Shear deformation in thermal bending analysis of laminated plates by the GDQ method

The interlaminar stresses and deflections in a laminated rectangular plate under thermal bending were determined by using the generalized differential quadrature method involving the effect of shear deformation. The approximate stress and deflection solutions are obtained under the bending of sinusoidal temperature of thermal load for layer in cross-ply laminates and angle-ply laminates. Numerical results show that the shear deformation has significant effects on the dominant interlaminar stresses and deflections in the laminated plate of thermal bending analysis.     

Thermal bending analysis of shear-deformable laminated anisotropic plates by the GDQ method

The generalized differential quadrature (GDQ) method was used to determine the inter-laminar stresses and deflections in a laminated rectangular anisotropy plate under thermal bending involving the effect of shear deformation. We obtained the non-dimensional stresses and transverse center deflection in cross-ply and angle-ply anti-symmetric, anisotropic laminates subjected to thermal load with sinusoidal temperature distribution. We found that the shear deformation has significant effects on the stresses and deflections for laminated anisotropic plate with moderately side-to-thickness ratio under thermal load and bending state.     

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.     

Steady-state aeroelasticity of fluid flow over a laminated composite plate

A stress-function-based variational approach is used to determine the interlaminar stresses in a multilayered strip of laminate subject to arbitrary combinations of axial extension, bending, and the steady-state aerodynamic loading of fluid flow over the upper surface of laminated composite plate. Symmetric four-layer, cross-ply and angle-ply laminates are considered in details. Some numerical solutions by using a personal computer are obtained. The present results for four-layer laminates show that the aerodynamic loading has significant effects on the interlaminar stresses near the free-edge regions.     

粘弹层合板的稳态振动和层间应力

应用混合分层理论和Ressiner混合变分原理，在板厚方向取二次位移插值函数和三次、四次横向应力插值函数推导出粘弹层合板的动力学方程，得出简支粘弹层合板稳态振动的解。不仅得出与三层弹性板精确的自振频率吻合良好的解，而且对于粘弹层合板，所计算的自振频率和结构损耗因子也与三维结果吻合较好。计算了自由阻尼层合板对应的低阶法向位移响应幅值和层问横向应力的幅值。结果表明，较高的层间横向正应力是低频稳态振动中引起粘弹层合板分层破坏的主要因素，采用适当模量和厚度的粘弹性材料将有效地降低粘弹层合板的层间横向正应力的幅值。     

Free-edge stresses in antisymmetric angle-ply laminates in extension and torsion

The first-order shear deformation theory and the layerwise theory of laminated plates are employed to analyze the edge-effect problem of an antisymmetric angle-ply laminate subjected to arbitrary combinations of extensional and torsional loads. The first-order theory is used for predicting the unknown constant parameters appearing in the reduced displacement field of elasticity which, on the other hand, signify the global behavior of the laminate. A layerwise theory is then utilized to determine the local interlaminar stresses within the boundary-layer regions of laminates. In order to closely examine the behavioral characteristics of interlaminar stresses, various numerical examples are presented for different antisymmetric angle-ply laminates under an axial force and a torque.     

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

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Boundary-layer hygrothermal stresses in laminated, composite, circular, cylindrical shell panels

Free-edge effects in laminated, circular, cylindrical shell panels subjected to hygrothermal loading are studied by utilizing displacement-based technical theories. Starting from the most general displacement field of elasticity for long, circular, cylindrical shells, appropriate reduced displacement fields are determined for laminated composite shell panels with cross-ply and antisymmetric angle-ply layups. An equivalent single-layer shell theory is used to analytically determine the constant parameters appearing in the reduced displacement fields. A layerwise shell theory is then employed to analytically determine the local displacement functions and the boundary-layer interlaminar stresses in cross-ply and antisymmetric angle-ply shell panels under hygroscopic and/or thermal changes. Several numerical examples for the distributions of transverse shear and normal stresses in various shell panels under a uniform temperature change are presented and discussed.     

