Fast probabilistic design procedure for axially compressed composite cylinders

A semi-analytic probabilistic procedure is presented that enables a fast prediction of the stochastic distribution of buckling load of cylindrical shells caused by the scattering of geometry, wall-thickness, material properties and loading imperfection. Compared to Monte Carlo simulations the semi-analytic method requires significantly fewer buckling load calculations giving equally accurate results. Knowing the distribution function of buckling load, a level of reliability is chosen and a design load is defined, which is lower than all test results and less conservative than NASA SP-8007.     

Determination of robustness for a stiffened composite structure using stochastic analysis

It is a common practice to only consider the nominal means as input variables for both classical solid mechanics and finite element (FE) analysis problems. A single solution based on the mean values is then used in design. In reality all input variables are stochastic, existing within a range of possible values. Different combinations of these stochastic input variables will lead to differing output responses and the introduction of variability will cause each structure to have a response that deviates from the original specification, sometimes with catastrophic consequences. In this paper two variables, influence and sensitivity, have been identified as parameters affecting structural robustness. Variability and uncertainty in loads, geometry and lamina stiffness are introduced via a stochastic finite element analysis (SFEA) procedure. The procedure is applied to the design of composite yacht hulls comparing the robustness of designs aimed at satisfying a range of performance and cost requirements. It is shown that influence and sensitivity are useful in identifying designs that lead to imperfection tolerant structures.     

Optimum buckling design of composite stiffened panels using ant colony algorithm

Optimal design of laminated composite stiffened panels of symmetric and balanced layup with different number of T-shape stiffeners is investigated and presented. The stiffened panels are simply supported and subjected to uniform biaxial compressive load. In the optimization for the maximum buckling load without weight penalty, the panel skin and the stiffened laminate stacking sequence, thickness and the height of the stiffeners are chosen as design variables. The optimization is carried out by applying an ant colony algorithm (ACA) with the ply contiguous constraint taken into account. The finite strip method is employed in the buckling analysis of the stiffened panels. The results shows that the buckling load increases dramatically with the number of stiffeners at first, and then has only a small improvement after the number of stiffeners reaches a certain value. An optimal layup of the skin and stiffener laminate has also been obtained by using the ACA. The methods presented in this paper should be applicable to the design of stiffened composite panels in similar loading conditions.     

High-order finite elements reduced models for modal analysis of stiffened panels

A method is presented to build reduced (equivalent) models of stiffened panels made of thin-walled composite materials. The technique is developed to be used in the modal analysis of panels and wing boxes, allowing finite element modelling and analysis using a single-type, three-dimensional orthotropic p-element. The use of a single element guarantees speed and flexibility in the (re)modelling of the structure and reduces the modelling and analysis errors connected to finite element analysis in preliminary-design/multidisciplinary-optimization environments. The method is tested on two types of representative wing boxes. Different approaches for the equivalencing are tested and compared to each other. The results show that the equivalent models give results within few percent from those obtained running a full model, saving as much as one order of magnitude in the number of degrees of freedom employed.     

Failure analysis in postbuckled composite T-sections

Blade-stiffened skin designs made of composite materials have the potential to produce highly efficient structures, when the large strength reserves in the postbuckling range are utilised. This paper investigates the failure under postbuckling deformations of T-section specimens cut from a blade-stiffened panel, by comparing experimental results to finite element models. In the experimental work, T-section specimens with a particular lay-up and geometry were tested to failure in antisymmetric and symmetric loading rigs. These loading rigs simulate deformations on skin-stiffener interfaces during panel postbuckling. For the numerical analysis, two-dimensional models of the interface cross-section were used with a strength-based criterion that monitored failure within each ply. The use of a zero-thickness layer of cohesive elements has also been investigated in order to simulate the delamination behaviour. The numerical predictions are compared to the experimental results in terms of the failure load, specimen stiffness and specimen behaviour. The analysis approach is shown to be capable of predicting the critical damage locations and initiation loads for both antisymmetric and symmetric loadings. The successful prediction of failure in skin-stiffener interfaces can be linked to a global-local approach for efficient analysis of large, fuselage-representative composite structures.     

