Three-dimensional semi-analytical model for the static response and sensitivity analysis of the composite stiffened laminated plate with interfacial imperfections

For the stiffened composite laminated plates with interfacial imperfections, the problem of static response and sensitivity analysis was investigated in Hamilton system. Firstly, the meshfree formulation of Hamilton canonical equation for the composite laminated plate with interfacial imperfections was deduced by the linear spring-layer and the state-vector equation theory. And then, based on the equation of plates and stiffeners, governing equation of the composite stiffened laminated plate was assembled by using the spring-layer model again to ensure the compatibility of stresses and the discontinuity of displacements at the interface between plate and stiffeners. At last, a three-dimensional hybrid governing equation was developed for the static response analysis and sensitivity analysis.     

一类双壳结构振动特性的半解析法

以Hamilton正则方程的半解析法为基础,为一类双壳结构的振动特性提出了一种新的数学模型。基本步骤:(1)独立地建立内外壳和连接筋的线性方程组;(2)考虑到内外壳和连接筋的界面上的应力和位移的连续性,联立内外壳和连接筋的方程,从而得到全结构的方程组。主要优点是:采用了同一种Hamiltonian等参元离散壳和连接筋,结构的转动惯性、剪切变形等因素都得到了考虑,而且不限制壳的厚度和筋的高度;该方法象一般的有限元法一样适应复杂的边界条件和由多种材料构成的结构。本文的方法可推广用来研究加筋复合材料或加筋压电材料层合壳及相应的双壳结构的动力学问题。     

An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

For the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in‐plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one‐dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in‐plane matrix cracks combined with the extend FEM. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental Investigation Into the Fatigue of Welded Stiffened 350WT Steel Plates Using Neutron Diffraction Method

Abstract: The propagation of fatigue cracks under constant amplitude cyclic loading was studied in welded stiffened steel plates. The residual stresses in the stiffened plates were measured using the neutron diffraction strain‐scanning technique. The neutron diffraction measurements indicated that, in general, the residual stresses were tensile near the welded stiffeners and compressive between the stiffeners and ahead of the starter notch tips. Fatigue testing indicated that the fatigue crack growth rates of the stiffened plates were, in general, lower than that of a corresponding unstiffened plate, especially near the notch tips, where compressive residual stresses existed. An analytical method, using Green's function, was developed to predict the fatigue crack growth rates. Reasonable accuracy was obtained.     

爆炸载荷作用下双向加筋方板的大挠度塑性动力响应

从分别列出加筋板面板以及加强筋的运动方程出发,分析了爆炸载荷作用下双向加筋固支方板的大挠度塑性动力响应。分析表明:取决于加强筋的相对刚度以及爆炸载荷峰值的大小,加筋板的运动将呈现3种不同的模式。该文限于讨论加筋板的总体变形模式,具体讨论了十字加筋以及双十字加筋固支方板在忽略弯矩影响下的薄膜解法。理论结果与已有的试验结果在多数情况下符合良好,表明该文提出的简化理论分析方法能对爆炸载荷下双向加筋方板的永久变形做出较为合理的预报。     

一种分析AGS结构的三角形加筋板壳单元

基于精细三角形Mindlin板单元构造了21个自由度三角形复合材料加筋板壳单元。在该单元构造过程中,考虑了肋骨弯曲、扭转、面内剪切和横向剪切变形的影响;由于肋骨和蒙皮的位移插值函数采用了相同的形函数,保证了两者变形的协调性,同时又放松了肋骨转动的约束,故与传统的板单元相比,能较好地反映了蒙皮和肋骨的变形特征。在此单元中,肋骨放置的数量、位置和角度可以任意,为结构的单元网格剖分带来了很大的便利。算例结果验证了单元的有效性,特别是在分析高肋结构时,显示出其比传统加筋板单元具有更高精度的优点。还以一典型的先进复合材料等格栅加筋板(AGS)为例,讨论了该结构弯曲变形的力学特性。     

Fatigue crack growth analysis of stiffened cracked panel repaired with bonded composite patch

