梯度功能压电复合材料球壳的热弹性近似解

针对梯度功能压电复合材料球壳热弹性响应提出了简单而精确的近似解。借鉴纤维复合材料层合结构的研究方法，将梯度功能压电复合材料球壳沿径向分为若干层，各层视为均匀材料，从而导出力-电-温度多场耦合近似解。只要层数足够大，解将收敛于精确解。该方法的另一个优点在于解的方法对材料性能的变化方式（函数）没有要求，具有普适性。这对其它非均匀材料结构的分析具有推广、应用价值。     

Thermoelastic solutions for anisotropic cracked thin films

Thermal stress intensity factors for cracks in anisotropic thin films subjected to uniform heat fluxes are investigated. Based on the method of analytic continuation associated with the alternating technique, the general solution of an anisotropic thin film/substrate under thermal loading is derived. Rapidly convergent series solutions for both the temperature and stress fields are obtained in terms of the corresponding homogeneous potentials. Using the technique of superposition and the Cauchy integral, the solution of the crack problem with arbitrary locations and angles is solved. Some typically numerical results are discussed, showing that a stiffer substrate can efficiently reduce the thermal stress intensity factors of the cracked thin films. The result also shows that the solution is accurate and rapidly converges as the thin film/substrate degenerates to a homogeneous medium.     

Interlaminar stresses in composite laminates: Thermoelastic deformation

An approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension was developed earlier [4]. In the present paper, the authors have extended that solution to treat thermal stresses and deformations induced by a uniform change in laminate temperature. The results have revealed not only the complex fields within the laminate, but also inter-relationships between the lamina axial and shearing coefficients of thermal expansion and the effective laminate coefficients of thermal expansion. Further, the solution is shown to recover laminated plate theory predictions for thermally induced fields at interior regions of the laminate, thereby confirming the boundary layer nature of the interlaminar phenomena for the thermoelastic case. Finally, the results exhibit the anticipated response in congruence with the mechanical solution of Ref. [4] and the thermoelastic results satisfy the conditions of self-equilibration necessary for the finite-width laminate subjected to free thermal deformation. Integration of the stress σ_x over the laminate cross-section in the y–z plane is shown to converge to zero as the number of Fourier terms is increased. While the exact solution for mechanical loading is known to exhibit singular behavior, non-convergence of the interlaminar shearing strain is also seen to occur at the intersection of the free edge and planes between lamina of +θ and −θ orientation under thermal loading. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem.     

Optimum weight design of fiber composite plates in flexure based on a two level strategy

This paper offers a method for weight optimization of multilayer fiber composite plates under the action of lateral loadings. The objective is to design a fiber composite plate of minimum thickness which can sustain multiple static loadings applied normal to its surface without exhibiting failure based on Tsai-Hill criterion in any of its layers. In this investigation, fiber orientation angles are treated as discrete variables, which can vary only by pre-assigned increments, while thicknesses of layers are treated as continuous variables. The optimization procedure is based on a two stage strategy; in the first of which only the fiber orientation angles for the layers are treated as variables, and in the second, only the layer thicknesses. A powerful criterion based on a load factor has been defined to find the best angle for a new layer in the first stage, and the method of center points has been used for thickness optimization in the second stage. After any angle and thickness optimization has been done, a new layer is added to the thickness and the procedure is repeated for other new layers. The end of the two stage procedure is signaled whenever the thickness of the new layer in the optimization process approaches zero; meaning that no new layers would improve the set of layers already found. In this way at the end of the optimization procedure the plate thickness would be made of a minimum number of layers whose fibers are optimally oriented, and whose thicknesses are minimal. A poor choice of layers in the stack produce near zero thickness for the respective layer, and are thus deleted from the set. A repeat process is performed after each cycle, to modify layer angles in order to compensate for errors due to approximations involved. The priorities exercised in the choice of new layers for inclusion in the set and exclusion of all the un-necessary ones, allow an optimal state of stacking sequence to be achieved. Several examples are given to demonstrate the operation of the algorithm.     

