Effects of multiple blade interaction on the containment of blade fragments during a rotor failure

A finite element analysis is used to study the impact and the containment aspects of rotor blade fragments that are produced during a aircraft jet engine rotor failure. The impact and containment studies are performed on a ring-type containment structure and various fragment types are considered in this study. For each type of fragment, the ring thickness is varied incrementally and the ring response, residual kinetic energy level of the fragments, magnitude of impact forces and the overall containment or failure are determined. First, only a single fragment is considered and the rotor is assumed to contain no other blades. Next, the remaining blades are introduced and the effects of multiple collisions with the other blades on the containment are analyzed. The explicit, nonlinear finite element code Dyna3d is used for the numerical computations in this study and the results are compared with the experimental results performed on a T58 rotor at the spin facility of the Naval Air Propulsion Test Center.     

Material model based on NURBS response surfaces

The development of new and complex models is typically required to gain an understanding of advanced materials and structures. The accuracy of a structural response obtained from finite element analysis is highly dependent on the extent to which a material model represents actual material behavior. This study proposes the application of rational surfaces to provide a smooth response surface for membrane material behavior. Constitutive material tensor is calculated by using the derivatives of rational surfaces. The surfaces possess two axes of strain and an axis of stress. The methodology is validated based on classical hyperelastic models. A set of results from an aluminum testing program illustrates the response surface construction procedure from the test results. The results indicate that it is easy to implement an extension of finite element codes to include the response surface approach based on NURBS.     

Finite element analysis of multi-particle impact on erosion in abrasive water jet machining of titanium alloy

Abrasive water jets (AWJs) are finding growing applications for machining a wide range of difficult-to-machine materials such as titanium alloys, stainless steel, metal matrix and fibre reinforced composites, etc. Current applications of AWJs include machining of Titanium alloys for aircraft components and bio-medical implants to removal of aircraft engine coatings. This paper presents the application of an elasto-plastic model based explicit finite element analysis (FEA) to model the erosion behaviour in abrasive water jet machining (AWJM). The novelty of this work includes FE modelling of the effect of multiple (twenty) particle impact on erosion of Grade 5 Titanium alloy (Ti-6Al-4V). The influence of abrasive particle impact angle and velocity on the crater sphericity and depth, and erosion rate has been investigated. The FE model has been validated for stainless steel and yields largely improved results. Further, the same FEA approach has been extended to model the multi-particle impact erosion behaviour of Titanium alloy.     

An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures北大核心CSCD

由于具有高比强、高比刚度等优点,多孔结构在土木工程、机械工程和航天航空工程等领域得到了广泛应用.在随机动力荷载作用下多孔结构的随机响应分析是值得关注的研究方向之一.采用多尺度渐近均匀化法,推导了周期性多孔结构动力问题的多尺度控制微分方程,并建立了多孔结构宏观和细观动力响应的时域显式表达式.在此基础上,结合结构随机振动时域显式法,实现了非平稳随机激励下多孔结构动力响应统计矩的计算.所提出的渐近均匀化-时域显式法,一方面可以发挥多尺度动力分析渐近均匀化法的计算优势,高效建立多孔结构宏观和细观动力响应的时域显式表达式;另一方面也可以利用随机振动时域显式法的计算特点,快速精确地求解非平稳随机激励下多孔结构的随机振动问题.通过数值算例,验证了所提方法在多孔结构非平稳随机振动问题求解中的计算精度和计算效率.     

颗粒弥散增强型核辐射屏蔽材料强度模型研究

基于微观力学的均匀化理论,旨在从核辐射屏蔽材料的微观结构、物理特性的角度出发,通过多尺度方法研究了材料宏观的机械力学性质.主要研究对象为颗粒弥散增强的孔隙基体材料,推导出了此类复合材料（金属基材料、非金属类材料）的强度准则模型,可预测微观孔隙率与颗粒相体积分数对材料宏观强度的影响.在塑性极限分析法的理论框架下,在介观上成功引入了速度场跳动来描述两相界面间的力学特性,利用刚性核的球体胞元模型进行求解.最后,选用了界面速度为0的速度场对模型进行研究,并初步探讨了界面效应对材料性能的影响.     

