Development of robust finite elements for general purpose structural analysis

The finite element method emerged out of the old work and energy methods and matrix structural analysis to become a numerical procedure to solve practical stress analysis problems in solid and structural mechanics. With the impetus given by the rapid development of computer technology, it became the most overwhelmingly popular analysis and design computational tool for a very wide spectrum of engineering science, e.g. fluid mechanics, heat transfer and electro-magnetics. Today, there are very powerful general-purpose software codes that make analyses and design tasks that were once considered to be intractable, routinely simple. Many of these are closely held proprietary codes owned and used in-house by large engineering firms or sold or licensed and supported by specialist companies. (Recent estimates indicate that the market for these codes has reached a turnover of a billion dollars and that industries and institutions spend several tens of billions of dollars in running such codes.) These codes are rarely given out in source code. In order to have an in-house code that could be continuously up-graded and enhanced, NAL initiated some work to develop a medium-sized general purpose code (about 20,000 lines of FORTRAN code) for the analysis of laminated composite structures (FEPACS - finite element package for analysis of composite structures), recognising the importance that laminated composites were assuming in aerospace structural technology. Several key elements commonly found in general purpose packages (GPP) used by the aerospace, automobile and mechanical engineering industries were identified. These were re-designed incorporating anisotropic composite capabilities and validated. Many hurdles were faced during this task and required an examination of the basic issues at a paradigmatic level. Concepts such as consistency and variational correctness were introduced and studied critically. These guidelines played a critical role in developing robust versions of the elements and are briefly covered in this review. The paradigms also helped to identify procedures to performa priori error estimates for the quality of approximation and this allowed the elements being developed to be critically validated. The article concludes with a summary of what has been achieved and also suggests areas where the concepts can be applied fruitfully in the study of the displacement type finite element method.     

周期性复合材料等效传热系数预测的渐进均匀化新算法及其实现

渐进均匀化方法具有严格的数学基础,预测周期性复合材料的等效热传导系数具有较高的计算精度。本文提出了基于渐进均匀化方法预测周期性复合材料等效热传导系数的新算法。相比原有的算法具有两个优点：它的实现与代表体元方法一样简单,新的算法以现有的有限元商业软件为黑箱,通过简单的几个分析步骤,即可以获得复合材料的等效热传导系数;可以利用商业软件提供的多种单元类型去离散同一个单胞,在处理复杂几何单胞结构时,可以节约大量的计算费用。通过几个典型的算例,验证了方法的有效性。该工作对于推广渐进均匀化方法在预测复合材料等效热传导系数的广泛应用具有积极作用。     

Influence of the constitutive characteristics of resins on the composite materials delamination

This paper discusses the problem of interlaminar delamination in composite materials, with particular attention focused on the important role played by the resin properties. A Double Cantilever Beam (DCB) specimen has been modelled for finite element analysis assuming that the crack is situated inside a thin pure resin layer, similarly to the models proposed by Ozdil and Crews. A test program on the epoxy resin EPON 828, a typical resin commonly used for advanced composite systems for aerospace applications, has been carried out, in order to evaluate the mechanical properties; the results have shown a non-linear elastic behaviour without hysteresis effect. The non-linear relationship has been introduced in the bidimensional finite element model for the DCB specimen analysis. The stress and strain fields are used for the evaluation of the Energy Release Rate by means of a numerical model, based on an energetic approach such as the J-integral of Rice. The results show a considerable dependence on the constitutive relationship and give the opportunity of a more accurate evaluation of the toughness for experimental results from DCB specimen.     

A boundary element analysis of metal matrix composite materials

The numerical modelling of metal matrix composites is an important part of the research now being conducted on these materials. Due to the numerical complexity of a fully three-dimensional analysis, two-dimensional approximations are normally used with finite element methods. While these analyses are informative, they cannot treat complex particle shapes or examine three-dimensional effects in the composite. The use of boundary element methods in place of the more widely used finite element methods significantly reduces the computing power necessary to obtain a solution to a given problem, making it possible to simulate fully three-dimensional geometries. In the present paper a two-dimensional form of the BEM is applied to the study of metal matrix composite materials, and its performance compared with that of similar FEM stadies. We also compare the predicted composite properties with existing and new experimental results. We conclude that the BEM is an effective tool for the analysis of this class of problems.     

Frictional contact analysis of composite materials

In this paper, the highly non-linear frictional contact problems of composite materials are analysed. A proportional loading, the potential contact zone method and finite element analysis are used to solve the problems. A tree-like searching method is used to obtain the solution of the parametric linear complementary problem, which may overcome the anisotropic properties of contact equations caused by composite materials. In the frictional contact analysis of composite materials, the distributions of normal contact pressures, tangential contact stresses and relative tangential displacements are presented for different contact material systems and different coefficients of friction. The results show that the solutions in the paper have good agreement with Hertzian solutions. The influence of different contact material systems and different coefficients of friction on the contact stresses and displacements is large. As a numerical example, ball-indentation tests of composite materials are modelled by the three-dimensional finite element method.     