Thermoelastic and infrared-thermography methods for surface strains in cracked orthotropic composite materials

Two quantitative thermoelastic strain analysis (TSA) experimental methods are proposed to determine the surface strain fields in mechanically loaded orthotropic materials using the spatial distribution of temperature gradient measured from the surface. Cyclic loadings are applied to orthotropic composite specimens to achieve adiabatic conditions. The small change in surface temperatures that resulted from the change in the elastic strain energy is measured using a high sensitivity infrared (IR) camera that is synchronized with the applied loading. The first method is applied for layered orthotropic composites with a coat layer made of isotropic or in-plane transversely isotropic material. In this case, one material parameter (pre-calibrated from the surface) is required to map the strain invariant to the temperature gradients. The proposed method can be used together with Lekhnitskii’s elasticity solution to quantify the full strain field and determine mixed-mode stress intensity factors (SIFs) for crack tips in composite plates subjected to off-axis loading. The second method is formulated for orthotropic layers without a coat and it requires thermo-mechanical calibrations for two material parameters aligned with the material axes. The virtual crack closure technique (VCCT), Lekhnitskii’s and Savin’s elasticity solutions, and finite element (FE) analyses are used for demonstrations and validations of the second experimental method. The SIFs from the TSA methods are very sensitive to the uncertainty in the location of the crack tip and the unknown inelastic or damage zone size around the crack tip. The two experimental methods are effective in generating the strain fields around notched and other FRP composites.     

A numerical approach for limit analysis of orthotropic composite laminates

A numerical approach for limit analysis of structures whose constituent material exhibits orthotropic behaviour is presented and discussed. Attention is focused on orthotropic composite laminates under plane stress conditions. The proposed approach is an extension, in the context of orthotropic materials, of the linear matching method (LMM). The latter is based on a sequence of linear analyses performed on the analysed structure made of a fictitious linear viscous material with spatially varying moduli. Here the LMM is applied to structures made of materials obeying the Tsai–Wu criterion. An appropriate choice of the fictitious material, which in this case is assumed linear, viscous, orthotropic and suffering a distribution of assigned initial stresses, reduces the number of parameters to be spatially varied thus rendering the whole procedure applicable and reliable. The results obtained are highly promising as witnessed by a number of numerical examples which are carried out to verify the effectiveness of the proposed approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Thermoelastic evaluation of composite laminates using digital imaging processing

The study of the variation of the curvature of non-symmetric composite laminates with temperature provides a measure of the magnitude of the thermal stresses and the mechanical behavior of the material with temperature. In the present work, an experimental method based on the pioneer use of a digital camera and image processing method is proposed to perform such measurements. Taking advantage of the method and by comparing experimental and CLT, extended-CLT and FEM simulation results, an evaluation of the residual stresses is described and an approach providing more precise determination of the residual thermal stresses in non-symmetric laminates is proposed.     

MITC finite elements for laminated composite plates

Within the framework of the first‐order shear deformation theory, 4‐ and 9‐node elements for the analysis of laminated composite plates are derived from the MITC family developed by Bathe and coworkers. To this end the bases of the MITC formulation are illustrated and suitably extended to incorporate the laminate theory. The proposed elements are locking‐free, they do not have zero‐energy modes and provide accurate in‐plane deformations. Two consecutive regularizations of the extensional and flexural strain fields and the correction of the resulting out‐of‐plane stress profiles necessary to enforce exact fulfillment of the boundary conditions are shown to yield very satisfactory results in terms of transverse and normal stresses. The features of the proposed elements are assessed through several numerical examples, either for regular and highly distorted meshes. Comparisons with analytical solutions are also shown. Copyright © 2001 John Wiley & Sons, Ltd.     

Damage tolerance of fully orthotropic laminates in compression

The compression after impact (CAI) strength of fully orthotropic composite laminates with up to 21 plies is presented, as analysed by an existing strip model. Candidate layups, which can be symmetric, anti-symmetric or non-symmetric, are preselected to exhibit no elastic coupling response, with manufacturing rules applied. These criteria, along with the use of a simple surrogate sublaminate buckling model, were chosen to allow analysis of all feasible laminates in the design space without excessive computation time. Results indicate that although the inclusion of non-symmetric layups in the design space does not give benefits with respect to maximum achievable damage tolerance, these laminates can exhibit damage tolerance close to that of an anti-symmetric design for some ply counts, and better than symmetric solutions in most cases. It is also noted that in some instances increasing the number of plies in a laminate can actually reduce the highest achievable threshold load for damage tolerance, as a result of the large influence Poisson’s ratio has on sublaminate buckling. Average errors in the surrogate model were low in all cases, with maximum non-conservative errors less than 1%. The surrogate buckling model reduced computational time by over 99% when compared to the fully exhaustive search.     