Compressive behaviour of thin-skin stiffened composite panels with a stress raiser

The in-plane compressive behaviour of thin-skin stiffened composite panels with a stress concentrator in the form of an open hole or low velocity impact damage is examined analytically. Drop weight impact in laminated polymer composites causes matrix cracking, delaminations and fibre breakage, which together can seriously degrade the laminate compressive strength. Experimental studies, using ultrasonic C-scan images and X-ray shadow radiography, indicated that the overall damage resembles a hole. Under uniaxial compression loading, 0° fibre microbuckling surrounded by delamination grows laterally (like a crack) from the impact site as the applied load is increased. These local buckled regions continued to propagate, first in discrete increments and then rapidly at failure load. The damage pattern is very similar to that observed in laminated plates with open holes loaded in compression. Because of this resemblance, a fracture mechanics model, developed initially to predict notched compressive strength, was applied to estimate the compression-after-impact (CAI) strength of a stiffened panel; in the analysis the impact damage is replaced with an equivalent open hole. Also, the maximum stress failure criterion is employed to estimate the residual compressive strength of the panel. The unnotched compressive strength of the composite laminate required in the analysis is obtained from a three-dimensional stability theory of deformable bodies. The influence of the stiffener on the compressive strength of the thin-skin panel is examined and included in the analysis. A good agreement between experimental measurements and predicted values for the critical failure load is obtained.     

先进复合材料格栅加筋板的总体稳定性分析

通过建立复合材料格栅结构单元的基本力学假设和分析模型, 推导了一种新的等效刚度计算方法, 用于分析复合材料格栅加筋板的总体稳定性。该方法充分考虑了筋条和面板的相互作用和中面偏移效应, 并具有通用性。结合Rayleigh-Ritz能量近似法, 推导出了求解加筋板总体屈曲载荷的通用特征方程; 分析了多种算例, 并与修正平铺法进行了比较, 结果吻合得很好。      

Damage monitoring of CFRP stiffened panels under compressive load using FBG sensors

FBG sensors were embedded in each of two CFRP stiffened panels fabricated by VaRTM. Low-velocity impacts were applied to one of the panels in order to compare the methods of monitoring impact events using FBG sensors. The main impact damage was an interlaminar delamination inside the skin, which could be observed by an ultrasonic C-scan. A monitoring method using the full spectral signals was more effective in evaluating the impact damages in detail than that using the center wavelength. Following the impact tests, buckling behaviors were investigated under compressive loading using FBG sensors and surface-attached strain gauges. The FBG sensors could evaluate strain changes resulting from buckling behaviors under relatively low compressive loading. They could also evaluate damage growth until the final failure and difference of buckling behaviors between panels with and without impact damages.     

复合材料加筋板屈曲/后屈曲分析的应用

研究了复合材料加筋板翼面结构稳定性问题,分析了加筋板在压缩和剪切等载荷作用下的稳定性安全裕度。利用计算复合材料加筋板屈曲及后屈曲承载能力的方法,验证复杂受载情况下结构的稳定性。验证对象是一个优化后的满足强度、刚度和工艺制造要求的复合材料机翼。该机翼在各种载荷工况下的内力分布情况由MSC.NASTRAN分析得到,通过本文提出的方法得到每块蒙皮的稳定性承载能力。然后给出复合材料层合板在复杂载荷下的屈曲及后屈曲安全裕度的计算准则,验证优化后的机翼加筋板是否满足稳定性设计要求。该方法可作为约束集成到结构优化系统平台中。     

Optimization of composite stiffened panels under mechanical and hygrothermal loads using neural networks and genetic algorithms

The present work develops an optimization procedure for a geometric design of a composite material stiffened panel with conventional stacking sequence using static analysis and hygrothermal effects. The procedure is based on a global approach strategy, composed by two steps: first, the response of the panel is obtained by a neural network system using the results of finite element analyses and, in a second step, a multi-objective optimization problem is solved using a genetic algorithm. The neural network implemented in the first step uses a sub-problem approach which allows to consider different temperature ranges. The compression load and relative humidity of the air are assumed to be constants throughout the considered temperature range.     

