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.     

Modeling of viscoelastic structures with random material properties using time-separated stochastic mechanics

Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.     

Theory and FE-analysis for structures with large deformation under magnetic loading

We introduce and discuss a reduced micropolar continuum theory to simulate structures with large deformations under magnetic loading. Three numerical examples show the motivation of this model and its use in practical applications. The question of how to choose the micropolar material parameters is addressed. We use that a finite strain micropolar model would reduce to classical elasticity in the absence of curvature effects and body couples and for certain parameter ranges. This gives us information about a proper choice of material parameters. Thus, we introduce in fact a nearly classical model, but with the feature to cover large deformations and non-classical types of loading. As in shell theories, our continuum theory treats angular momentum as an explicit complementary principle. Thus, net couples—the typical loading of magnetized bodies in a magnetic field—can be modelled. Note that, in this case, the possibility for nonsymmetric Cauchy stresses is required for equilibrium, unlike classical shell theories. Micropolar theories are not commonly used, by comparison to the Boltzmann continuum. One reason may be that micropolar theories often require greater modelling effort without significant advantage. However, the simplicity of introducing physical effects like magnetic loading compensates those efforts.     

Non-stationary random response analysis of structures with uncertain parameters

This paper proposes a non-stationary random response analysis method of structures with uncertain parameters. The structural physical parameters and the input parameters are considered as random variables or interval variables. By using the pseudo-excitation method and the direct differentiation method (DDM), the analytical expression of the time-varying power spectrum and the time-varying variance of the structure response can be obtained in the framework of first order perturbation approaches. In addition, the analytical expression of the first-order and second-order partial derivative (e.g., time-varying sensitivity coefficient) for the time-varying power spectrum and the time-varying variance of the structure response expressed via the uncertainty parameters can also be determined. Based on this and the perturbation technique, the probabilistic and non-probabilistic analysis methods to calculate the upper and lower bounds of the time-varying variance of the structure response are proposed. Finally the effectiveness of the proposed method is demonstrated by numerical examples compared with the Monte Carlo solutions and the vertex solutions.     

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.     

Buckling of composite circular cylindrical shells with random material properties

Composite materials exhibit a scatter in their properties. This is generally ignored in conventional structural analysis leading to results that may be non-conservative. The present study discusses the critical buckling analysis for circular cylindrical shells of laminated composites incorporating the effects of randomness in the material properties. A perturbation approach has been employed to develop expressions for the mean and variance of the critical buckling load in terms of material property statistics. Working of the approach has been illustrated with an example.     

Free vibration of composite cylindrical panels with random material properties

Virtually in all structural systems, and in particular composites, there are uncertainties in the system parameters because of practical bounds on the quality control. In the present work the effect of variations in the mechanical properties of laminated composite cylindrical panels on its natural frequency has been obtained by modeling these as random variables. The transverse shear and rotatory inertia effects have been included in the governing equations. A perturbation approach is presented to obtain the mean and variance of the random natural frequencies. The effects of thickness ratios, edge support conditions and standard deviation of material properties on response of shallow square panels have been investigated. Results have been obtained by employing the finite element method. The approach has been validated by comparison of results with other approaches.     

功能梯度材料梁的非线性随机振动响应

基于大变形理论建立功能梯度材料(FGM)梁运动方程,将梁的横向位移假定为时间函数和梁线性模态乘积之和,利用伽辽金方法离散为非线性常微分方程组;然后,运用等效线性化方法求得随机激励作用下简支约束的功能梯度材料梁均方位移,与NewMark法和蒙特卡罗方法获得的结果对比,验证该等效线性化方法的可靠性.最后讨论材料梯度指数、激励强度和梁长细比对功能梯度材料梁振动响应的影响.     

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.     

Thermo-acoustic random response of temperature-dependent functionally graded material panels

A nonlinear finite element model is provided for the nonlinear random response of functionally graded material panels subject to combined thermal and random acoustic loads. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are derived using the first-order shear-deformable plate theory with von Karman geometric nonlinearity and the principle of virtual work. The thermal load is assumed to be steady state constant temperature distribution, and the acoustic excitation is considered to be a stationary white-Gaussian random pressure with zero mean and uniform magnitude over the plate surface. The governing equations are transformed to modal coordinates to reduce the computational efforts. Newton–Raphson iteration method is employed to obtain the dynamic response at each time step of the Newmark implicit scheme for numerical integration. Finally, numerical results are provided to study the effects of volume fraction exponent, temperature rise, and the sound pressure level on the panel response.     