Exact solutions for free vibrations of orthotropic rectangular Mindlin plates

Exact closed-form solutions are obtained for free vibrations of orthotropic rectangular Mindlin plates by using the separation of variables method although it is difficult to solve them. The plates have two opposite edges simply supported and all possible combinations of classical boundary conditions at the other two edges. The exact solutions of orthotropic rectangular Mindlin plates are compared with those of isotropic ones and their differences are discussed. The exact solutions are validated through both mathematical proof and numerical comparisons with available p-Ritz solutions and the differential quadrature finite element method solutions calculated by the authors.     

A survey of test methods for multiaxial and out-of-plane strength of composite laminates

This review paper gives an overview of test methods for multiaxial and out-of-plane strength of composite laminates, with special consideration of non-crimp fabrics (NCF) and other textile systems. Tubular and cruciform specimens can provide arbitrary in-plane loading, while off-axis and angle-ply specimens provide specific biaxial loadings. Tensile and compressive out-of-plane strength may be determined by axial loading of specimens with a waisted gauge section, while bending of curved specimens allow determination of the out-of-plane tensile strength. Tests suited for out-of-plane shear strength include the short beam shear test, the inclined double notch test and the inclined waisted specimen. Testing of arbitrary tri-axial stress states using tubular or cruciform specimens with superimposed through-the-thickness loading is highly complex and significant problems have been reported in achieving the intended stress states and failure modes. Specific tri-axial stress states can be obtained by uniaxial loading of specimens with constrained expansion, as in the die channel test.     

New exact solutions for free vibrations of thin orthotropic rectangular plates

In this paper, a novel separation of variables is presented for solving the exact solutions for the free vibrations of thin orthotropic rectangular plates with all combinations of simply supported (S) and clamped (C) boundary conditions, and the correctness of the exact solutions are proved mathematically. The exact solutions for the three cases SSCC, SCCC, and CCCC are successfully obtained for the first time, although it was believed that they are unable to be obtained. The new exact solutions are further validated by extensive numerical comparisons with the solutions of FEM and those available in the literature.     

A variational asymptotic approach for hygrothermal analysis of composite laminates

A hygrothermal model for analyzing composite laminates under both mechanical and hygrothermal loadings is constructed by the variational asymptotic method (VAM). The original 3-D nonlinear, one-way coupled, hygrothermoelasticity problem is formulated based on a set of intrinsic variables defined on the reference plane and for arbitrary deformation of the normal line. Then the VAM is used to rigorously split the 3-D problem into two problems: a nonlinear, 2-D, plate analysis over the reference plane to obtain the global deformation and a linear analysis through the thickness to provide the 2-D generalized constitutive law and the recovering relations to approximate the original 3-D results. The nonuniqueness of asymptotic theory correct up to a certain order is used to cast the obtained asymptotically correct second-order free energy into a Reissner–Mindlin type model to account for transverse shear deformation. The present theory is implemented into the computer program, Variational Asymptotic Plate and Shell Analysis (VAPAS). Results from VAPAS for several cases have been compared with the exact hygrothermal solutions, classical lamination theory and first-order shear-deformation theory to demonstrate the accuracy and power of the proposed theory and use of VAPAS. The proposed theory can achieve an accuracy comparable to high-order layerwise theories with many more degrees of freedom at the cost of a first-order shear-deformation theory.     

