Reliability formulation for composite laminates subjected to first-ply failure

Methods formulated on the basis of the concept of first-ply failure and the structural reliability theory are presented for the reliability analysis of laminated composite plates. In the reliability formulation, an appropriate phenomenological failure criterion is used to establish the limit state equation of the laminated composite plates, and different numerical techniques are employed to evaluate the reliability of the plates. Experimental investigations of lamina strengths and first-ply failure loads of laminated composite plates were performed. Baseline probability distributions of lamina strength parameters constructed from the test data are used to study the reliability of the laminated plates. The accuracy of the proposed models in reliability assessment of the laminated plates are verified by the experimental results on first-ply failure load distributions.     

Reliability analysis of nonlinear laminated composite plate structures

A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration.     

Stochastic nonlinear failure analysis of laminated composite plates under compressive transverse loading

This paper present the second ordered statistics of first-ply failure response of laminated composite plate with random material properties under random loading. The basic formulation is based on higher order shear deformation plate theory (HSDT) with the geometrically nonlinearity in the von-Karman. The direct iterative based C⁰ nonlinear finite element method combined with mean centered first order perturbation technique developed by the authors are extended and successfully applied nonlinearity for failure problem with a reasonable accuracy to predict the second order statistics (standard deviation) of first-ply failure response using Tsai-Wu and Hoffman failure criterion with macroscopic analysis. Typical numerical results for various combinations of boundary conditions, plate thickness ratios, aspect ratios, laminates scheme and layers, elastic modulus ratios have been presented to illustrate the application of developed procedure. Some new results are presented and examined which clearly demonstrated the importance of the randomness in the system parameters in the failure response of the structures subjected to transverse loadings.     

First-ply failure analysis of laminated composite plates based on the layerwise linear displacement theory

A finite element formulated on the basis of the layerwise linear displacement theory is used to study the first-ply failure of moderately thick laminated composite plates. In the finite element formulation, a laminated composite element is divided into a number of mathematical layer groups and displacements are assumed to vary linearly in each layer group which contains eight nodal points. The accuracy of the finite element in predicting displacements and stresses has been verified by comparing results with experimental data and previously obtained analytical results. The finite element is used to determine the first-ply failure loads of a number of laminated composite plates on the basis of several phenomenological failure criteria. The capabilities of the failure criteria in predicting first-ply failure loads are investigated by comparing the finite element first-ply failure loads with the experimental ones. It has been found that the failure criteria can yield reasonably good results for the cases considered.     

First-ply failure strength of laminated composite pressure vessels

Strengths of laminated composite pressure vessels are studied via both analytical and experimental approaches. Experimental techniques are presented to determine the first-ply failure and burst strengths of laminated composite pressure vessels with different lamination arrangements. Different analytical methods, together with various failure criteria, are used to predict the first-ply failure strengths of the laminated pressure vessels. The accuracy of the theoretical prediction of first-ply failure strength is verified by the test data. The suitability of the failure criteria, as well as the limitations of the analytical methods are discussed.     

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

Abstract

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C⁰ finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

Stochastic post buckling analysis of laminated composite cylindrical shell panel subjected to hygrothermomechanical loading

In this paper, the effect of random system properties on the post buckling load of geometrically nonlinear laminated composite cylindrical shell panel subjected to hygrothermomechanical loading is investigated. System parameters are assumed as independent random variables. The higher order shear deformation theory and von-Karman nonlinear kinematics are used for basic formulation. The elastic and hygrothermal properties of the composite material are considered to be dependent on temperature and moisture concentration using micromechanical approach. A direct iterative based C⁰ nonlinear finite element method in conjunction with first-order perturbation technique proposed by present author for the plate is extended for shell panel subjected to hygrothermomechanical loading to compute the second-order statistics (mean and variances) of laminated composite cylindrical shell panel. The effect of random system properties, plate geometry, stacking sequences, support conditions, fiber volume fractions and temperature and moisture distributions on hygrothermomechanical post-buckling load of the laminated cylindrical shell panel are presented. The performance of outlined stochastic approach has been validated by comparing the present results with those available in the literature and independent Monte Carlo simulation.     

Stochastic progressive failure analysis of laminated composite plates using Puck's failure criteria

The present work deals with second-order statistics of the progressive failure response of laminated composite plates subjected to in-plane uniaxial and bi-axial loadings with random system properties. A stochastic finite element method based on higher-order shear deformation theory combined with first- and second-order perturbation technique is used for solution of random progressive failure equation. A Puck failure criterion is used for the evaluation of first ply and last-ply failure load. The results obtained using the present solution approach are validated with the results available in the literature and Monte Carlo simulation.     

