Stress analysis of perforated composite plates

Thin-walled plates and panels of various constructions find wide use as primary structural elements in simple and complex configuration. In aerospace structures, panels with variously shaped cutout are often used. The understanding of the effects of cutout on the load bearing capacity and stress concentration of such plates is very important in designing of complex structures. An analytical investigation is used to study the stress analysis of plates with different central cutout. Particular emphasis is placed on flat square plates subjected to a uni-axial tension load. The results based on analytical solution are compared with the results obtained using finite element methods. The main objective of this study is to demonstrate the accuracy and simplicity of presented analytical solution for stress analysis of composite plates with central cutout. The effect of cutout geometry (circular, square, or special cutouts), material properties (isotropic and orthotropic), fiber angles, and cutout curvature are considered. The results presented herein, indicated that the presented method can be used to determine accurately the stresses and stress concentration in composite plates with special shape cutouts.     

An assessment of buffer strips for reduction of stress concentration at cutouts in composite laminates

A shear lag solution for a hybrid unidirectional buffer strip laminate containing a rectangular cutout is presented. Fiber stresses and displacements in the main panel and buffer strips are given as explicit functions of fiber and matrix properties, and laminate and cutout configurations. Stress concentration factors and laminate ultimate strengths for both soft and stiff buffer strips are presented. A substantial improvement in the notched strength is shown to be possible by using low modulus and high strength fibers for buffer strips. The stress concentration factors for a rectangular cutout are compared with those of a rectilinear crack in a buffer strip laminate.     

Cutout reinforcements for shear loaded laminate and sandwich composite panels

This paper presents the numerical and experimental studies of shear loaded laminated and sandwich carbon/epoxy composite panels with cutouts and reinforcements aiming at reducing the cutout stress concentration and increasing the buckling stability of the panels. The effect of different cutout sizes and the design and materials of cutout reinforcements on the stress and buckling behaviour of the panels are evaluated. For the sandwich panels with a range of cutout size and a constant weight, an optimal ratio of the core to the face thickness has been studied for the maximum buckling stability. The finite element method and an analytical method are employed to perform parametric studies. In both constant stress and constant displacement shear loading conditions, the results are in very good agreement with those obtained from experiment for selected cutout reinforcement cases. Conclusions are drawn on the cutout reinforcement design and improvement of stress concentration and buckling behaviour of shear loaded laminated and sandwich composite panels with cutouts.     

Influence of cut-out hole on multi-layer Kevlar-29/epoxy composite laminated plates

This paper presented the effect of cutout hole on multi layer of Kevlar-29/epoxy composite laminated plates this effect occurred and fiber orientation angle. An experimental procedure was developed to study the performance of these effects under quasi-static compressive and tensile load using a servo-hydraulic testing machine. The work involved investigation on the variety of orientation angles of Kevlar-29 fiber. The ultimate load of failure for each Kevlar-29/epoxy laminated plates had been determined and specified the optimum angle orientation and the load reduction due to the effect of fiber orientation angle (+45°/−45°) was low in the case for compared (0°/90°) orientation angle of fiber. To simulate this problem the researcher used Explicit Mesh for AUTODYN under ANSYS-12.1 software, where the researcher found that the results obtained via this simulation agreed reasonably well with the experimental results and the maximum difference between the experimental conditions and the simulation was 5.8%.     

Engineering design against fracture at stress concentrators

Abstract

Methods for taking into account the effects of stress concentrations in design are described and treatments for analysing fracture and fatigue problems from such regions using fracture-mechanics methods are discussed. Consideration is given to cases when behaviour at the stress concentration remains wholly elastic, and also to cases where yielding occurs. Examples are presented showing the application of fracture-mechanics methods to practical cases representing structural situations.

MST/67     

Two-dimensional strain mapping in model fiber-polymer composites using nanotube Raman sensing

The feasibility of using Raman spectroscopy to map strain fields in model composites is demonstrated by means of two experiments. (1) The mapping of the stress concentration in the vicinity of a break in a strained E-glass fiber, using the Raman spectrum of single-wall nanotubes dispersed in the polymer around the fiber. (2) The mapping of strain using the Raman response of a strained high modulus carbon fiber and, simultaneously, from the surrounding polymer matrix using single-wall nanotubes dispersed in the polymer. The size and shape of the ‘zone of influence’ resulting from the stress concentration effects around the fiber breaks are evaluated in both cases. Model experiments of this type provide fundamental design information about the fiber–matrix stress transfer mechanisms in composites.     

Machinability characteristics evolution of CFRP in a continuum of fiber orientation angles

Circular orthogonal milling tests on unidirectional carbon fiber reinforced polymer (UD-CFRP) laminate disks were conducted to investigate the machinability characteristics evolution in a continuum of fiber orientation angles (β). Experimental results show that surface cavities are the main machined surface damages, which elevate the surface roughness Ra. The surface cavities systematically appear between angles β?=?25° and β?=?75° for down-milling and β?=?20° and β?=?50° for up-milling and their occurrence may not be influenced by the cutting velocity and the feed rate. In the surface cavity region, low-level cutting forces are generated, which is highly correlated with the occurrence of fiber–matrix debonding for both down-milling and up-milling. SEM micrographs show that the formation of the surface cavities is mainly caused by the occurrence and propagation of fiber–matrix debonding, followed by bending-induced fiber fractures and compression-induced fiber fractures. Based on those observations, a novel milling strategy taking the fiber orientation angle into consideration is proposed to avoid the surface cavities; this unique approach provides a new way to milling typical aerospace CFRP laminates with high machined surface quality.     

