材料非线性对复合材料层合板热自由边界效应的影响

本文用准三维有限元法研究了材料非线性对复合材料层合板热自山边界效应的影响,给出了修正型Hahn-Tsai非线性应力-应变关系的三维形式。由本文非线性分析方法得到的层间应力与以往由线性分析方法得到的层间应力做了比较,结果表明:材料非线性能显著降低层间剪应力的集中程度,但对层间正应力影响不太明显。     

Free-edge interlaminar stress analysis of piezo-bonded composite laminates under symmetric electric excitation

A stress function-based approach is proposed to analyze the free-edge interlaminar stresses of piezo-bonded symmetric laminates. The proposed method satisfies the traction free boundary conditions, as well as surface free conditions. The symmetric laminated structure was excited under electric fields that can generate induced strain, resulting in pure extension in the laminated plate. The governing equations were obtained by taking the principle of complementary virtual work. To verify the proposed method, cross-ply, angle-ply and quasi-isotropic laminates were analyzed. The stress concentrations predicted by the present method were compared with those analyzed by the finite element method. The results show that the stress function-based analysis of piezo-bonded laminated composite structures is an efficient and accurate method for the initial design stage of piezo-bonded composite structures.     

复合材料层合板在加工固化后期降温速率对残余热应力的影响

本文采用非线性有限元方法，对材料性质与温度有关的复合材料层合板在加工固化后期降温过程中的温度速场和热应力场进行了分析，对降温度速率对板中固化残余热应力的影响进行了研究，获得一些对层合板固化成型工艺和固化残余热应力分析模型的选取均有意义的结果。     

3-D numerical study on the bending of symmetric composite laminates

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Layup optimization with GA for tapered laminates with internal plydrops

Layup optimization of the maximum strength of laminated composites with internal ply-drops is performed by genetic algorithm (GA). Interlaminar stresses are considered in estimating the strength of laminates and calculated by the stress function based complementary virtual work principle. Out-of-plane stress functions are expanded in terms of harmonic series through the thickness direction and initially satisfied the traction free boundary conditions of laminates automatically. As the number of expansion terms is increased, stress concentration near the dropped plies is predicted with better accuracy. Since the proposed analysis is relatively simple and efficient in the prediction of interlaminar stress concentration near the ply-drops, the layup optimization of composite laminates with dropped plies considering interlaminar strength can be easily performed by GA. In the formulation of genetic algorithm, a repair strategy is adopted to satisfy given constraints and multiple elitism scheme is implemented to efficiently find multiple global optima or near-optima.     

Interlaminar hygrothermal stresses in laminated plates

Within the elasticity formulation the most general displacement field for hygrothermal problems of long laminated composite plates is presented. The equivalent single-layer theories are then employed to determine the global deformation parameters appearing in the displacement fields of general cross-ply, symmetric, and antisymmetric angle-ply laminates under thermal and hygroscopic loadings. Reddy’s layerwise theory is subsequently used to determine the local deformation parameters of various displacement fields. An elasticity solution is also developed in order to validate the efficiency and accuracy of the layerwise theory in predicting the interlaminar normal and shear stress distributions. Finally, various numerical results are presented for edge-effect problems of several cross-ply, symmetric, and antisymmetric angle-ply laminates subjected to uniform hygrothermal loads. All results indicate high stress gradients of interlaminar normal and shear stresses near the edges of laminates.     

Computer-aided photoelastic analysis of orthogonal 3D textile composites: Part 2. Combining least squares and finite-element methods for stress analysis

An approach combining least squares methods and finite element methods (FEM) is presented for subsequent photoelastic stress analysis of orthogonal 3D textile composites withR and α obtained in Part 1. Through this approach, these photoelastic stresses are obtained over a region of interest as if the composites were homogeneous materials. The least squares method is used for requiring the solution strain fields to best correlate with the distribution of the two photoelastic strain data of ɛ _x − ɛ _y and γ _xy calculated directly from the measuredR and α. The FEM uses the homogenized composite properties to construct the nodal force equilibrium equations as constraints in the least squares formulation. As a result of combining this least squares method and FEM with lagrange multipliers, a linear system of equations is formulated with the unknown nodal displacements. Once these nodal displacements are solved, the strains and stresses can be calculated through FEM formulations. This approach is tested with the two experimental results completed in Part 1 for the aluminum and composite plates. The stresses obtained for the aluminum plate show close agreement with those obtained with the plain FEM computation. In the case of the orthogonal 3D composite plate, the local variations as observed inR and α are already necessarily eliminated from these solved photoelastic stresses. Furthermore, these stresses also match well with those computed with the plain FEM from the homogenized composite properties.     

基于升阶谱有限条法的复合材料壁板结构稳定性分析

通过将升阶谱与有限条方法相结合,得到了以多项式级数为形函数的升阶谱有限条方法,并采用该方法对复合材料壁板结构在复杂边界条件下,受轴压、侧压及剪切载荷复合作用下的临界稳定性问题进行分析。数值算例结果表明,该方法综合了升阶谱和有限条的优点,可以快速稳定的精确求解复合材料壁板结构的临界失稳载荷。     

具有自由边的复合材料层合板的解析解

从三维弹性力学基本方程出发,通过假设自由边的边界位移函数,建立了正交异性层合板的状态方程,给出了对边自由,对边简支矩形板的解析解.此解满足层合板的基本方程和层间连续条件.用本文的方法比较容易处理层合板的自由边.算例表明,数值结果具有较高的精度.     

Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method

The interlaminar stresses in a thin laminated rectangular orthotropic plate with four sides simply supported edges under bending was determined by using the generalized differential quadrature (GDQ) method involving the effects of thermal expansion strain and transverse load. The approximate stress and displacement solutions are obtained under the effects of thermal expansion force and uniform pressure load for eight-layer unidirectional laminates, symmetric cross-ply laminates. Numerical results on the dominant interlaminar stresses and displacement of bending analysis are compared to the Navier solution. The thermal induced forces have significant effect on the bending of plates.     

复合材料层合板粘弹性固化残余应力分析

基于Ｓｃｈａｐｅｒｙ积分型粘弹性本构关系，推导了考虑横向剪切效应的复合材料层合板线性热粘弹性有限元分析列式，对层合板的粘弹性响应和加工成型过程中的残余应力进行了分析，给出一些有意义的结果     

Accurate transverse stress evaluation in composite/sandwich thick laminates using a C0 HSDT and a novel post-processing technique

An efficient method for accurate evaluation of through-the-thickness distribution of transverse stresses in thick composite and sandwich laminates, using a displacement-based C⁰ higher-order shear deformation theory (HSDT), is presented. The technique involves a least square of error (LSE) method applied to the 3D equilibrium equations at the post-processing phase, after a primary finite element analysis is performed using the HSDT. This is distinctly different from the conventional method of integrating the 3D equilibrium equations, for transverse stress recovery in composite laminates during post-processing. Competence of the technique is demonstrated in the numerical examples through comparison with results from first-order shear deformation theory (FSDT), another HSDT and those from analytical and 3D elasticity solutions available in literature.     

Analytical solutions to edge effect of composite laminates based on symplectic dual system

In the symplectic space composed of the original variables, displacements, and their dual variables, stresses, the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper. In contrast to the traditional technique using only one kind of variables, the symplectic dual variables include displacement components as well as stress components. Therefore, the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously. After being introduced into the symplectic dual system, the uniform schemes, such as the separation of variables and symplectic eigenfunction expansion method, can be implemented conveniently to analyze composite laminate problems. An analytical solution for the free edge effect of composite laminates is obtained, showing the effectiveness of the symplectic dual method in analyzing composite laminates.     

复合材料层板边缘效应的准相似元解法

用准相似单元法研究了复合材料层板直边和孔边的自由边缘效应，得到了一些具有工程意义的结果。准相似单元法是相似单元法的推广，利用这一方法可以求解三维的应力集中问题，避免了求单刚时的重复计算。由于采用了按相似层求解的技术，应用准相似单元法求解应力集中问题时对计算机容量的要求大为降低     

具有中心圆孔的[0°/90°]_s复合材料层合板的边界元法分析

本文在文[1]的基础上,采用子结构法建立了多层复合板的边界元方法,对具有中心园孔[0°/90°]_s的层合板的层间应力作了计算,同有限元法的结果进行了比较,结果表明,应用边界元法处理这类问题,单元划分少,节约了计算机时,而且有较高的计算精度。     

材料沿厚度方向的非线性对复合材料层板分层的影响

基于修正的Ｈａｈｎ－Ｔｓａｉ非线性本构关系,用准三维有限单元分析了由层间应力引起的材料沿厚度方向的非线性对复合材料层板分层后屈及能量释放率的影响,结果表明材料非线性对能量释放率的影响与后屈曲形态密切相关,其中对Ⅱ型分层能量释放率的影响较大,而分层尖端应力场降低,局部变形增大。     

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations.     

平面广义四节点等参元GQ4及其性能探讨

广义节点有限元是将传统有限元方法中的节点广义化,在不增加节点个数的前提下,仅通过提高广义节点的插值函数的阶次,从而达到提高有限元解精度的目的.与现有的p型和hp型有限元不同,在这种新的有限元中,节点自由度全部定义在节点处,在理论与程序实现上与传统有限元方法具有很好的相容性,传统有限元方法是这种新方法的广义节点退化为0阶时的特殊情形.文中主要讨论了这一新方法的四节点等参元（记为GQ4）的形式.对GQ4进行的各种数值试验表明,所发展的广义四节点等参单元具有精度高且无剪切自锁与体积自锁等的特点.     

Stress-function variational method for interfacial stress analysis of adhesively bonded joints

High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc.     

Three-dimensional exact solutions for the free vibration of laminated transversely isotropic circular,annular and sectorial plates with unusual boundary conditions

New state space formulations for the free vibration of circular, annular and sectorial plates are established by introducing two displacement functions and two stress functions. The state variables can be separated into two independent catalogues and two kinds of vibrations can be readily found. Expanding the displacements and stresses in terms of Bessel functions in the radial direction and trigonometric functions in the circumferential direction, we obtained the exact frequency equation for the free vibration for some uncommon boundary conditions. Numerical results are presented and compared with those of FEM to demonstrate the reliability of the proposed method. A parametric investigation is also performed.