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.     

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.     

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.     

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.     

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.     

An analysis of interface delamination mechanisms in orthotropic and hybrid fiber-metal composite laminates

The onset and propagation of interlaminar defects is one of the main damage mechanisms in composite materials. This is even more the case when considering layered materials comprising metallic laminae (typically Aluminium) and FRP laminae. Propagation of delamination mainly depends on the initial crack extension and its loading mode.This work presents some results of a combined analytical-numerical-experimental study on the onset and propagation mechanisms regarding interlaminar defects. Two cases have been analysed in particular, the first consisting of a glass-fibre reinforced epoxy resin laminate, and the second consisting of a hybrid laminate where a lamina of aluminium is layered between FRP laminae.     

Stress distribution in damaged composite laminates under transverse impact

Studies on damage in composite laminates subjected to central and normal impact are conducted by a 3-D finite element analysis. The stress analysis is carried out by developing a constitutive equation of composite laminates coupled with the damage. Effects of the damage on the stress distribution in the laminates are investigated in details. The obtained contact force history correlates well with the results reported in literatures. Stress distributions across the thickness of the elastic non-damaged laminate show a probable distribution of delamination. The simulated result for delamination is coincided with the observation of experiments. Stress distributions for the damaged laminates show that the damage releases strain energy and lessens stress concentration.     

A general solution for a bolt loaded-hole in piezoelectric composite laminates

In this paper the two-dimensional problem of a bolt loaded-hole in an infinite piezoelectric laminate is considered in terms of the complex variable method. Firstly, an explicit form Green function for a generalized point load acted at an arbitrary point outside the hole is derived. Secondly, the Green function for a generalized point load acted at the rim of the hole, as a special case, is obtained, and then a general solution for the case of arbitrarily distributed mechanical and electric loading on the hole surface is presented based on the superposition principle. In general, the solution is in the form of series, but its novel feature is that the coefficients involved in the solution can be easily written out once the distributed loading is specified. Finally, several examples useful for engineering are given.     

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.     

Thermoelastic Fluctuations in Solids

Adiabatic thermoelastic heating can be used to monitor stress fluctuations in solids. Previous studies of the effects on the temperature fluctuations both of applied static stress and of the finite amplitude of the stress fluctuations have used approximate theory. The present rigorous thermodynamic treatment distinguishes between adiabatic second-order derivatives needed for finite amplitude and mixed derivatives needed for static applied stress. A detailed analysis is given for purely compressive stress, followed by computations for KCl, NaCl, Al, Cu, Ti, and the alloy Ti-6Al-4V. Additional terms revealed by the new analysis prove to be substantial, including the difference between the adiabatic and mixed derivatives. Revised forms are then proposed for earlier approximations. For unidirectional stress, expressions are taken from an analysis given elsewhere; and computations made for Al, Cu, Ti and Ti-6Al-4V. Corrections to earlier approximations are relatively smaller than for compressive stress, and of opposite sign because the shear component of the unidirectional stress dominates the second order effects.     

Bearing strength prediction for reinforced composite laminates for cryogenic and aerospace applications

The procedures of bearing strength prediction for composite laminates reinforced with high-strength unidirectional fibers at room and cryogenic temperatures are discussed. The best agreement between the calculated and experimental data is observed when the temperature dependence of effective mechanical parameters of plies is allowed for within the framework of the elastic theory of laminated heterogeneous bodies. __________ Translated from Problemy Prochnosti, No. 2, pp. 11–25, March–April, 2008.     

A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes

A reliable process for the design of blast-resistance composite laminates is needed. We consider here the use of carbon nanotubes (CNTs) to enhance the mechanical properties of composite interface layers. The use of CNTs not only enhances the strength of the interface but also significantly alters stress propagation in composite laminates. A simplified wave propagation simulation is developed and the optimal CNT content in the interface layer is determined using multi-objective optimization paradigms. The optimization process targets minimizing the ratio of the stress developed in the layers to the strength of that layer for all the composite laminate layers. Two optimization methods are employed to identify the optimal CNT content. A case study demonstrating the design of five-layer composite laminate subjected to a blast event is used to demonstrate the concept. It is shown that the addition of 2% and 4% CNTs by weight to the epoxy interfaces results in significant enhancement of the composite ability to resist blast.     

Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory

A two-dimensional finite element model is presented to perform the linear static analysis of laminated orthotropic composite plates based on a refined higher order shear deformation theory. The theory accounts for parabolic distributions of transverse shear stresses and requires no shear correction factors. A finite element program is developed using serendipity element with seven degrees of freedom per node. The present solutions are compared with those obtained using three-dimensional elasticity theory and those obtained by other researchers. The theory accurately predicts displacements and transverse shear stresses compared to previously developed theories for thick plates and are very close to three-dimensional elasticity solutions. The effects of transverse shear deformation, material anisotropy, aspect ratio, fiber orientation and lamination sequence on transverse shear stresses are investigated. The error in values of transverse shear stresses decreases as the number of lamina increases, for a plate of same thickness. An increase in degree of anisotropy results in lower values of deflection in the plate. For cross-ply plate an increase in anisotropy results in an increase in effective stress whereas for angle-ply plate the effect is almost negligible. Through thickness variation of transverse shear stresses are independent of anisotropy. The maximum effective stress increases exponentially at lower values of anisotropy and reaches to an asymptotic value at higher values. The stacking sequence has a significant effect on the transverse deflections and shear stress. Rectangular plates experience less effective, in-plane and transverse shear stresses compared to square plates.