On the description of anisotropic damage in composite laminates

A general anisotropic damage theory of cracked laminates is formulated here. The deformation of composite laminates is composed of matrix elastic strains, pseudo-elastic damage strains due to cracking and permanent damage strains due to interlaminar slip. The surface of damage initiation is constructed according to the concept of linear elastic fracture mechanics for the virgin material. After the initial damage, a pesudo-elastic damage can be used to describe the damage behaviour if interlaminar slip is negligible. Damage evolution, load induced anisotropy and interlaminar intralaminar interaction for composite laminates are examined; the latter can perturb the normality structure of damage strain rate. Explicit expressions are given for pseudo-elastic (or secant) moduli of the damaging composite laminates, under a non-interacting assumption imposed on the cracks between different families.     

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。     

A quadrilateral element based on refined global-local higher-order theory for coupling bending and extension thermo-elastic multilayered plates

In this paper a refined higher-order global-local theory is presented to analyze the laminated plates coupled bending and extension under thermo-mechanical loading. The in-plane displacement fields are composed of a third-order polynomial of global coordinate z in the thickness direction and 1,2–3 order power series of local coordinate ζ_k in the thickness direction of each layer, which is identical to the 1,2–3 global-local higher-order theory by Li and Liu [Li, X.Y., Liu, D., 1997. Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Methods Eng. 40, 1197–1212] Moreover, a second-order polynomial of global coordinate z in the thickness direction is chosen as transverse displacement field. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns does not depend on the layer numbers of the laminate.Based on this theory, a quadrilateral laminated plate element satisfying the requirement of C¹ continuity is presented. By solving both bending and thermal expansion problems of laminates, it can be found that the present refined theory is very accurate and obviously superior to the existing 1,2–3 global-local higher-order theory. The most attractive feature of this theory is that the transverse shear stresses can be accurately predicted from direct use of constitutive equations without any post-processing method. It is also shown that the present quadrilateral element possesses higher accuracy.     

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.     

The distributions of the interlaminar stress in a laminated shell with free end boundary

This paper studies the free edge effect yielded by interlaminar stress in a laminated cylindrical shell made up of fiber reinforced layer [0°], [90°] and the isotropic material layer under axisymmetric thermal load or radial pressure. Both ends of the shell are in free boundary condition. The exact solution of the problem can be obtained by using the three-dimensional theory of elasticity. For illustration, the numerical laminar stresses in a double-layer laminated shell under thermal load or radial pressure are calculated.     

THE ANALYSIS OF INTERLAMINAR STRESSES FOR COMPOSITE LAMINATED SHALLOW SHELLS WITH INTERFACIAL DAMAGE

Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis and nonlinear theory of shallow shells, considering the damage effect of the interlaminar interface and using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated shallow shells with interfacial damage are derived. Then, considering a simply supported laminated shallow shell with damage and under normal load, an analytical solution is presented by using finite difference method to obtain the interlaminar stresses. Numerical results show, the stiffness of the shell is weakened, greater absolute values of displacements as well as smaller interlaminar stresses are obtained by interfacial damage. When the interfacial damage is further increased, delamination occurs obviously under normal pulling load and pure shear slip occurs under normal pressure load. The portion of the load undertaken by the two sides of the interface is more different. Different mechanical behaviors are shown in both sides of the interface, and the discontinuation of stresses and displacements takes place in the interface.     

A general vibration model of angle-ply laminated plates that accounts for the continuity of interlaminar stresses

This paper presents the generalisation of a well documented two-dimensional shear deformable laminated shell theory [Compos. Struct. 25 (1993) 165] that, based on a fixed number of unknown variables, was initially proposed for laminates made of specially orthotropic layers only. The theory is here specialised for laminated plates but is able to encompass monoclinic layers in a general multilayered configuration. Moreover, it is able to account for the interlaminar continuity of both displacements and transverse shear stresses. Higher-order effects, as shear deformation and rotary inertia, are naturally included into the formulation. In order to obtain the relevant governing differential equations, both Hamilton's variational principle and a recently proposed vectorial approach [Compos. Engng. 3 (1993) 3] have been independently used. The effectiveness of the present model is tested numerically by comparing its results with exact three-dimensional elasticity results obtained under the particular condition that the plates vibrate in cylindrical bending.     

