Influence of uncertainties on the response and reliability of self-adaptive composite rotors

Advanced composite structures are becoming increasingly popular because of their high specific strength and stiffness, as well as ability to provide improved performance through passive morphing via intrinsic bend–twist deformation coupling. Self-adaptive composite structures tend to be more susceptible to geometric, material, and loading uncertainties because of their complex configuration, manufacturing process, and dependence on fluid–structure interaction (FSI) response. The objective of this work is to quantify the effects of material, geometric, and loading uncertainties on the response of self-adaptive composite propellers and overall system reliability. A fully-coupled, 3-D boundary element method–finite element method is used to compute the dynamic FSI response. Variability in propeller performance is estimated by considering variations in operating conditions, as well as blade geometry and stiffness. Modeling uncertainties are considered by employing various mechanistic-based failure initiation models. Random variations in material strengths are implemented and an estimate of the structural reliability is determined. The results indicate that adaptive composite structures that depend on FSI are more sensitive to natural, random variations than equivalent rigid, isotropic structures. Therefore, it is necessary to quantify the effects of material, geometric, and loading uncertainties on the responses, safe operating envelopes, and reliability of self-adaptive composite structures.     

Reliability-based design and optimization of adaptive marine structures

The objectives of this work are to quantify the influence of material and operational uncertainties on the performance of self-adaptive marine rotors, and to develop a reliability-based design and optimization methodology for adaptive marine structures. Using a previously validated 3D fluid–structure interaction model, performance functions are obtained and used to generate characteristic response surfaces. A first-order reliability method is used to evaluate the influence of uncertainties in material and load parameters and thus optimize the design parameters. The results demonstrate the viability of the proposed reliability-based design and optimization methodology, and demonstrate that a probabilistic approach is more appropriate than a deterministic approach for the design and optimization of adaptive marine structures that rely on fluid–structure interaction for performance improvement.     

混凝土杆系结构滞回全过程分析

本文基于非线性有限元原理,采取由材料本构关系直接形成单元M—N—φ关系的方法,推导了混凝土杆系结构的单元刚度矩阵,该矩阵考虑了材料非线性、几何非线性、轴力二次矩、混凝土的裂面效应、预应力的特点、钢筋的粘结滑移以及材料的双切线模量等的影响;编制了相应的分析程序,并对两榀混凝土门架的滞回性能进行了模拟计算,计算值与试验结果吻合较好。本文程序实现了混凝土杆系结构包括下降段在内的滞回全过程分析,从而为该类结构的抗震研究提供了一个准确、实用的工具。     

Efficient explicit formulation for practical fuzzy structural analysis

This paper presents a practical approach based on High Dimensional Model Representation (HDMR) for analysing the response of structures with fuzzy parameters. The proposed methodology involves integrated finite element modelling, HDMR based response surface generation, and explicit fuzzy analysis procedures. The uncertainties in the material, geometric, loading and structural parameters are represented using fuzzy sets. To facilitate efficient computation, a HDMR based response surface generation is employed for the approximation of the fuzzy finite element response quantity.     

Transient Dynamic Response and Failure of Sandwich Composite Structures under Impact Loading with Fluid Structure Interaction

The objective of this study is to examine the Fluid Structure Interaction (FSI) effect on transient dynamic response and failure of sandwich composite structures under impact loading. The primary sandwich composite used in this study consisted of a 6.35?mm balsa core and a multi-ply symmetrical plain weave 6?oz E-glass skin. Both clamped sandwich composite plates and beams were studied using a uniquely designed vertical drop-weight testing machine. There were three impact conditions on which these experiments focused. The first of these conditions was completely dry (or air surrounded) testing. The second condition was completely water submerged. The final condition was also a water submerged test with air support at the backside of the plates. The tests were conducted sequentially, progressing from a low to high drop height to determine the onset and spread of damage to the sandwich composite when impacted with the test machine. The study showed the FSI effect on sandwich composite structures is very critical such that impact force, strain response, and damage size are generally much greater with FSI under the same impact condition. As a result, damage initiates at much lower impact energy conditions with the effect of FSI. Neglecting to account for FSI effects on sandwich composite structures results in very non-conservative analysis and design. Additionally, it was observed that the damage location changed for sandwich composite beams with the effect of FSI.     