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.     

复合材料层合板分层损伤数值模拟方法研究现状

复合材料层合板在航空航天等领域受到广泛应用,分层损伤作为复合材料层合板主要的损伤形式,对复合材料结构的强度和刚度有显著的影响,是限制其重大工程应用的热点问题之一.通过实验的方法对复合材料结构进行研究,往往需要耗费大量的时间和成本,成熟的有限元数值模拟技术可以较低成本实现复合材料结构的分层行为模拟,成为分层损伤研究的重要...     

A three-constituent multicontinuum theory for woven fabric composite materials

Multicontinuum theory (MCT) refers to the use of phase averaged constituent stress/strain fields for predicting failure in composite structural analysis. Given the composite material mechanical properties as well as those of the constituents, well known closed form algebraic expressions exist to decompose the composite stress/strain fields down to the constituent level. Recent research indicates constituent based failure algorithms show a great deal of promise in predicting material failure when coupled to nonlinear finite element codes. A limitation of MCT is that the traditional constituent decomposition is only valid for materials composed of two constituents. In this paper, the MCT decomposition is generalized to handle composite materials composed of three constituents. The application of interest is a woven fabric composite material. The three constituents consist of the warp bundles, fill bundles, and pure matrix pockets. Numerical results are presented for the proposed three-constituent decomposition and are shown to be in good agreement with phase averaged stresses obtained from direct volume averaging of finite element micromechanics models.     

Numerical prediction of damage in composite structures from soft body impacts

The paper summarises recent progress on materials modelling and numerical simulation of soft body impact damage in fibre reinforced composite aircraft structures. The work is based on the application of finite element (FE) analysis codes to simulate damage in composite shell structures under impact loads. Composites ply damage models and interply delamination models have been developed and implemented in commercial explicit FE codes. Models are discussed for predicting impact loads on aircraft structures arising from deformable soft bodies such as gelatine (synthetic bird) and ice (hailstone). The composites failure models and code developments are briefly summarised and applied in the paper to numerical simulation of synthetic bird impact on idealised composite aircraft structures.     

Buckling Analysis of Laminated Composite Plates Using Higher Order Semi—Analytical Finite Strip Method

Rectangular plates made of laminated composite material because of the advantageously high strength and stiffness to weight ratio are used frequently as structural component in various branches of engineering, chief of which are aerospace and marine engineering. Design concepts of these plates that lead to the increase in the buckling load can directly lower the structural cost and/or weight. The finite strip method is one of a number of procedures which can be used to solve the buckling problem of plate structures. In the present work the main concern is with the buckling behavior of plates with simply supported ends subjected to uni-axial pure compression loads. The solution is sought by implementing the higher order semi-analytical finite strip method which incorporates additional degrees of freedom for each nodal line by using Reddy’s higher order plate theory. Therefore the current method is more universal in dealing with different plate thicknesses. In addition, in this semi-analytical finite strip method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The solution is based on the concept of principle of minimum potential energy and an eigen-value analysis is subsequently carried out. From the presented results it can be concluded that the higher order semi-analytical finite strip method is very reliable for the preliminary design of composite plates especially in the case of buckling analysis of relatively thick plates.     

基于分布式计算的复合材料机翼优化设计

将遗传算法与高精度的通用有限元分析软件相结合, 并将其应用于复合材料机翼满足气动弹性要求的优化设计中。为了提高采用遗传算法的复合材料机翼优化设计的效率, 探讨了将分布式计算与遗传算法进行集成, 形成了基于分布式计算和遗传算法的复合材料机翼优化设计方法, 并应用该方法解决某大展弦比复合材料机翼副翼和舵面操纵反效问题。计算结果表明, 该方法可用于解决工程上复杂结构优化问题。      

A FEM/BEM for axisymmetric electromagnetic and thermal modelling of induction furnaces

In this paper, we propose a numerical method to solve a mathematical model for axisymmetric induction furnaces used for melting materials like metals or silicon. A finite/boundary element method (FEM/BEM) is introduced to solve the eddy current problem giving the electromagnetic field. In order to solve the non‐linear heat transfer problem involving change of state, we use an enthalpy formulation and propose an iterative algorithm to solve the corresponding finite element approximation. Numerical results for an industrial induction heating system are presented. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimization of the Inspection of Large Composite Materials Using Robotized Line Scan Thermography

