Bonded lap joints of composite laminates with tapered edges

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite lap joints with tapered and/or non tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesives and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman’s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layers between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress–strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, the in-plane and bending stiffness matrices of the adherents are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesives of a single- and double-lap joint.     

Deterministic and stochastic optimization of composite cylindrical laminates

The paper is focused on optimization of prestress and placement of fibers in laminated cylindrical composites. It also involves a stochastic study of prestress deviation in particular layers. Optimization (design) parameters considered in control of internal stresses are the eigenstrains. The behavior of a certain functional serving for optimization of the eigenstrains with stochastically perturbed and correlated values in a laminated cylindrical structure is examined. In the first part, a deterministic optimization of composite laminated cylinders is performed by means of the eigenstrains produced in the layers during the fabrication process. Because fabrication of laminates is sensitive to deviation of eigenstrain magnitudes, as shown from stochastic study, an additional minimization of the eigenstrains is introduced.     

Robust handling of non‐linear constraints for GA optimization of aerodynamic shapes

A new approach to the robust handling of non‐linear constraints for GAs (genetic algorithms) optimization is proposed. A specific feature of the approach consists of the change in the conventional search strategy by employing search paths which pass through both feasible and infeasible points (contrary to the traditional approach where only feasible points may be included in a path). The method (driven by full Navier–Stokes computations) was applied to the problem of multiobjective optimization of aerodynamic shapes subject to various geometrical and aerodynamic constraints. The results demonstrated that the method retains high robustness of conventional GAs while keeping CFD computational volume to an acceptable level, which allowed the algorithm to be used in a demanding engineering environment. Copyright © 2004 John Wiley & Sons, Ltd.     

基于铺层参数的铺层方式与纤维分布协同优化的层合板最大刚度设计

纤维增强复合材料层合板的弹性性质依赖于单层板的纤维含量(体分比)以及铺层方式(总层数、各单层的厚度与铺设方向)。本文研究在给定材料用量条件下层合板的最大刚度设计问题,采用铺层参数作为铺层方式的描述参数、以铺层参数和单层板纤维含量体分比在层合板面内的分布的描述参数为设计变量,以层合板的柔顺性最小为目标,建立了铺层方式和纤维分布协同优化的层合板最大刚度设计问题的提法和求解方法,给出了具有最大刚度的层合板最优铺层方式和纤维含量的分布规律的设计实例。     

Performance analysis and optimization of convective annular fins with internal heat generation

An analysis of the thermal performance for convective annular fins, having a general trapezoidal profile and internal heat generation, is presented. The solution of the optimal problem is also given when either the heat dissipation rate or the volume of the fin is specified. The results are expressed in suitable nondimensional variables that are specified by the problem, and presented graphically. The effect of the fin's profile and thermal conductivity upon the optimum dimensions is discussed. It is shown that the presence of heat generation reduces the ability of the fin to convect heat. Furthermore, certain limiting values of the heat generation that may be imposed on the fin for a feasible optimization are also derived.     

含界面脱粘压电复合材料层合板的非线性动力稳定性分析

基于Reddy提出的板高阶剪切变形简化理论,研究了含界面脱粘损伤压电复合材料层合板非线性动力稳定性问题.首先,建立了分层模型,推导了考虑几何非线性、阻尼效应、纵向惯性力和力-电耦合效应的Mathieu方程,并且给出了该方程解的解析表达式.其次,通过典型算例讨论了界面脱粘损伤以及反馈控制力对该层合板动力不稳定区域、纵向、横向共振频率和最大"牵引"深度的影响.由典型算例讨论可知:随着层合板界面脱粘损伤的扩大,其动力稳定性能逐渐减弱,其中在损伤较小时,反馈控制力对智能结构几乎没有影响;而在损伤比较大的情况下,反馈控制力将能有效地减少动力不稳定区域重合面积.     

Mixed-mode failure of composite laminates with cracks

The behavior of quasi-isotropic graphite/epoxy laminates with cracks subjected to various biaxial-stress fields was studied experimentally. This was accomplished by uniaxial tensile loading of specimens with cracks of various orientations with the loading axis. It was found that the critical stress-intensity factor, based on a projected crack length increased by a characteristic damage dimension, is nearly constant with stress biaxiality and initial crack length. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

A two-dimensional continuum theory for angle-ply laminates

A two-dimensional continuum theory of microstructure is developed for stress analysis of angle-ply laminates under in-plane loading. An example problem is used to evaluate the results of the theory against a reference solution obtained by the finite element method. The results are in satisfactory agreement; they also show that the in-plane stresses reach somewhat higher peak values than reported in previous literature.The theory is also presented in a simplified version, which is found to be adequate for predicting interlaminar stresses and in-plane stress resultants, but does not give acceptable results for the variation of in-plane stresses through the thickness of the laminations.     