Degenerated shell element with composite implicit time integration scheme for geometric nonlinear analysis

A degenerated shell element with composite implicit time integration scheme is developed in the present paper to solve the geometric nonlinear large deformation and dynamics problems of shell structures. The degenerated shell element is established based on the eight‐node solid element, where the nodal forces, mass matrices, and stiffness matrices are firstly obtained upon virtual velocity principle and then translated to the shell element. The strain field is modified based on the mixed interpolation of tensorial components method to eliminate the shear locking, and the constitutive relation is modified to satisfy the shell assumptions. A simple and practical computational method for nonlinear dynamic response is developed by embedding the composite implicit time integration scheme into the degenerated shell element, where the composite scheme combines the trapezoidal rule with the three‐point backward Euler method. The developed approach can not only keep the momentum and energy conservation and decay the high frequency modes but also lead to a symmetrical stiffness matrix. Numerical results show that the developed degenerated shell element with the composite implicit time integration scheme is capable of solving the geometric nonlinear large deformation and dynamics problems of the shell structures with momentum and energy conservation and/or decay. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust design – A concept for imperfection insensitive composite structures

Robust design is a philosophy that aims to ensure that a structure will be tolerant to unknown variations and imperfections. This is an important consideration as highly optimised critical structures are required to survive unexpected loading and operating conditions. In some ways, robust design appears to be similar to damage tolerant design but its application to aerospace structural design is neither well established nor understood. In order to demonstrate the differences between the two concepts, a stiffened composite panel has been analysed for damage tolerance and robustness properties. Damage tolerance has been studied experimentally with the panel subjected to impact damage. The effect of laminate stacking sequence on the robustness of the panel has been assessed using finite element analysis and a Robust Index applied to quantify the robustness. The differences between designs are discussed together with the possible future directions for robust design applied to aerospace composite structures.     

Transient response of a submerged cylindrical foam core sandwich panel subjected to shock loading

Predicting the dynamic response of submerged vehicles subjected to hydrostatic pressure and underwater shock loading is of great interest to many structural designers and engineers for improving material and configuration design in recent years. In this paper, the finite element method is used to evaluate the dynamic response of a submerged cylindrical foam core sandwich panel subjected to shock loading. The sandwich panel consists of a foam core surrounded by fiber-reinforced laminates. The effect of fluid–structure coupling is included in the finite element analysis whereas the fluid is assumed to be compressible and inviscid. Time histories of circumferential stress for different composite plies are presented in graphical form and the effects of core type on circumferential stress and velocity of stand-off point are also investigated. Additionally, the distribution of pressure in fluid domain and the deformation of cylindrical foam core sandwich panel are estimated. To the best of the authors’ knowledge, the specialized literature addressing the dynamic response of submerged cylindrical foam core sandwich panel to underwater shock loading is rather scanty. This work is likely to fill a gap in the specialized literature on this topic.     

Dynamic response of full-scale sandwich composite structures subject to air-blast loading

Glass-fibre reinforced polymer (GFRP) sandwich structures (1.6 m × 1.3 m) were subject to 30 kg charges of C4 explosive at stand-off distances 8–14 m. Experiments provide detailed data for sandwich panel response, which are often used in civil and military structures, where air-blast loading represents a serious threat. High-speed photography, with digital image correlation (DIC), was employed to monitor the deformation of these structures during the blasts. Failure mechanisms were revealed in the DIC data, confirmed in post-test sectioning. The experimental data provides for the development of analytical and computational models. Moreover, it underlines the importance of support boundary conditions with regards to blast mitigation. These findings were analysed further in finite element simulations, where boundary stiffness was, as expected, shown to strongly influence the panel deformation. In-depth parametric studies are ongoing to establish the hierarchy of the various factors that influence the blast response of sandwich composite structures.     