Analysis for buckling and vibrations of composite stiffened shells and plates

This paper deals with development of triangular finite element for buckling and vibration analysis of laminated composite stiffened shells. For the laminated shell, an equivalent layer shell theory is employed. The first-order shear deformation theory including extension of the normal line is used. In order to take into account a non-homogeneous distribution of the transverse shear stresses a correction of transverse shear stiffness is employed. Based on the equivalent layer theory with six degrees of freedom (three displacements and three rotations), a finite element that ensures C⁰ continuity of the displacement and rotation fields across inter-element boundaries has been developed. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Results of vibration and buckling analysis of stiffened plates and shells are discussed.     

Free vibration analysis of axially compressed laminated composite beam-columns with multiple delaminations

In this work free vibration analysis is performed for multi-delaminated composite beam-columns subjected to axial compression load. In order to investigate the effects of multi-delaminations on the natural frequency and the elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-delamination tip. The characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delaminated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and the elastic buckling load for multi-delaminated beam-columns are obtained in this work. The latter is based on the incremental load of axial compression, which is limited to the maximum elastic buckling load of the sound laminated beam-column. To verify the results of the present models, experimental results are obtained for isotropic single delaminated beam-columns. Comparisons are conducted between these experimental results and the present analysis. Good agreement is obtained from this comparison of results. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on the natural frequency and the elastic buckling load, specifically the latter ones.     

复合材料加筋壁板长桁终止端混合连接设计分析

对缩短胶接面长度以提高起裂载荷的复合材料加筋壁板长桁终止端新型混合连接设计进行了研究。采用经试验验证的有限元方法,对长桁终止端混合连接的传载与失效机制进行分析,并研究了胶接面长度对结构起裂载荷的影响规律。研究结果表明：新型混合连接设计中紧固件提供的法向约束以及剪切载荷传递路径可显著提升终止端结构的起裂载荷,并增强终止端处界面的抑制损伤扩展能力;结构的起裂载荷随着胶接面的缩短而提高;当胶接面前缘退至连接区末排紧固件之后,可避免结构在最终破坏前发生界面失效,结构强度由蒙皮的机械连接强度决定。     

复合材料加筋板长桁终止端失效机制

由于设计要求或设计限制条件, 壁板的长桁常常在翼肋或机身框附近、 机翼的前后梁附近、 机翼与机身的开口附近、 机翼的油箱附近等部位终止。在面内载荷作用下, 截面形状突变和传载路径偏移在端头处会产生应力集中, 极易引起缘条/蒙皮界面脱胶分层。对三种构型的长桁终止端典型件在单向拉、 压载荷下的破坏机制进行了试验研究与数值模拟, 结果表明, 拉伸时的失效是由面外剥离应力与层间剪应力的共同作用所致, 而压缩时的失效主要是由层间剪应力所致。     

考虑脱粘的复合材料加筋板屈曲后屈曲及承载能力数值分析

建立了复合材料层合加筋壁板的屈曲后屈曲有限元分析模型。该模型采用界面单元以有效模拟筋条和壁板之间的连接界面, 连接界面和复合材料层板分别采用Quads和Hashin失效准则作为失效判据, 引入材料刚度退化模型, 采用非线性有限元方法, 研究了复合材料加筋壁板在压缩载荷下的前后屈曲平衡路径及破坏过程。数值分析结果与实验结果吻合良好, 证明了该方法的合理有效性。详细探讨了筋条尺寸及界面单元强度等参数对加筋壁板屈曲后屈曲行为及承载能力的影响规律, 研究表明增加筋条截面惯性矩及筋条密度在一定程度上能有效提高加筋板的屈曲载荷与极限强度, 筋条密度增加到一定程度会引起结构破坏形式由失稳破坏?湮顾跗苹? 界面强度与铺层方式对极限强度有重要影响, 界面脱粘是引起加筋板最终破坏的重要因素。      