The emergence of composite materials has started a revolution in the aerospace industry. When using composite materials, it is possible to design larger and lighter components. However, due to their anisotropy, composite materials are usually difficult to inspect and detecting internal defects is a challenge. Line scan thermography (LST) is a dynamic thermography technique, which is used to inspect large components of metallic surfaces and composites, commonly used in the aerospace industry. In this paper, the robotized LST technique has been investigated on a large composite component which contains different types of internal defects located at a variety of depths. For theoretical analysis, the LST inspection was simulated using a mathematical formulation based on the 3D heat conduction equation in the transient regime in order to determine the optimum parameters. The solution of the model was performed using the finite element method. The LST parameters were adjusted to detect the deepest defects in the specimen. In order to validate the numerical results with experimental data, a robotized system in which the infrared camera and the heating source move in tandem, has been employed. From the experimental tests, it was noted that there are three sources of noise (non-uniform heating, unsynchronized frame rate with scanning speed and robot arm vibration) which affect the performance of the test. In this work, image processing techniques that were initially developed to be applied on pulse thermography have been successfully implemented. Finally, the performance of each technique was evaluated using the probability of detection approach.     

Investigations on Buckling Behaviour of Laminated Curved Composite Stiffened Panels

In Industrial applications structural efficiency is primary concern, this brings about the need of strong and lightweight materials. Due to their high specific strength, fibre reinforced polymers find wide application in these areas. Panels made of composite materials are widely used in aerospace structures, automobile, civil, marine and biomedical industries because of their good mechanical properties, impact resistance, excellent damage tolerance and also low fabrication cost. In this Paper, buckling and post-buckling analysis was performed on composite stiffened panel to obtain the critical load and modes of failures, with different parameters like ply-orientation, different composite materials, and stiffeners and by changing the number of stiffeners was derived. To analyze the post buckling behaviour of composite stiffened panels the nonlinear finite element analysis is employed and substantial investigations are undertaken using finite element (FE) model. Effect of critical parameters on buckling behaviour is studied and parametric studies were conducted with analytical tool to understand the structural behaviour in the post buckling range.     

特定弹性性能材料的细观结构设计优化

针对具有特定弹性性质的两相复合材料, 研究了特定性能材料优化设计问题的数学模型,提出了基于形状优化的材料设计方法。该方法利用形状优化技术, 设计两相复合材料的细观结构形式, 以使复合材料具有特定的弹性性质。材料的宏观性质由均匀化方法确定。最后给出了零泊松比材料的设计过程和结果。      

复合材料构件步行车辆的弹性振动分析

复合材料具有高强度-重量比和高刚度-重量比,它用于步行车辆结构设计可减轻相对运动部件的重量,降低能量消耗,抑制弹性振动.本文利用动力学虚功原理建立了具有复合材料构件步行车辆系统的动力学有限元模型,对四足步行车辆模型进行了模拟计算,以说明使用复合材料的优越性.     

Multi-objective Genetic Topological Optimization for Design of Blast Resistant Composites

Composites make it possible to produce materials with properties that are unattainable with single phase materials. This paper examines the use of multi-objective genetic topological optimization to design blast resistant composites. The fundamental problem of the design of a two-layer composite plate that is subjected to blast is considered using the finite element method. Two materials are used to form the microstructure of each layer. The microstructure and thickness of each layer is optimized for the two-layer plate to minimize the weight and stress-to-strength ratio. A set of optimal blast resistant composite microstructures that meet design requirements is demonstrated.     

基于界面单元的复合材料层间损伤分析方法

为了研究复合材料层间损伤, 建立了一种新型零厚度界面单元模型, 可以准确地预测复合材料 Ⅰ 型层间裂纹扩展。模型包括本构关系建立、损伤准则和损伤演化引入, 并在大型商用有限元软件ABAQUS用户单元子程序VUEL中实现, 采用显示积分方法求解, 不存在收敛性问题, 同时允许使用较粗的有限元网格。最后将该模型应用于国产碳纤维增强树脂基复合材料(CCF300/5428)双悬臂梁试验(DCB)模拟分析中, 结果表明, 此界面单元模型能够准确模拟复合材料层板 Ⅰ 型裂纹扩展, 为复合材料层间损伤分析提供了一种有效的方法。     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。     

Analysis of unsymmetric CFRP–metal hybrid laminates for use in adaptive structures

The potential of using multistable composite materials for adaptive structures is currently receiving interest from the aerospace community because they possess more than one single equilibrium configuration. Unsymmetric CFRP laminates are studied which have an inner isotropic metallic layer. These hybrid laminates are studied using analytical, finite element and experimental techniques. The thermal contraction of the isotropic layer upon cool down from cure induces large in-plane thermal loads which act remotely from the laminate’s neutral plane, increasing snap-through moments and out-of-plane displacements. The curvatures of the hybrid laminates can be doubled compared to pure unsymmetric CFRP laminates.