Configuration design of a lightweight torpedo subjected to an underwater explosion

The response of a lightweight torpedo when subjected to an underwater explosion (UNDEX) is an important criterion for multidisciplinary design. This paper investigates the effect of structural stiffeners on the performance of a lightweight torpedo. The finite element package ABAQUS was used to model the UNDEX and the fluid–structure interaction (FSI) phenomena, which are critical for accurate evaluation of torpedo stress levels. The pressure wave resulting from an underwater explosion was modeled using similitude relations and it was assumed to be a spherical wave. Various explosive weights and explosion distances were explored to determine the critical distance both for an un-stiffened and a stiffened torpedo. Once it was established that the stiffened torpedo performed better under explosive pressure loads, various configurations were studied to determine the optimal number of ring and longitudinal stiffeners. A final configuration was obtained for the torpedo that had minimum weight and was least sensitive to small manufacturing variations in the dimensions of the stiffeners. This paper presents details of the torpedo and fluid models and the finite element analysis method for FSI.     

Study of filament wound grid-stiffened composite cylindrical structures

Grid-stiffened composite structures are known for their very high efficiency under compressive loading environment. The grid of stiffening ribs is the primary feature in these structures and filament winding is employed as the most convenient manufacturing technique. Three different types of circular cylindrical structures – unstiffened shell (with skin only), lattice cylinder (with ribs only) and grid-stiffened shell (with skin and ribs) – are considered for experimental study and a series of these structures have been manufactured adopting a simplified and cheap manufacturing process. Different aspects of manufacturing that include tooling and other processing aspects are presented in this paper. Axial compression tests have been carried out and the results are compared with finite element analysis. Based on the test results and comparison with finite element analysis, conclusions are drawn on the efficacies of this relatively new class of structures.     

复合材料层合板非线性系统随机振动的样条有限元分析

工程结构中的复合材料的几何参数往往具有随机性质,如何研究随机参数非线性系统的随机响应及统计特性,对结构的可靠性设计和优化设计有着非常重要的意义。应用摄动法、随机中心差分法和线化和校正法,建立了复合材料非线性系统的振动方程和计算模型,采用样条有限元法研究了复合材料层合板具有随机参数的非线性系统在确定性荷载下的随机响应,数值算例说明了本算法的正确性。     

GBT formulation to analyse the buckling behaviour of FRP composite open-section thin-walled columns

This paper presents a Generalised Beam Theory (GBT) formulation to analyse the local and global buckling behaviour of FRP (fibre-reinforced polymer) composite thin-walled columns with arbitrary open cross-sections, which takes into account both shear deformation and cross-section deformation effects. After describing the steps and procedures involved in performing the GBT cross-section analysis of an arbitrarily branched composite (laminate plate) thin-walled member, the paper addresses the numerical implementation of the proposed GBT formulation, carried out by means of the finite element method (GBT-based beam element) – particular attention is devoted to the derivation of the element linear and geometric stiffness matrices, which incorporate all the material coupling effects. In order to illustrate the application and capabilities of the proposed formulation and implementation, several numerical results are presented and discussed, dealing with the local and global buckling behaviour of FRP composite I-section columns with different ply orientations and stacking sequences. Taking advantage of the GBT modal features, deep insight is acquired on the complex composite member buckling mechanics, namely those involving bending–torsion or global–local coupling effects. In particular, one investigates the influence of (i) the constitutive assumption regarding the transverse extension occurring in the cross-section composite walls and (ii) the distribution of pre-buckling normal stresses (due to axial compression) on the buckling behaviour of I-section columns. For validation purposes, the above results are compared with values recently reported in the literature and estimates obtained from shell finite element analyses.     

