfied by a method of formulation previously reported in [1].It is shown that the problem involves the determination of four continuous stress functions which may have discontinuous normal derivatives at material interfaces. In the case in which the number of laminations increases without limit, a Correspondence Principle is derived which relates the stress field in the laminated plate to the stress field in a ‘corresponding’ homogeneous, anisotropic plate subjected to the same loading. Numerical results are exhibited which show that the maximum strain error obtained by applying the Correspondence Principle to a plate with as few as three plies is less than 1 per cent.     

Vibration Analysis of Arbitrarily Shaped Sandwich Plates via Ritz Method

This article presents the Ritz method for the vibration analysis of sandwich plates having an orthotropic core and laminated facings. The planform of the plate may take on any arbitrary shape. On the basis of the Mindlin plate theory and the Ritz method, the governing eigenvalue equation for determining the natural frequencies was derived. The Ritz method was automated and made computationally effective for general-shaped plates with any boundary conditions by (1) adopting the product of polynomial functions and boundary equations that were raised to appropriate powers and (2) applying Green's theorem to transform the integration over the general-shaped domain into a closed line integration. The Ritz formulation and software were verified by the close agreement with vibration frequencies obtained by previous researchers for a wide range of subset plate problems involving isotropic, laminated, and sandwich plates of various shapes. Moreover, sample natural frequencies of sandwich plates with laminated facings are presented for some quadrilateral plate shapes. These frequencies should be useful as reference results to researchers who are developing new methods or software for vibration analysis of sandwich plates.     

A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters

The purpose of this paper is to propose an effective solution scheme of simultaneous optimization design of layup configuration and fiber distribution for maximum stiffness design of laminated plates. Firstly, a numerical analysis of the lamination parameters feasible region for a laminated plate consisting of various given number of ply groups (each ply group may have different thickness and all the fibers in one ply group are orientated in an identical direction) is carried out, and it is found that the feasible region based on only a few ply groups is very close to the overall one determined by infinite plies. Therefore, it is suggested that the feasible region of lamination parameters of a laminated plate could be approximately determined by the layup configuration of least ply groups. Secondly, a two-step simultaneous optimization scheme of layup configuration and fiber distribution for maximum stiffness design of laminated plates is proposed. Accordingly, by using ply thickness, fiber orientation angle and fiber volume fraction in a laminated plate of least ply groups as design variables, the optimal lamination parameters for maximum stiffness is obtained. Then, taking the optimal lamination parameters as the design objective, a detailed layup design optimization is implemented by considering some limitations on manufacturing, such as preset ply thickness, and specific fiber orientation angle and a limited maximum number of consecutive plies in the same fiber orientation. Numerical examples are also presented to validate the proposed two-step optimization scheme.     

对称非均匀层合板梁的弯扭耦合效应

为了研究复合材料风力机叶片的弯扭耦合效应,将风力机叶片简化为对称非均匀铺层层合板梁,采用实验和数值分析方法研究耦合区域对叶片弯扭耦合效应的影响。给出了对称非均匀层合板梁的铺层方式及其制作工艺,设计了对称非均匀层合板梁的弯扭耦合效应实验,给出了实验原理及测量方法,测量了对称非均匀层合板梁的挠度和扭转角。基于ANSYS软件建立了对称非均匀层合板梁的有限元模型,计算了在集中力载荷作用下梁的变形。通过有限元数值分析结果与实验结果对比,结果表明:耦合区域对对称非均匀层合板梁的变形行为产生重要影响,采用中部耦合区域铺层方式可以获得显著的弯扭耦合效应。     

Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics

This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Kármán-type equation for the geometric nonlinearity, the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions.     

双模量面板泡沫铝芯夹层圆板的非线性弯曲

采用弹性理论建立了双模量面板泡沫铝芯圆形夹层板在均布载荷作用下的静力平衡方程,利用静力平衡方程确定了夹层板的中性面位置。在考虑剪切变形影响的基础上,采用能量法研究了双模量面板泡沫铝芯圆形夹层板的轴对称非线性弯陆问题,求得了夹层板中心挠度与均布载荷的关系式,并把该方法计算结果与有限元计算结果进行了比较,验证了该方法是可靠...     

长厚比对正六边形铝蜂窝夹层板等效板模型动力学计算精度的影响

为提高正六边形铝蜂窝夹层板的数值计算精度,研究了长厚比对其等效板模型动力学计算精度的影响。针对芯层均匀壁厚的正六边形铝蜂窝夹层板,首先研究了它的等效板模型,包括Reissner理论模型、蜂窝板理论模型和层合板低阶剪切理论模型;然后,将等效板模型与精细化模型相同模态振型的模态频率进行比较,分析了长厚比对等效板模型动力学计算精度的影响。结果表明:芯层均质化后模型模态频率的计算误差很小;层合板低阶剪切理论模型是计算精度较高的等效板模型;Reissner理论模型在长厚比为7.37时计算精度最低,蜂窝板理论模型对厚板的计算精度比薄板低,层合板低阶剪切理论模型对厚板的计算精度比薄板高。