Stress—Strain state of thin-walled cylinders with a stiffened cutout taking into account physical and geometric nonlinearities

The basic equations and numerical results of investigations of the stress — strain state of a cylinder near a stiffened circular cutout are presented. The influence of nonlinear factors on the stress distribution near the cutout is studied as a function of the stiffness of the stiffeners on the basis of a numerical solution of different variants of nonlinear and linear problems. The most suitable parameters of a stiffening element are determined for a cylinder under prescribed internal pressure.Translated from Problemy Prochnosti, No. 8, pp. 65–71, August, 1993.     

Stress singularity analysis in the restorations of premolar class ii cavities

Abstract

This paper presents the singular stress analysis near the apex of a structure formed during dental restoration of a premolar class II cavity. Based on the elasticity theory, the stresses may go to infinity at the junctions of different materials (e.g. dentine, enamel, restoration materials). Tensions will cause material separation and then material fracture. In order to reduce the failure probability, the degree of stress concentration has to be reduced. The stress singularity order and the stress intensity factor are two parameters, which are often used in fracture analysis. The objective of this paper is to find conditions such that non‐singular stress fields are possible. Three critical positions in the restoration structure are discussed.

They are the tips of interface between (1) enamel and restoration; (2) dentine and restoration; and (3) enamel, dentine and restoration. In the last two cases, the restoration may be bonded or debonded to enamel or dentine. After employing Kolosov‐Muskhelishvili complex functions together with the eigenfunction expansion method, the singularity orders are computed theoretically. Weak stress singularity conditions can be sought by properly selecting cutting angles or restoration materials.     

Buckling analysis of rectangular composite plates with rectangular cutout subjected to linearly varying in-plane loading using fem

A numerical study is carried out using finite element method, to examine the effects of square and rectangular cutout on the buckling behavior of a sixteen ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate [0°/+45°/-45°/90°]_2s, subjected to various linearly varying in-plane compressive loads. Further, this paper addresses the effects of size of square/rectangular cutout, orientation of square/rectangular cutout, plate aspect ratio(a/b), plate length/thickness ratio(a/t), boundary conditions on the buckling bahaviour of symmetrically laminated rectangular composite plates subjected to various linearly varying in-plane compressive loading. It is observed that the various linearly varying in-plane loads and boundary conditions have a substantial influence on buckling strength of rectangular composite plate with square/rectangular cutout.     

A complex potential-variational formulation for thermo-mechanical buckling analysis of flat laminates with an elliptic cutout

A semi-analytical method is developed for pre-buckling and buckling analyses of thin, symmetrically laminated composite panels with an elliptical cutout at an arbitrary location and orientation under general thermo-mechanical loading conditions. Both the pre-buckling and buckling analyses are based on the principle of stationary potential energy utilizing complex potential functions and complete polynomials. The complex potential functions capture the steep stress gradients and local deformations around the cutout, and the “complete” polynomials improve the global buckling response of the laminate. The complex potential functions in the pre-buckling state automatically satisfy the in-plane equilibrium equations, thus reducing the first variation of the total potential energy in terms of line integrals only. Because the complex potential functions for out-of-plane displacements are augmented by the “complete” polynomials, the area integral terms in the second variation of the total potential energy, referred to as the Treftz criterion, are retained in the buckling analysis. The kinematic boundary conditions are idealized by employing extensional and rotational springs (elastic restraints) with appropriate stiffness values. Based on the numerous validation problems, this analysis is proven credible for predicting the buckling load of rectangular and non-rectangular panels with a cutout.     

剪切载荷下含椭圆形大开口层合板的试验研究

在面内纯剪切载荷作用下, 采用试验与有限元模拟方法研究了结构中心设置椭圆形大开口的正方形复合材料层合板的应力/应变集中现象及屈曲、 后屈曲行为, 通过测试结果对试验件失效模式进行了评估。研究结果表明: 层合板开口附近应力/应变集中程度很高; 大尺寸开口使结构稳定性显著降低, 且开口层合板具有较好的后屈曲承载能力; 由于弯曲产生高水平的层间应力, 导致局部分层损伤并伴有基纤剪切破坏; 随着横向挠度的增加, 各应力集中区域的纤维发生拉伸断裂, 导致整体结构瞬间发生脆性失效。有限元模拟结果与试验结果符合较好。     

Improvement of plane stress solutions using adaptive finite elements

Abstract

A finite element method is combined with an adaptive meshing technique to improve the accuracy of the finite element solution. The effectiveness of the combined method is evaluated by a plane stress problem that has an exact solution. The problem is that of a panel with a circular cutout subjected to an applied load. The result demonstrates that the adaptive meshing technique can reduce the numbers of the finite elements, the analysis computational time, and improve the accuracy of the analysis solution.     