Positive size and scale effects of all-cellulose composite laminates

Negative size effects are commonly reported for advanced composite materials where the strength of the material decreases with increasing volume of the test specimen. In this work, the effect of increasing specimen volume on the mechanical properties of all-cellulose composites is examined by varying the laminate thickness. A positive size effect is observed in all-cellulose composite laminates as demonstrated by a 32.8% increase in tensile strength as the laminate thickness is increased by 7 times. The damage evolution in all-cellulose composite laminates was examined as a function of the tensile strain. Enhanced damage tolerance concomitant with increasing specimen volume is associated with damage accumulation due to transverse cracking and strain delocalisation. A transition from low-strain failure to tough and high-strain failure is observed as the laminate thickness is increased. Simultaneously, scale effects lead to an increase in the void content and cellulose crystallinity at the core, with increasing laminate thickness.     

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

The contribution of this work is the implementation of a new elastic solution method for thick laminated composites and sandwich structures based on a generalized unified formulation using finite elements. A quadrilateral four‐node element was developed and evaluated using an in‐house finite element program. The C‐1 continuity requirements are fulfilled for the transversal displacement field variable. This method is tagged as Caliri's generalized formulation. The results employing the proposed solution method yielded coherent results with deviations as low as 0.05% for a static simply supported symmetric laminate and 0.5% for the modal analyses of a soft core sandwich structure. Copyright © 2016 John Wiley & Sons, Ltd.     

Biodegradability of all-cellulose composite laminates

The high mechanical properties of single-polymer composites based on degradable non-derivatised cellulose, aka all-cellulose composites, have recently captured the attention of researchers. All-cellulose composites possess the intriguing combination of high strength and biodegradability. However, the biodegradation behaviour of all-cellulose composites has so far not been reported. In this work, soil burial experiments were carried out to compare the biodegradation behaviour of all-cellulose composites with conventional biocomposites in order to investigate the end-of-life disposal of this relatively new class of bio-based composite materials. All-cellulose composites are characterised by exceptional biodegradability with mass losses of up to 73% following a soil burial time of 70 days. An investigation of the mechanisms of biodegradation of all-cellulose composites is undertaken for the first time.     

复合材料非对称正交薄层板的固化变形

利用Rayleigh-Ritz 法研究了复合材料非对称正交薄层板的固化变形。建立了考虑几何非线性的固化变形分析模型, 预报了其固化后的变形形状及变形量。利用热压釜工艺进行了实验研究。实验发现, 方板边缘发生了较大的向内卷曲变形, 板边缘附近理论预报值与实验结果差别较大, 在距板边缘一定距离内理论预报值和实验结果吻合较好, 矩形板实验结果与理论预报值吻合良好。      

Benchmark three-dimensional elasticity solutions for the buckling of thick orthotropic cylindrical shells

Benchmark solutions to the problem of buckling of orthotropic cylindrical shells, which are based on the three-dimensional theory of elasticity, are presented in this review article. It is assumed that the shell is under external pressure or axial compression or a combination of these loadings. These solutions provide a means of accurately assessing the limitations of the various shell theories in predicting critical loads. A comparison with some classical shell theories shows that the classical shell theories may produce, in general, highly non-conservative results on the critical load of composite shells with thick construction. One noteworthy exception: the Timoshenko shell buckling equations produce conservative results under pure axial compression.     

Review of z-pinned composite laminates

This paper reviews published research into polymer composite laminates reinforced in the through-thickness direction with z-pins. Research into the manufacture, microstructure, delamination resistance, damage tolerance, joint strength and mechanical properties of z-pinned composites is described. Benefits of reinforcing composites with z-pins are assessed, including improvements to the delamination toughness, impact damage resistance, post-impact damage tolerance and through-thickness properties. Improvements to the failure strength of bonded and bearing joints due to z-pinning are also examined. The paper also reviews research into the adverse effects of z-pins on the in-plane mechanical properties, which includes reduced elastic modulus, strength and fatigue performance. Mechanisms responsible for the reduction to the in-plane properties are discussed, and techniques to minimise the adverse effect of z-pins are described. The benefits and drawbacks of z-pinning on the interlaminar toughness, damage tolerance and in-plane mechanical properties are compared against other common types of through-thickness reinforcement for composites, such as 3D weaving and stitching. Gaps in our understanding and unresolved research problems with z-pinned composites are identified to provide a road map for future research into these materials.