Singular potentials and double-force solutions for anisotropic laminates with coupled bending and stretching

Summary Exact solutions are obtained in the framework of the classical theory of laminates subjected to the action of normal moments, double forces, double moments or momentless double dipoles. Seven cases of such loads are considered and completed by considering the case of given transversal discontinuity of normal deflection. It is shown that, in contrast to the case of infinite straight dislocations in a pure in-plane problem, the energy of this eighth solution depends on the discontinuity orientation. Some numerical examples are presented. Besides the formal value, the obtained double-force and double-moment solutions, as well as dimensionless double dipoles, can be used to construct kernels of additional boundary integral equations (BIE). Due to the coupling phenomena in the BIE system for the region with a corner point, additional variable such as corner forces appear and require the mentioned equation. Received 22 June 1999; accepted for publication 6 March 2000     

The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.     

Analysis of complex stress intensities for cracked laminates

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In-plane properties of composite laminates with through-thickness pin reinforcement

Laminated fibre-reinforced composites can be reinforced by through-thickness pins to reduce their susceptibility to delamination. However, the presence of the pins creates resin pockets and disrupts the alignment of the fibres, and may thereby lead to a degradation of the in-plane strength of the composite. Experiments and numerical simulations show that the presence of through-thickness reinforcing pins decreases the tensile strength of the composite by 27%, and the compressive strength of the composite by at least 30%. It is also shown that the pattern in which the pins are inserted has a strong influence on the compressive strength. A pin pattern is identified in order to minimise fibre alignment disruption and thereby maximise the compressive strength.     

Large deflection of unsymmetric laminates with mixed boundary conditions

This paper is analytically concerned with non-linear bending of an unsymmetrically laminated angle-ply rectangular plate under lateral load. The plate edges are subjected to the varying rotational constraints. A series solution satisfying the von Karman-type non-linear equations and the required boundary conditions of the plate is presented. In the formulation the edge moments are replaced by an equivalent lateral pressure near the plate edges. Governing equations are reduced to a set of algebraic equations. Numerical results for maximum deflection, bending moment and inplane force of unsymmetric angle-ply plates are graphically presented for various high-modulus materials, aspect ratios, geometries of lamination and boundary conditions. Present results are also compared with available data.     

Singular full-field stresses in composite laminates with open holes

A method of the superposition of a hybrid and displacement approximation was developed to provide the accurate stress fields in a multilayered composite laminate, including the singular neighborhood of the ply interface and the hole edge. Asymptotic analysis was used to derive the hybrid stress functions. The displacement approximation is based on the polynomial B-spline functions. The method provides the determination of the coefficient of the singular term along with convergent stress components including the singular regions. Reissner’s variational principle was employed. Simple [45/−45]_s and quasi-isotropic IM7/5250 [45/90/−45/0]_s laminates were analyzed. Uniaxial loading and residual stress calculation (quasi-isotropic laminate) were considered. A convergence study showed that accurate values of the coefficient of the singular term of the asymptotic stress expansion could be obtained with coarse out-of-plane and in-plane subdivisions. The interaction between the singular terms on the neighboring interfaces was found to be important for the convergence with coarse subdivisions. Converged transverse interlaminar stress components as a function of the distance from the hole edge, were shown for all examples.     

State-vector equation with damping and vibration analysis of laminates

Based on the modified mixed Hellinger-Reissner(H-R)variational principle for elastic bodies with damping,the state-vector equation with parameters is directionally derived from the principle.A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method.The general solutions for the free vibration of underdamping,critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory.The effect of viscous damping force on the vibration of com- posite laminates is investigated through numerical examples.The state-vector equation theory and its application areas are extended.     

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.     

Stability of graphite/epoxy structures with arbitrary symmetrical laminates

This paper is concerned with compression testing of thin-walled graphite/epoxy structures and the development of empirical stability methods of analysis. The laminates of the structures tested were T-300/5208 graphite/epoxy with arbitrary, symmetrical stacking sequences. Crippling tests were performed on flat plates to generate no-edge-free and one-edge-free empirical crippling curves for use in buckling analysis of thin-walled graphite/epoxy short columns. Crippling tests of square tubes confirmed correlation with flat plates. Short-column tests of similar square tubes and tests of lsection members substantiated use of the Johnson short-column method. Ultimate compression tests were performed for most laminates, and nonlinear stress-strain curves were recorded in all cases.     

Modeling plastic shocks in periodic laminates with gradient plasticity theories

Steady plastic shocks generated by planar impact on metal-polymer laminate composites are analyzed in the framework of gradient plasticity theories. The laminate material has a periodic structure with a unit cell composed of two layers of different materials. First- and second-order gradient plasticity theories are used to model the structure of steady plastic shocks. In both theories, the effect of the internal structure is accounted for at the macroscopic level by two material parameters that are dependent upon the layer's thickness and the properties of constituents. These two structure parameters are shown to be uniquely determined from experimental data. Theoretical predictions are compared with experiments for different cell sizes and for various shock intensities. In particular, the following experimental features are well-reproduced by the modeling:

•

the shock width is proportional to the cell size;

•

the magnitude of strain rate is inversely proportional to cell size and increases with the amplitude of applied stress following a power law.

While these results are equally described by both the plasticity theories, the first gradient plasticity approach seems to be favored when comparing the structure of the shock front to the experimental data.