Multiaxial constitutive modeling of aircraft engine materials

Based on a newly developed theory (Lu and Weng, Acta Mech., in press) the high temperature behavior of an aircraft engine material is studied under combined stress state. Both monotonic and cyclic deformations are examined to uncover its stress-strain response, as well as its cyclic hardening and strain-ratchetting characteristics. Under a biaxial loading it is disclosed that tensile cyclic hardening is greatly magnified with a superimposed lateral tension, whereas the strain-ratchetting process is led to an enhanced, unsettling state with a superimposed lateral compression. The biaxial transient and steady-state creep strains have also been calculated. The results suggest that while a superimposed lateral tension will inhibit the creep deformation, a lateral compression can greatly promote the inelastic flow. To reflect the practical service conditions of an aircraft engine, the theory is further applied to examine the effect of loading frequency on the development of inelastic strains under concurrent thermal and mechanical loading. It is found that a more frequently flying aircraft will have a greater accumulation of creep strains and, consequently, a greater possibility of material damage in its engine components over the same total flying time.     

An extended sequential limit analysis based on moving coordinates for pressurized spherical cap membranes with large shape change

Sequential limit analysis (SLA) is an effective and normally used method to calculate the plastic limit load of structures with large deformation. However, attribute to the assumption of neglecting the changing behavior of shape and plane stress direction, the conventional SLA method would be inaccurate in the plastic response prediction for the large-shape-change structures, especially for the pressurized spherical cap. This research develops a novel analytical model for the pressurized spherical cap based on the advanced SLA method, which features introducing the moving coordinate system and considering of the changing behavior of shape and plane stress direction into the conventional method. With the proposed method, the effects of geometry and material parameters on the plastic limit load are analyzed. Compared with the validating FE simulation results of ABAQUS software, the newly extended SLA method performances a more precise prediction of the load deflection response and plastic limit load than the normal one. Due to the limit yield degree and bending moment, the accuracy of the new model will increase with the increase of yield strength and radius. The larger the initial deflection of the pressurized spherical cap is, the smaller the relative error between the analysis results of advanced SLA and FE method is. Moreover, this newly proposed SLA remains effective and accurate within a wide range of the initial thickness-curvature radius ratio, especially for low elasticity modulus materials.     

Use of composite materials in airframes

One of the most promising ways of tackling the problems of cushioning the response of an aircraft under dynamic and shock influences and reducing aerothermoelastic strains is examined. This is the use of composite materials in the airframe and engine. The characteristics of the composites most developed at the present time and of ordinary construction materials are compared. Examples are given of the use of modern composites in aircraft and their engines.Professor N. E. Zhukovskii Moscow Air Force Engineering Academy. Translated from Mekhanika Polimerov, No. 1, pp. 105–112, January–February, 1972.     

Mathematical modelling of the stochastic mechanical properties of wood and its extensibility at small scales

This paper investigates the relation between the uncertain mechanical properties of wood and its extensibility at the ultrastructural scale. A statistical approximation to the output of a multi-scale constitutive model is adopted to predict the extensibility of wood in the presence of parametric uncertainty. By means of this procedure, a very large number of computationally intensive fully-coupled multi-scale simulations are avoided. Following this approach, four different micromechanical parameters are chosen to assess their influence on the extensibility of the material under tensile loading conditions. These are the degree of cellulose crystallinity, the ultimate strain and Young’s modulus of the hemicellulose–lignin matrix, and the thickness of the amorphous cellulose layer which covers the periodic crystalline portions of cellulose. We believe that a better understanding of the mechanisms of deformation and extensibility in wood and in natural materials can pave the way for the development of new strategies to design more advanced materials in engineering structures.     

Optimization in aircraft engineering including approximate structural evaluations by support vector machines

The minimum weight design of structures made of fiber reinforced composite materials leads to a class of mixed‐integer optimization problems for which evolutionary algorithms (EA) are well suited. Based on these algorithms the optimization tool package GEOPS has been developed at TU Dresden. For each design generated by an EA the structural response has to be evaluated. This is often based on a finite element analysis which results in a high computational complexity for each single design. Typical runs of EA require the evaluation of thousands of designs. Thus, an efficient approximation of the structural response could improve the performance considerably. To achieve this aim the constraints on the structural response are approximated by means of support vector machines (SVM). It is trained by means of exact structural evaluations for selected design alternatives only. Several ways to enhance the efficiency of such an optimization procedure are presented. As an example for a typical aircraft structure, a stiffened composite panel under compressive and shear loading is considered. The SVM is trained on geometrical and material data. Representing the design space of composite panels by ABD matrices turned out to be a valuable means for obtaining well trained SVMs. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