含分层损伤复合材料加筋层合板的动承载能力

采用有限元方法研究了含穿透分层损伤复合材料加筋层合板的动力响应和承载能力。根据复合材料层合板一阶剪切理论, 推导了复合材料层合板单元的刚度阵和质量阵列式;同时采用Adams 应变能法与Rayleigh阻尼模型相结合的方法, 构造了相应的阻尼阵列式;为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象, 建立了含分层损伤复合材料加筋层合板动力分析中分层分析模型和虚拟界面联接模型。并采用Tsai提出的刚度退化准则和动力响应分析的精细积分法, 对在动荷载作用下含分层损伤复合材料加筋层合板结构进行了破坏和承载能力分析。通过典型算例分析, 分别讨论了外载频率、分层深度、筋的位置以及破坏过程中刚度退化对含损伤复合材料加筋层合板动力响应特征和承载能力的影响, 得到了一些具有理论和工程价值的结论。     

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论,用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值,推导了复合材料层合板刚度阵,质量阵列式,阻尼阵列式,并由Lagrange方程导出了层合板的动力学方程,通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性,在Kirchhoff假设的基础上,对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计,数值算列验证了算法的有效性。     

Thermal postbuckling analysis of laminated composite plates by the finite element method

The thermal postbuckling behavior of composite laminated plates subjected to a nonuniform temperature field is investigated by the finite element method. Based on the principle of minimum potential energy, the nonlinear stiffness matrix and geometry matrix are derived. The assumed displacement state over the middle surface of the plate element is expressed as a product of one-dimensional, first-order Hermitian polynomials. An iterative method is employed to determine the thermal postbuckling load. The results of the computations reveal that the thermal postbuckling behavior of composite laminated plates is influenced by lamination angle, plate aspect ratio, modulus ratio and the number of layers.     

Non-linear response statistics of composite laminates with random material properties under random loading

Laminated composite plates find extensive use in many engineering applications. Some of these incorporate large deflections that may not be in the linear range. The external loading may be random in nature. The laminate material properties show an inherent dispersion around a mean value. In this paper the static response of laminated composite flat plates to transverse random loading has been studied. The material properties have been taken as random variables for accurate prediction of the system behaviour. The basic formulation of the problem has been developed based on the classical laminate theory and the Von-Karman non-linear strain–displacement relationship. A first order perturbation technique has been used to obtain the second order response statistics. Typical results have been presented for a plate with all edges simply supported. A comparison has been drawn with Monte Carlo simulation results for validation of the proposed approach. The effects of side-to-thickness ratio, aspect ratio and change in standard deviation of input random variables have been investigated for cross-ply symmetric and anti-symmetric laminates.     

Stochastic nonlinear bending response of functionally graded material plate with random system properties in thermal environment

This study deals with the stochastic nonlinear bending response of functionally graded materials (FGMs) plate with uncertain system properties subjected to transverse uniformly distributed load in thermal environments. The system properties such as material properties of each constituent’s material, volume fraction index and transverse load are taken as independent random input variables. The material properties are assumed to be temperature independent (TID) and temperature dependent (TD). The basic formulation is based on higher order shear deformation theory with von-Karman nonlinear strain kinematics using modified C ⁰ continuity. A direct iterative based nonlinear finite element method in conjunction with first-order perturbation technique developed by last two authors for the composite plate is extended for the FGM plate to compute the second order statistics (mean and standard deviation) of the nonlinear bending response of the FGM plates. Effects of TD, TID material properties, aspect ratios, volume fraction index and boundary conditions, uniform temperature and non-uniform temperature distribution on the nonlinear bending are presented in detail through parametric studies. The present outlined approach has been validated with the results available in the literature and independent Monte Carlo simulation.     

Free vibration of laminated composite conical shells with random material properties

In the present study, the sensitivity of randomness in material parameters on linear free vibration response of conical shells is presented. Higher order shear deformation theory is used to model system behavior and uncertain lamina material properties are modeled as basic random variables. A finite element method is successfully combined with first-order perturbation technique to obtain the response statistics of the structure. The solution methodology is validated with the results available in the literature and an independent Monte Carlo simulation. Typical numerical results for second-order statistics of linear free vibration response of simply supported laminated composite conical shells are obtained for different lamination schemes and thickness to radius ratios.     