Sampling analysis of concrete structures for creep and shrinkage with correlated random material parameters

The latin hypercube sampling method, which represents the most efficient way to determine the statistics of the creep and shrinkage response of structures, has previously been developed and used under the assumption that the random parameters of the creep and shrinkage prediction model are mutually independent. In reality they are correlated. On the basis of existing data, this paper establishes, by means of the method of maximum likelihood, the joint multivariate probability distribution of the random parameters involved, tests the hypothesis of mutual dependence of parameters on the basis of the χ²-distribution, and generalizes the latin hypercube sampling method to the case of correlated multinormal random parameters. The generalization is accomplished by an orthogonal matrix transformation of the random parameters based on the eigenvectors of the inverse of the covariance matrix. This yields a set of new random parameters which are uncorrelated (independent) and can be subjected to the ordinary latin hypercube sampling, with samples of equal probabilities. Numerical examples of statistical prediction of creep and shrinkage effects in structures confirm the practical feasibility of the method and reveal a good agreement with the scatter observed in some previous experiments.     

Hypervelocity impact response of spaced composite material structures

The design of a spacecraft for a long-duration mission must take into account the possibility of high-speed impacts by meteoroids and orbiting space debris and the effects of such impacts on the spacecraft structure. With the advent of many new high-strength composite materials and their proliferation in aircraft applications, it has become necessary to evaluate their potential for use in long-duration space and aerospace structural systems. One aspect of this evaluation is the analysis of their response to hypervelocity projectile impact loadings. The analyses performed in this study indicate that the extent of damage to a dual-wall composite structure can be written as a function of the geometric and material properties of the projectile/structure system. A comparative analysis of impact damage in composite specimens and in geometrically similar aluminum specimens is also performed to determine the advantages and disadvantages of employing certain composite materials in the design of structural wall systems for long-duration spacecraft.     

The mechanical properties of pressed processed wheat material

Breakfast wheatflake materials, produced by two methods, were milled and different sieve fractions reconstituted by hot pressing into bar-shaped test pieces, to reduce the geometry and structure effects of flakes. The stiffness and fracture properties of these pressed bars of different particle size in ranges <0.5 mm, 0.5–1 mm, 1–1.4 mm, 1.4–2 mm and of different water content were compared. Dynamic mechanical thermal analysis showed that the bending modulus, E, superimposed as a function of temperature in the range -40 to 140 °C. The value of E at 20 °C decreased with increasing water content corresponding to depression of the glass transition temperature. Microscopy of the test pieces revealed that starch was the continuous phase. The stiffness properties were similar in many respects to data published for pressed starch specimens. However, the energy to break samples at 7% water content (wet weight basis) was greater when a range of particle sizes was used compared to the results of narrow particle size ranges. This is consistent with published results on fracture toughness of particulate compacts. The energy to break samples increased with increasing water content.     

材料力学性能对液力胀接过程的影响分析

为寻求装配式空心凸轮轴结构设计和材料选择的理论依据,应用弹塑性力学分析了弹性模量和流动应力对液力胀接的影响.将内外管的变形过程简化为平面应变问题,根据典型点应力-应变曲线分析了液力胀接过程,并给出了不同材质套管的连接条件.研究结果表明:影响液力胀接的主要因素是内外管弹性模量和流动应力,这两个材料参数决定胀后内外管弹性回复量的大小;实现液力胀接内外管应满足的条件是:内外管弹性模量的比值大于内外管流动应力的比值.     