飞机退役时限及补充数量的预测研究

飞机的退役是航空装备管理中的重要问题之一.为科学合理地确定飞机退役时限,针对部队飞机使用情况,以某型飞机为例,对飞机的剩余寿命进行详细分析,应用统计学方法,探讨了飞机退役时限和数量的变化规律,在此基础上建立了飞机补充数量预测模型.并结合空军装备发展的实际,对飞机使用过程中的更新换代问题进行了探讨.     

Diffusions in random environment and ballistic behavior

In this article we investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T^′) of the discrete setting, cf. [A.-S. Sznitman, On a class of transient random walks in random environment, Ann. Probab. 29 (2) (2001) 723–764; A.-S. Sznitman, An effective criterion for ballistic behavior of random walks in random environment, Probab. Theory Related Fields 122 (4) (2002) 509–544], that imply, when d2, a law of large numbers with non-vanishing limiting velocity (which we refer to as ‘ballistic behavior’) and a central limit theorem with non-degenerate covariance matrix. As an application of our results, we consider the class of diffusions where the diffusion matrix is the identity, and give a concrete criterion on the drift term under which the diffusion in random environment exhibits ballistic behavior. This criterion provides examples of diffusions in random environment with ballistic behavior, beyond what was previously known.     

Resistance of three-layered structures to static and cyclic bending

Conclusions The above studies of two types of three-layer structural elements showed that the types have different resistances to static deformation in bending. Regardless of the materials, the use of structures which are symmetrical in regard to stiffness makes it possible to obtain a stiffness and strength for the structure which are 10–15% lower than the stiffness and strength of the external plates if the thickness of the latter does not account for more than 25% of the thickness of the structure. This finding, in turn, permits a substantial reduction in the weight of the structure by the use of a lower-density material for the internal layer. Resistance to static bending is determined mainly by the resistance of the structure to shear stresses. The mechanism of fatigue fracture differs appreciably from the fracture mechanism in static deformation. Regardless of the thickness of the structural elements, fatigue fracture for both types of structure occurs as a result of the acting normal compressive stresses. The endurance limit of the hybrid structure is determined by the fatigue resistance of the external layers, and its value is nearly equal to the resistance of the pure materials.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 878–882, September–October, 1986.     

On Stability of a Thin‐Walled Shaft with Active Piezoelectric Fibers

The paper is concerned with the problem of active stabilisation of a rotating flexible shaft made of a composite material containing piezoelectric fibers being controllable by the applied electric field. Rotating shafts exhibit fluttertype instability while exceeding the critical angular velocity. The factor responsible for the loss of stability is internal friction present in the material of the shaft. In the case of a composite structure the internal friction is increased in comparison with steel shafts, and so is the susceptibility of the laminated shaft to self‐excitation. In the paper a method of stabilisation, i.e. shifting the critical threshold towards greater rotation speeds, possibly outside the operating range, is presented. The method is based on incorporation of piezoceramic fibers embedded into the host structure of the shaft. Such integral materials, reflecting the concept of a polymer matrix reinforced with active fibers, are known as Piezoelectric Fiber Composites (PFCs). The carried out examinations have proved that the method is efficient, however limited. It is shown that the critical rotation speed can be increased by several percents, but only within a certain range of structural parameters of the considered system.     

Multimaterial Lattice Structures With Thermally Programmable Mechanical Behaviors北大核心CSCD

传统的点阵结构一旦制备完成,其力学性能通常在使用寿命内保持不变。设计和制造具有环境适应特性的智能点阵结构,可编程地感知和响应外界变化(例如光强、压强、溶液、温度、电磁场、电化学激励),并在时间和空间上进行形状重构、模式转换和性能调控,仍然是人造材料研究领域重要的科学挑战。该文采用具有不同玻璃化转变温度和温度依赖性的多种聚合物材料,通过合理设计材料空间分布,提出了一类具有热可编程力学响应能力的多材料点阵结构。结合理论分析和有限元模拟,研究了组分材料相对刚度对多材料点阵结构的Poisson比、变形模式以及结构稳定性的影响。通过温度变化实现了对多材料点阵结构弹性常数、压溃响应和结构稳定性的调控,使多材料点阵结构表现出极大的热变形、超弹性和形状记忆效应。为设计和制造自适应保护装备、生物医学设备、航空航天领域的变形结构、柔性电子设备、自组装结构和可变形软体机器人等开辟了新途径。     

Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters

Based on interval mathematical theory, the interval analysis method for the sensitivity analysis of the structure is advanced in this paper. The interval analysis method deals with the upper and lower bounds on eigenvalues of structures with uncertain-but-bounded (or interval) parameters. The stiffness matrix and the mass matrix of the structure, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. In terms of structural parameters, the stiffness matrix and the mass matrix take the non-negative decomposition. By means of interval extension, the generalized interval eigenvalue problem of structures with uncertain-but-bounded parameters can be divided into two generalized eigenvalue problems of a pair of real symmetric matrix pair by the real analysis method. Unlike normal sensitivity analysis method, the interval analysis method obtains informations on the response of structures with structural parameters (or design variables) changing and without any partial differential operation. Low computational effort and wide application rang are the characteristic of the proposed method. Two illustrative numerical examples illustrate the efficiency of the interval analysis.     

Vibration analysis of rectangular plates coupled with fluid

The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders’ shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli’s equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.     

Nondestructive Evaluation of One-Dimensional Periodic Structures by Transmission of Laser-Excited Wide-Band Acoustic Pulses

The propagation of ultrasound in a one-dimensional model and actual periodic structures (PSs) is studied experimentally by the method of optoacoustic spectroscopy based on the laser thermooptical excitation and wide-band piezodetection of short acoustic pulses. It is shown that the ultrasound transmission spectrum of a PS has stop and pass bands, and the greater the number of layers in the PSs, the deeper the stop bands. The case where the thickness, density, and ultrasound velocity of one or several layers in the PS are modified is studied in detail. In this case, a narrow local maximum of ultrasound transmission appears in the stop band, whose location depends considerably on the position of the defective layer in the PS. The experimental data obtained coincide well with the theoretical calculation. The nondestructive evaluation of actual PSs consisting of two epoxy-glued identical aluminum plates is carried out by the optoacoustic method. Such materials are widely used in aircraft industry. It is shown that the ultrasound transmission spectrum for these materials depends considerably on the thickness of the epoxy-glue layer.     

Analysis of Micro- and Macro-Instability Phenomena in Computational Homogenization of Finite Electro-Statics

Dielectric materials such as electro-active polymers (EAPs) belong to the class of functional materials which are used in advanced industrial environments as sensors or actuators and in other innovative fields of research. Driven by Coulomb-type electrostatic forces EAPs are theoretically able to withstand deformations of several hundred percents. However, large actuation fields and different types of instabilities prohibit the ascend of these materials. One distinguishes between global structural instabilities such as buckling and wrinkling of EAP devices, and local material instabilities such as limit- and bifurcation-points in the constitutive response. We outline variational-based stability criteria in finite electro-elastostatics and design algorithms for accompanying stability checks in typical finite element computations. These accompanying stability checks are embedded into a computational homogenization framework to predict the macroscopic overall response and onset of local material instability of particle filled composite materials. Application and validation of the suggested method is demonstrated by representative model problems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational Treatment and Stability Analysis of Coupled Electro-Mechanics

Dielectric materials such as electro-active polymers (EAPs) belong to the class of functional materials which are used in advanced industrial environments as sensors or actuators and in other innovative fields of research. Driven by Coulomb-type electrostatic forces EAPs are theoretically able to withstand deformations of several hundred percents. However, large actuation fields and different types of instabilities prohibit the ascend of these materials. One distinguishes between global structural instabilities such as buckling and wrinkling of EAP devices, and local material instabilities such as limit- and bifurcation-points in the constitutive response. We outline variational-based stability criteria in finite electro-elastostatics and design algorithms for accompanying stability checks in typical finite element computations. These accompanying stability checks are embedded into a computational homogenization framework to predict the macroscopic overall response and onset of local material instability of particle filled composite materials. Application and validation of the suggested method is demonstrated by a representative model problem. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)