An experimental and analytical investigation of the rail shear-test method as applied to composite materials

This report presents the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test. The effects of nonuniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates are shown. A two-dimensional linearly elastic finite-element model was used to analytically determine how various geometric parameters influenced the magnitude and distribution of inplane normal and shear stresses in a tensile-rail-shear specimen. Rail shear tests were conducted at room temperature and 589 K (600°F) on selected graphite-polyimide composite laminates using two titanium rail configurations. The analysis and test methods are discussed, and the results of the effects of the various parameters on shear modulus and ultimate strength are presented.     

一种预测层合板层间剪应力的新后处理方法

层合板是航空航天领域典型的承力构件,过大的层间应力是导致其分层失效的主要原因.准确的层间应力预测往往依赖于三维平衡方程后处理方法(TPM).然而,该方法需要计算面内应力的一阶导,使得基于C0型板理论构造的线性单元无法使用TPM计算横向剪应力.本文在三维平衡方程后处理方法的基础上,提出了一种新后处理方法(NPM).新后处理方法通过虚功等效法消除了三维平衡方程后处理方法中产生的位移参数的高阶导.基于提出的新后处理方法和C0型板理论,仅需使用线性单元就可以预测层合板的横向剪应力.为了验证所提方法的有效性,本文基于修正锯齿理论(RZT)和所提方法构造了一种C0连续的三节点三角形线性板单元.数值算例表明,所提方法和三维平衡方程后处理方法具有相同的计算精度,提出的板单元能够准确高效地预测层合板的横向剪应力.此外,所提方法便于结合现有的有限元商用软件使用,基于商用软件中板壳单元获得的节点位移,使用新后处理方法极易获得准确的层间剪应力.     

Matrix crack initiation and progression in compositelaminatessubjected to bending and extension

An experimental investigation of matrix crack initiation and progression inglass/epoxy laminates of differentstacking sequences is presented. The laminates have beenloaded in extension and bending, and the degree ofdamage as function of the load has beenrecorded. The changes in certain elastic properties caused by the damagewere also measured, andare compared to results from a previously developed approximate analytic model. Anenergyrelease rate resistance curve is adopted in an attempt to describe the initiation and progression ofmatrixcracks in the laminates. The amount of cracking is also viewed in relation to the straintransverse to the fibres inthe ply under consideration, and the ply stresses at the onset of crackingare calculated. The different damageevolution criteria are compared to the experimental results,and their validity and reliability are discussed. By use ofthe ply strain transverse to the fibres as acritical parameter for damage evolution, the load–deformation curves ofthe tested laminates aresimulated taking damage progression into account.     

An analytic solution for interlaminar stresses in a fiber-reinforced double-layer cylindrical shell

The present paper investigates the basic characteristics of the interlaminar stresses in a double-layer cylindrical shell with both ends simply-supported under uniform external or internal pressure. The double layer shell is composed of a 0° fiber-reinforced composite layer and an isotropic layer. In this paper, this axisymmetric problem is solved exactly with the three-dimensional theory of elasticity. Both the displacement field and the stress field of each layer of the shell are expressed in Fourier series and Fourier-Bessel series. Then we illustrate the effects of the various parameters, such as geometry, material constants, loading conditions and stacking sequence, on the interlaminar stresses.     

厚热塑性复合材料AS4/PEEK角铺设层合板的层间应力分析

将表征热塑性复合材料AS4 /PEEK非线性行为和应变速率相关行为的三维弹塑性模型通过程序加以实现。将程序计算结果和文献实验结果相比较可以发现,二者吻合较好,验证了所生成程序的有效性。计算了厚的AS4 /PEEK角铺设层合板[±25]s4在不同界面上的层间应力。由层间应力的三维分布图,分析了不同界面上层间应力的分布特征,并说明了可能引起层间分层的主要因素。