受火后叠合板组合梁受力性能试验研究

为研究受火后叠合板组合梁的受力性能,分别对五个火灾后叠合板组合梁和一个常温下叠合板组合梁进行静力加载试验,研究了后浇层厚度、栓钉间距、预制底板在钢梁上翼缘的搁置长度、预制底板接缝形式、是否受火等因素对叠合板组合梁的破坏形态、承载能力和抗弯刚度的影响。结果表明:火灾后整体式叠合板组合梁的极限承载力较分离式叠合板组合梁提高9%;后浇层厚度和栓钉间距是影响火灾后整体式叠合板组合梁初始抗弯刚度的主要因素;火灾前后整体式叠合板组合梁在荷载作用下均发生受弯破坏,且破坏形态基本相同,但经历火灾高温作用后,整体式叠合板组合梁出现裂缝的时间提前,其抗弯承载力和延性均有不同程度的降低,本次试验中火灾后整体式叠合板组合梁在荷载作用下的抗弯承载力和延性较常温下分别降低23.3%和55.4%;分离式叠合板组合梁中预制底板接缝的存在,破坏了预制底板的连续性,造成试件发生粘结破坏,但在远离接缝处,叠合板的协同工作性能良好;提出火灾后叠合板组合梁剩余承载力和抗弯刚度的计算方法,该方法具有良好的精度。     

Multiscale analysis of viscoelastic laminated composite plates using generalized differential quadrature

In this paper, a laminated composite plate is analyzed using a multiscale method. At first, material properties of a lamina are obtained using an analytical micromechanical approach called simplified unit cell method (SUCM), and then in structural level, the generalized differential quadrature method (GDQM) is used to analyze a laminated composite plate. By means of the Boltzmann superposition principle, the viscoelastic behavior of the matrix is obtained. The Prony series is considered to define the compliance of matrix. To verify the results, graphiteT300/epoxy5208 composite material is analyzed and the results are compared with existing experimental data. The multiscale algorithm includes obtaining overall properties of the composite by SUCM; then, these properties are used to define the bending stiffness. Governing equations of motion of laminated composite plate are solved via GDQM and Newton–Raphson method. Variations of stresses and displacements versus time and volume fraction of the fibers are shown for laminated composite plates with different boundary conditions.     

Nonlinear static response of laminated composite plates by discrete singular convolution method

In this paper, large deflection analysis of laminated composite plates is analysed. Nonlinear governing equation for bending based on first-order shear deformation theory (FSDT) in the von Karman sense is presented. These equations have been solved by the method of discrete singular convolution (DSC). Regularized Shannon’s delta (RSD) kernel and Lagrange delta sequence (LDS) kernel are selected as singular convolution to illustrate the present algorithm. The effects of plate aspect ratio, fiber orientation, boundary conditions, thickness-to-side ratio, and applied load on the nonlinear static response of the laminated plate are investigated.     

Time-varying reliability method based on linearized Nataf transform

In actual engineering, material properties, load effects, and other factors of mechanical structures change due to long-term use. In order to understand the operation of a mechanical structure in real time, it is crucial to obtain the dynamic trajectory of its reliability. Considering the time variability of a mechanical structure over time, uncertain random variables are introduced to express the uncertainty of various parameters of structures, and the Wiener process is used to describe the strength degradation process of structures so as to solve the calculation problem of time-varying reliability of mechanical structures. Based on the advanced first-order and second moment method (AFOSM), the proposed linearized Nataf change is used to complete the transformation from related nonnormal variables to independent standard normal variables in order to simplify the calculation process of reliability solution and solve the reliability calculation problem of random parameters subjected to arbitrary distribution. The deduced random variable sensitivity factor indicates the degree of influence of different random variables on the reliability of the mechanical structure, providing a theoretical basis for the optimal design and maintenance of a mechanical structure. The proposed method is analyzed using the cantilever beam and compared with the nonlinear Nataf transform and verified by the Monte Carlo simulation results. The results show that the proposed method can effectively solve the reliability sensitivity problem of structural system strength degradation.     

On the damping analysis of FRP laminated composite plates

This paper presents the damping analysis of fiber reinforced plastics laminated composite plates. For this purpose, the maximum strain and kinetic energies of a cross-ply laminated plate are evaluated analytically based on the three-dimensional theory of elasticity. The displacements of the simply supported rectangular plates are expanded into the polynomial forms with respect to a thickness coordinate, and then governing equations are formulated by using the Ritz's method. In the numerical calculations, natural frequencies and modal damping ratios are calculated for the plates with different stacking sequence and thickness ratios. The validity of the assumption of deformations and the applicability of the other plate theories (e.g. classical lamination theory (CLT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory) to the laminated thick plates are discussed by comparing the numerical results obtained by the present method with the CLT and the FSDT solutions.