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber‐reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three‐dimensional solid approach and first‐order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright © 2012 John Wiley & Sons, Ltd.     

复合材料蒙皮-加筋大开口结构优化设计

采用有限元法对复合材料蒙皮-加筋大开口结构进行了优化设计,研究孔边补强和加筋补强对大开口结构屈曲特 性的影响.结果表明:孔边翻边补强可使应力集中远离孔的自由边,增加翻边深度和宽度皆能提高屈曲载荷;采用共固化加筋要比整体加筋效果明显,同等条件下,优先考虑低而密的筋条布置,同时增加横向筋的数量.     

Dynamic characterization of the thickness-tapered laminated plant fiber-reinforced polymer composite plates

Evolution of the laminated woven natural fiber fabric-reinforced polymer composite structures makes a way to the development of the non-uniform laminated composite structures in order to achieve the stiffness variation throughout the structure. An attempt is made in this work to carry out the experimental and numerical investigations on the dynamic characteristics of the thickness-tapered laminated woven jute/epoxy and woven aloe/epoxy composite plates. The governing differential equations of motion for the thickness-tapered laminated composite plate are developed using the h-p version FEM based on higher order shear deformation theory. The validation of the present finite element formulation is carried out by comparing the natural frequencies obtained using the finite element formulation with those natural frequencies determined experimentally. The developed model is further validated with the available literature works on tapered composite plate to confirm the efficiency of h-p version FEM. This work also explores the study of the vibrational characteristics of composite plates under the influence of plant fiber’s transverse isotropic material characteristics and porosity associated with plant fiber composites through the elastic constants evaluated in the author’s previous work. Also the influences of aspect ratios, ply orientations, and taper angles under various end conditions on the natural frequencies of the woven jute/epoxy composite plate are studied using the present finite element formulation. The forced vibration response of the thickness-tapered laminated woven jute/epoxy composite plate under the harmonic force excitation is carried out considering CFCF and CFFF end conditions.     

正交异性钢桥面构造细节的日照温度次应力分析

为研究正交异性钢桥面板构造细节的日照温度次应力行为,多次在高温和强日照天气下现场实测了某自锚式悬索桥钢箱梁外周和实腹式横隔板上温度场,基于观测到的最大顶底板温差拟合了横隔板竖向温度梯度表达式;在ANSYS中建立了钢箱梁节段有限元模型并施加外周温度,计算其24 h温度场,并与横隔板实测竖向温度的对比校验了温度场模拟的合理性;开展了钢箱梁节段和子模型的精细化热应力分析,得到了纵肋-横隔板和弧形切口共4个构造细节的温度应力时程曲线。研究表明：在强太阳辐射和高温环境下,钢箱梁横向温差不明显,但存在明显的竖向温度梯度,横隔板竖向温度梯度可拟合为四折线形式,最大温差明显小于欧规值。正交异性钢桥面板产生热变形并在构造细节处产生明显热应力集中,特别是弧形切口热应力大。仅日照竖向温度梯度作用,或仅桥面货车通行加载,弧形切口均为无限疲劳寿命;但二者共同作用产生的应力幅,大于构造细节的常幅疲劳极限,可能是该构造细节出现疲劳开裂的原因。     

Capillary effects on flax fibers – Modification and characterization of the wetting dynamics

Introducing bio-based composites has now become an opportunity of development for industry. Accordingly, Liquid Composite Moulding (LCM) processes are increasingly used for manufacturing those composites, mainly in the transportation industry, since they are considered as effective and low cost routes to manufacture bio-based composites fitting high quality requirements, even for parts with complex shape. However observations of a large amount of voids in bio-based composites call for an improved understanding of the local wetting phenomena that occur during impregnation of the natural reinforcements. The purpose of the present work is to study the influence of flax fiber surface chemistry on the local wetting dynamics. Flax reinforcements were submitted to a thermal treatment to modify the chemical composition of fiber surface. In order to analyze the fiber’s wetting behavior, some methods for measuring apparent static contact angles and surface energy were firstly validated on solids of defined geometry, and subsequently applied to untreated and treated flax fibers. The Owens–Wendt’s approach was used to determine both components of apparent surface energy, indicating polar and dispersive interactions in materials. Subsequently dynamic tests were carried out on both types of chopped flax fibers in order to evaluate apparent advancing dynamic contact angles. Considerations about morphological effects have also been included. Finally bio-based composite plates reinforced with untreated and treated flax quasi-UD were simultaneously fabricated by LCM process, and observation of the porosities highlighted some benefits of using treated flax fibers.     

《开孔对矩形板动力性能影响分析》

以超椭圆方程描述开孔边界,利用ANSYS有限元软件,数值分析开孔的形状、面积（尺寸）、位置及转动对典型矩形板前二阶固有频率的影响。研究结果发现开孔能显著改变矩形板的固有频率,其影响效果受板的边界约束条件和开孔形状设计影响很大。实际工程结构中,开孔形状设计应当引起足够的重视。