A micromechanical characterization of angular bidirectional fibrous composites

A micromechanical numerical algorithm to efficiently determine the homogenized elastic properties of bidirectional fibrous composites is presented. A repeating unit cell (RUC) based on a pre-determined bidirectional fiber packing is assumed to represent the microstructure of the composite. For angular bidirectional fiber distribution, the symmetry lines define a parallelepiped unit cell, representing the periodic microstructure of an angular bidirectional fiber composite. The lines of symmetry extrude a volume to capture a three dimensional unit cell. Finite element analysis of this unit cell under six possible independent loading conditions is carried out to study and quantify the homogenized mechanical property of the cell. A volume averaging scheme is implemented to determine the average response as a function of loading in terms of stresses and strains. The individual elastic properties of the constituents’ materials, as well as, the composite can be assumed to be completely isotropic to completely anisotropic. The output of the analysis can determine this degree. The logic behind the selection of the unit cell and the implementation of the periodic boundary conditions as well as the constraints are presented. To verify this micromechanics algorithm, the results for four composites are presented. The results in this paper are mainly focused on the impact of the fiber cross angles on the stiffness properties of the composites chosen. The accuracy of the results from this micromechanics modeling procedure has been compared with the stiffness/compliance solutions from lamination theory. The methodology is to be accurate and efficient to the extent that periodicity of the composite material is maintained. In addition, the results will show the impact of fiber volume fraction on the material properties of the composite. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis.     

Partitioned vibration analysis of internal fluid‐structure interaction problems

A partitioned, continuum‐based, internal fluid–structure interaction (FSI) formulation is developed for modeling combined sloshing, acoustic waves, and the presence of an initial pressurized state. The present formulation and its computer implementation use the method of localized Lagrange multipliers to treat both matching and non‐matching interfaces. It is shown that, with the context of continuum Lagrangian kinematics, the fluid sloshing and acoustic stiffness terms originate from an initial pressure term akin to that responsible for geometric stiffness effects in solid mechanics. The present formulation is applicable to both linearized vibration analysis and nonlinear FSI transient analysis provided that a convected kinematics is adopted for updating the mesh geometry in a finite element discretization. Numerical examples illustrate the capability of the present procedure for solving coupled vibration and nonlinear sloshing problems. Copyright © 2012 John Wiley & Sons, Ltd.     

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。     

The use of Monte Carlo techniques in statistical finite element methods for the determination of the structural behaviour of composite materials structural components

The main purpose of this paper is to develop an alternative approach to the classical deterministic design to account for uncertainties encountered during design, construction and lifetime of structures. This approach is based on the use of statistical tools in material characterisation and structural design by means of the finite element method combined with Monte Carlo techniques. In the first instance, the mechanical behaviour of different materials, including composite materials, is characterised by means of stochastic tools. A procedure based on the combination of various methods for estimating distribution parameters has been set up to ensure correct estimation. The second part of the paper focuses on the finite element modelling of structures combined with Monte Carlo simulation to deal with the stochastic aspects of the input parameters (material properties, structure geometry and loading conditions) and determine the probability distribution characterising the structural response.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.     

船用长方体形空气弹簧隔振器刚度特性

长方体形空气弹簧因其结构特点可以通过改变特性参数和工况获得理想的垂向和横向刚度比,从而可以更好地满足工程应用的要求。综合考虑橡胶-帘布复合材料的材料非线性、大变形过程中的几何非线性以及基座刚性板与胶囊柔性体之间的接触非线性,建立长方体形空气弹簧的有限元模型,分别计算并绘制在不同的初始工作气压、气体容积、帘线层数以及帘线角度下空气弹簧的垂向与横向刚度特性曲线,并研究这些因素对其刚度特性的影响。最后,通过试验证明有限元分析结果的可靠性。     

Thermal-Cyclic Fatigue Life Analysis and Reliability Estimation of a FCCSP based on Probabilistic Design Concept

To study the fatigue reliability of a flip-chip chip scale package (FCCSP) subject to thermal cyclic loading, a Monte Carlo simulation-based parametric study is carried out in the present study. A refined procedure as compared with the recently released Probabilistic Design System (PDS) of ANSYS is proposed and employed in particular. The thermal-cyclic fatigue life of the package is discussed in detail since it is related directly to the reliability of the package. In consideration of the analytical procedure as well as real manufacturing processes, a few geometric dimensions and material properties of the package are assumed random. The empirical parameters used in the fatigue life prediction formula are also assumed random to account for their uncertainties. Numerical calculation is performed following the standard finite element analysis procedure. The result indicates that PDS can indeed be employed to find the cumulative thermal-cyclic fatigue life distribution of the electronic package owing to various uncertainties. The proposed refined design procedure can further improve the accuracy of the quantitative reliability estimation.