Postbuckling behaviour of a pressurized stiffened composite panel – Part I: Experimental study

Results of an experimental study of the buckling and postbuckling behaviour until the collapse of a cylindrical stiffened composite panel are presented. The specimen is subjected to a uniform pressure on one of its faces using a combination of gas and liquid inside a hermetic box. The present analysis shows the postbuckling load carrying capacity of elements of this kind without developing failure mechanism. Due to the high sensitivity to geometric imperfections of these structures, a simple procedure to obtain their measurements once the specimen is placed in the experimental device is set out. The data registered in these tests will be used for the subsequent validation of the numerical model in order to develop more accurate solutions. This will produce a significant increment in the fidelity of those predictions, making possible a reduction in the number of tests to be performed in real applications.     

压缩载荷下复合材料整体加筋板渐进损伤非线性数值分析

建立了考虑脱粘的复合材料整体加筋板渐进损伤有限元分析模型。该模型采用界面单元模拟筋条与壁板之间的连接界面, 连接界面和复合材料层板分别采用Quads准则和Hashin准则作为失效判据, 基于ABAQUS软件, 建立了含连续损伤状态变量的材料刚度退化方案。基于该模型, 采用非线性有限元方法研究了压缩载荷下复合材料整体加筋壁板在考虑初始几何缺陷时的破坏过程, 分析了结构相应失效模式的细观损伤机制; 详细讨论了轴向刚度比对结构承载能力及破坏模式的影响。结果表明: 考虑脱粘损伤的有限元模型能有效模拟加筋板的破坏过程; 在加筋板铺层设计合理的情况下, 增加筋条与壁板刚度比能有效提高加筋板截面单位面积的承载能力。      

含离散源损伤复合材料加筋板的拉伸特性

通过对含有离散源损伤的复合材料加筋板的拉伸试验和有限元模拟,研究了离散源损伤的损伤扩展与破坏特性。结果表明:复合材料加筋板的离散源损伤用穿透蒙皮切断桁条的切口来模拟是合适的,蒙皮上的穿透切口前端有很高的应力集中,桁条被切断导致加筋板传力路线改变;基于Hashin失效准则的渐进损伤有限元数值模拟方法,可以有效地模拟含切口加筋板的宏观损伤扩展和破坏过程,计算结果与试验值吻合较好。      

复合材料加筋板低速冲击损伤的数值模拟

建立了复合材料加筋板在横向低速冲击载荷作用下的渐进损伤有限元模型.该模型考虑了复合材料加筋板受低速冲击时的纤维断裂、基体开裂及分层脱粘等五种典型的损伤形式,在层内采用应变描述的失效判据,结合相应的材料性能退化方案,通过编写VUMAT用户自定义子程序以实现相应损伤类型的判断和演化.在层间以及筋条与层板间加入界面元,模拟层间区域的情况,结合传统的应力失效判据和断裂力学中的能量释放率准则来判断分层损伤的起始和演化规律.通过对数值模拟结果与实验数据的比较,验证了模型的合理性和有效性.同时探讨了不同位置、不同冲击能量以及含初始损伤(脱粘)等因素对复合材料加筋板低速冲击性能的影响.     

复合材料加筋板低速冲击损伤的数值模拟

建立了复合材料加筋板在横向低速冲击载荷作用下的渐进损伤有限元模型。该模型考虑了复合材料加筋板受低速冲击时的纤维断裂、基体开裂及分层脱粘等五种典型的损伤形式, 在层内采用应变描述的失效判据, 结合相应的材料性能退化方案, 通过编写VUMAT用户自定义子程序以实现相应损伤类型的判断和演化。在层间以及筋条与层板间加入界面元, 模拟层间区域的情况, 结合传统的应力失效判据和断裂力学中的能量释放率准则来判断分层损伤的起始和演化规律。通过对数值模拟结果与实验数据的比较, 验证了模型的合理性和有效性。同时探讨了不同位置、不同冲击能量以及含初始损伤(脱粘)等因素对复合材料加筋板低速冲击性能的影响。