Fatigue crack growth behavior in a stiffened thin 2024-T3 aluminum panel repaired with one-sided adhesively bonded composite patch was investigated through experiments and analyses. The patch had three plies of unidirectional boron/epoxy composite. 2024-T3 aluminum stiffeners were riveted as well as bonded on the panel. Stiffeners were oriented in the loading direction and were spaced at either 102 mm or 152 mm with a crack centered between them. Also, un-repaired cracked panel with and without stiffeners were studied. Experiment involved tension-tension fatigue at constant amplitude with maximum stress of 120 MPa and stress ratio of 0.05. Bonded composite patch repair increased fatigue life about five-fold in the case of stiffened panels while it increased about ten fold in the case of un-stiffened panels. Fatigue life also increased with decrease of the distance between the stiffeners for both repaired and un-repaired panels. A three-dimensional finite element method was used to analyze the experiments. Residual thermal stresses, developed during patch bonding, requires the knowledge of temperature at which adhesive becomes effective in creating a bond between the structure and patch in the analysis. A simple method to estimate the effective curing temperature range is suggested in this study. The computed stress intensity factor versus measured crack growth relationships for all panel configurations were consistent and in agreement with the counterpart from the test material. Thus, the present approach provides a means to analyze the fatigue crack growth behavior of stiffened structures repaired with adhesively bonded composite patch.     

Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory

A two-dimensional global higher-order deformation theory is presented for thermal buckling of cross-ply laminated composite and sandwich plates. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated Mth-order approximate theories are applied to solve the eigenvalue problems of a simply supported multilayered plate. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Numerical results are compared with those of the published three-dimensional layerwise theory in which both in-plane and normal displacements are assumed to be C⁰ continuous in the continuity conditions at the interface between layers. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise theory and the global higher-order theory are clarified in thermal buckling problems of multilayered composite plates.     

Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory

This paper deals with elastic buckling analysis of stiffened and un-stiffened corrugated plates via a mesh-free Galerkin method based on the first-order shear deformation theory (FSDT). The corrugated plates are approximated by orthotropic plates of uniform thickness that have different elastic properties along the two perpendicular directions of the plates. The key to the approximation is that the equivalaent elastic properties of the orthotropic plates are derived by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates. The stiffeners are modelled as beams. The stiffness matrix of the stiffened corrugated plate is obtained by superimposing the strain energy of the equivalent orthotropic plate and the beams after implementing the displacement compatibility conditions between the plate and the beams. The mesh free characteristic of the proposed method guarantee that the stiffeners can be placed anywhere on the plate, and that remeshing is avoided when the stiffener positions change. A few selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results obtained for these examples, when possible, are compared with the ANSYS solutions or other available solutions in literature. Good agreement is evident for all cases. Some new results for both trapezoidally and sinusoidally corrugated plates are then reported.     

Consistent higher-order free vibration analysis of composite sandwich plates

The consistent higher-order dynamic formulation for foam-type (soft) core sandwich beams was extended to the case of composite sandwich plates. Eight dynamic governing equations and the corresponding boundary conditions were derived through the application of Hamilton’s principle. The extended formulation was applied to the free vibration analysis of soft-core and honeycomb-core sandwich plates with anti-symmetric and symmetric lay-ups. The vibration results for the thin and thick composite sandwich plates obtained using the extended formulation were consistent with the predictions of the higher order mixed layerwise theory for laminated and sandwich plates. To simplify the formulation for the case of symmetric sandwich plates, the general dynamic formulation was decoupled into two systems of equations representing symmetric and anti-symmetric vibrations. The numerical study demonstrates the importance of the present formulation for the prediction of higher mode vibration response of composite sandwich plates.     

Finite element fatigue propagation of induced cracks by stiffeners in repaired panels with composite patches

Fatigue crack growth analyses of aluminum panels with stiffeners repaired by composite patches have been rarely investigated. Generally, cracks may occur around the rivets which are capable to propagate under cyclic loadings. A composite patch can be used to stop or retard the crack growth rate. In this investigation, finite element method is used for the crack propagation analyses of stiffened aluminum panels repaired with composite patches. In these analyses, the crack-front can propagate in 3-D general mixed-mode conditions. The incremental 3-D crack growth of the repaired panels is automatically handled by a developed ANSYS Parametric Design Language (APDL) code. Effects of rivets distances and their diameters on the crack growth life of repaired panels are investigated. Moreover, the obtained crack-front shapes at various crack growth steps, crack trajectories, and life of the unrepaired and repaired panels with various glass/epoxy patch lay-ups and various patch thicknesses are discussed.     

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.     

Stable numerical simulations of propagations of complex damages in composite structures under transverse loads

In this paper, to deal with complex damage propagations in various composite structures under quasi-static transverse loads, a numerical simulation methodology based on the three-dimensional (3D) finite element method (FEM) is proposed. In this numerical model, two categories of damage patterns existing in composite structures under transverse loads are tackled independently. First, a kind of stress-based criteria is adopted to deal with the first category, which includes various in-plane damages, such as fiber breakage, transverse matrix cracking, matrix crushing, etc. Second, a bi-linear cohesive interface model is employed to deal with the second category, i.e., interface damages, such as delaminations. Also, to overcome the numerical instability problem when using the cohesive model, a simple and useful technique is proposed. In this technique, the move-limit in the cohesive zone is built up to restrict the displacement increments of nodes in the cohesive zone of laminates after delaminations occurred. The effectiveness of this method is illustrated using a DCB example and its characteristic is discussed in detail. This numerical model is further applied to various composite structures, such as 2D laminated plates and 3D laminated shells under transverse loads. The results of the numerical simulations are compared with the experimental results and good agreements are observed. The obtained information is helpful for understanding the propagation mechanisms of various damages in composite structures.     