Probability density evolution analysis of stochastic seismic response of structures with dependent random parameters

Performance evaluation and reliability assessment of real-world structures under earthquakes is of paramount importance. Generally, different mechanical property parameters of a structure are usually not independent, nor completely dependent, but partly dependent or correlated. Therefore, how to reasonably characterize such partial dependency and whether such partial dependency real matters in the stochastic response and reliability of structures under earthquakes are crucial issues. For this purpose, in the present paper, a novel physically-guided data-driven methodology of capturing the correlation configuration of basic random variables and the probability density evolution method are synthesized. The physically-guided data-driven methodology is firstly outlined. In this methodology, the underlying physical mechanism between dependent random variables is firstly involved to establish a random function model, and then the available observed data are adopted to identify the parameters in this model. What is more, physical constraints are also revealed for the initial modulus of elasticity and compressive strength of concrete. The probability density evolution method is then adopted, and the point selection by minimizing the GF-discrepancy is adjusted according to the correlation configuration and physical constraints. A reinforced concrete frame structure subjected to earthquake input is studied. It is found that when the structure is in the strongly nonlinear stage, the correlation configuration has considerable effects on the standard deviation of the stochastic responses, by a factor of nearly 2. In addition, whether the mechanical parameters in different floors are independent or not has great effects on the stochastic responses as well. Problems to be further studied are also outlined.     

The mechanical properties of a transverse isotropic voided material

The mechanical properties of a transverse isotropic honeycomb porous material were investigated by the experiment and the finite element method. The relative density dependence of the macroscopic elastoplastic constants along the in-plane and out of plane directions (e.g., Young’s modulus, Poisson’s ratio, yielding stress, etc.) was systematically studied. Good agreement between the experimental and numerical results was observed. In addition, the three dimensional numerical results were compared with simplified foam models and self-consistent estimates, showing the necessity to improve available models for foams in order to achieve a better predictive capability. At the same time, the elastic–plastic failure mechanism was discussed in detail.     

煤粉对PVC材料力学性能的影响

将煤粉与PVC塑料混炼制得煤粉/PVC复合材料,研究了煤粉含量和分布状态对PVC材料力学性能的影响。结果表明,煤粉(平均粒径34.5μm)能够均匀地分布于PVC塑料中;当煤粉含量达到7%时,所得复合材料的综合力学性能最佳,其中拉伸强度为66MPa,弯曲强度为68MPa,断裂伸长率为84%,冲击强度可达16.46kJ/m2,邵氏硬度为87.16。煤粉之所以能够增强PVC材料的力学性能,主要是由于均匀分布的煤粉承担了应力在复合材料中的传递。     

On-line measurement of material properties for composite wing structures

Structures will encounter degradation of material properties in changing service environments. To improve structural safety and prevent accident, it is necessary to examine material properties of structures in nondestructive ways. Although several nondestructive evaluation techniques have been developed in the literature, most of them detect local damages not global material properties. In this paper, an on-line and real-time detection system is developed through the concept of inverse analysis. In this system, the detectors are selected to be natural frequencies and static strains whose relations with material properties can be obtained from analytical solution or commercial finite element software or experimental data. Transferring their relations into training patterns of artificial neural networks, the elastic properties of composite wing structures can be determined on-line with frequency and strain sensors embedded into structures. To illustrate this on-line measurement system, an example of NACA 2412 composite wing is provided in this paper. This example shows that the material properties determined through this on-line system well agree with the values obtained from the conventional testing methods. The difference is that the present method determines the properties on-line and real-time without cutting any specimen on the structures and testing specimens in the laboratory.     

非贯通球形空腔型轻质仿生结构的设计及其力学性能

为设计并开发轻量型仿生复合材料,分析了东方龙虱鞘翅断面的微观结构,发现龙虱鞘翅的内部空腔结构为非贯通球形空腔。受龙虱鞘翅独特结构的启发设计了一种轻质仿生结构,球形空腔以正六边形的形式分布于该结构内部。为考察该仿生结构的力学特性,引入了两种常见的中空结构,并借助有限元分析软件ANSYS分别对该仿生结构和其他两种常见的中空结构的压缩、拉伸及弯曲性能进行了有限元分析和对比研究。结果表明:该仿生结构较其他两种常见的中空结构具有更强的抗压能力、抗拉能力及更高的屈服强度,力学性能优异。该仿生结构在材料结构方面为研制新型仿生复合材料提供了仿生学参考。