阻尼夹芯复合材料加筋板的振动分析与数值模拟

以阻尼夹芯复合材料加筋板为研究对象,依据一阶剪切变形理论(FSDT)和Hamilton原理,推导板和加强筋的应变能、动能表达式,采用变分原理建立控制微分方程,根据相关边界条件和傅里叶级数求解方程。建立了ANSYS阻尼夹芯复合材料加筋板的有限元模型,该模型考虑到阻尼夹芯复合材料加筋板中阻尼材料与纤维预浸料间的结合方式,用模态应变能有限元数值模拟方法研究了结构的动力学性能,并通过对数值模拟结果与理论解的比较,验证了模型的合理性和有效性。探讨了不同的筋条尺寸、不同的筋条数量、不同的筋条分布方式对阻尼夹芯复合材料加筋板动力学性能的影响,得出了阻尼夹芯复合材料加筋板的一阶模态频率和损耗因子随不同参数的变化曲线,其结论为阻尼夹芯复合材料加筋板的优化设计提供参考。     

Stiffened cracked plates analysis by dual boundary element method

In this paper a boundary element formulation for analysis of shear deformable stiffened cracked plates is presented. By coupling boundary element formulation of shear deformable plate and two dimensional plane stress elasticity, dual boundary integral equations are presented. The interaction forces between stiffeners and the plate are treated as line distributed body forces along the attachment. Both concentric and eccentric stiffeners have been considered. Rectangular stiffened plate containing a single crack and double cracks subjected to uniform distributed moment on the crack surface and uniform shear load on the plate are analysed by the proposed method. Good agreement has been achieved compared with analytical solutions.     

频率相关自由阻尼层复合材料加筋板动力分析

采用子空间迭代法和精细积分对敷设粘弹性阻尼层的含损伤复合材料加筋板结构进行了频率和动力响应分析。分析中对层合板和层合梁采用了Adams应变能法与Raleigh阻尼模型相结合的阻尼矩阵构造方法;对表面粘弹性阻尼材料则考虑了材料性质和耗散系数对激振频率与温度的依赖性,建立了频率相关粘弹性材料阻尼矩阵的计算方法。通过有限元分析,分别研究了敷设自由阻尼层无损伤和含分层损伤复合材料加筋板的自振频率和模态特征,并根据幅频曲线讨论了阻尼材料模量、耗散系数和阻尼层厚度等因素对结构响应的影响,提出的计算方法对通过合理选择阻尼层材料与几何参数来有效地控制加筋板结构的振动特性,具有一定的参考价值。     

the compounding method applied to cracks in stiffened sheets

The compounding method for determining approximate stress intensity factors is extended and applied to cracks in stiffened sheets. The accuracy of the method is assessed by using configurations for which alternative solutions are available. An approximate solution is obtained for a crack located asymmetrically between stiffeners.     

Finite element analysis of stiffened laminated plates under transverse loading

A finite element model is developed to study the behavior of stiffened laminated plates under transverse loadings. Transverse shear flexibility is incorporated in both beam and plate displacement fields. A laminated plate element with 45 degrees of freedom is used in conjunction with a laminated beam element having 12 degrees of freedom for the bending analysis of eccentrically-stiffened laminated plates. The validity of the formulation is demonstrated by comparing with the available solutions in the literature. The numerical results are presented for eccentrically-stiffened layered plates having various boundary conditions and with stiffeners varying in number.     

Static and free vibration analyses of composite and sandwich plates by an edge-based smoothed discrete shear gap method (ES-DSG3) using triangular elements based on layerwise theory

An edge-based smoothed stabilized discrete shear gap method (ES-DSG3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. In this paper, the ES-DSG3 is extended and incorporated with a layerwise theory for static and free vibration analyses of composite and sandwich plates. In the layerwise theory, the behavior of each layer follows the first-order shear deformation theory and the condition of displacement continuity is imposed at the interfaces of layers. This hence does not require shear correction factors and improves significantly the accuracy of transverse shear stresses. The stiffness formulation of the ES-DSG3 is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements for each layer. The accuracy and reliability of the proposed method are confirmed in several numerical examples.