An extended layerwise/solid-element method of stiffened composite plates with delaminations and transverse crack

The stiffened composite plates with the transverse crack and delamination were studied in this paper, and an extended layerwise/solid-element (XLW/SE) method was developed. In the proposed method, the governing equations of composite plates and stiffeners were established based on the extended layerwise method and 3D solid elements, respectively. The final governing equation of stiffened composite plates is assembled by using the compatibility conditions and internal force equilibrium conditions at the joint interface between the plates and stiffeners. For the stiffened composite plates with damages, the XLW/SE method can obtain the local stress and displacement fields accurately and simulate the in-plane transverse cracks and delaminations simultaneously, considering complicated stiffeners without any assumptions. In the numerical examples, the results obtained by the proposed method are compared with those obtained by the 3D elastic models developed in the general finite element code, and the good agreements were achieved for the stiffened composite plates with/without delaminations and/or transverse crack.     

具有初始几何缺陷加劲板的动态屈曲

针对工程中常用的加劲板,研究了动态屈曲的求解方法。将加劲板分为母板与加劲肋两个部分考虑,其中母板按经典薄板理论计算,加劲肋视为Euler梁。假定加劲板的位移,利用Hamilton原理结合系统能量和振型叠加法建立了加劲板的动态屈曲特征方程。最后,选择四边简支加劲板进行数值分析,分析中考虑初始几何缺陷的影响,并讨论了初始几何缺陷、加劲肋的数量及其刚度的变化对动态屈曲临界荷载的影响。结果表明：一阶模态的初始几何缺陷对加劲板的临界荷载影响很大,而增加加劲肋的数量及其刚度可以提高加劲板的抗动态屈曲能力。研究结果也为加劲板的结构设计方法提供一定的参考。     

Buckling of folded plate structures subjected to partial in‐plane edge loads by the FSDT meshfree Galerkin method

This paper presents a meshfree Galerkin method that is based on the first‐order shear deformation theory (FSDT) to study the elastic buckling behaviour of stiffened and un‐stiffened folded plates under partial in‐plane edge loads. The un‐stiffened folded plates are modelled as assemblies of flat plates. The stiffness and initial stress matrices of the flat plates are derived by the meshfree Galerkin method. A treatment is implemented to modify the stiffness and initial stress matrices, and the matrices are then superposed to obtain the stiffness and initial stress matrix of the entire folded plate. The analytical process for stiffened folded plates is similar, except that the effects of the stiffeners must be taken into account. Because no mesh is required, the proposed method is superior for studying problems that would involve remeshing in the finite element method. Several examples are employed to show the convergence and accuracy of the proposed method. The results obtained show good agreement with the results computed from the finite element analysis software ANSYS. Copyright © 2005 John Wiley & Sons, Ltd.     

联肢加劲钢板剪力墙滞回性能试验研究与数值分析

完成了3个1/3比例的3层联肢钢板剪力墙试件的低周反复加载试验。3个试件的钢板剪力墙分别采用非加劲、槽钢竖向加劲和井字加劲的形式,钢板剪力墙的竖向边缘构件采用方钢管混凝土。得到了联肢钢板剪力墙试件的荷载-位移滞回曲线和破坏形态,对试件的骨架曲线、应力发展、延性及耗能能力等进行了分析。采用有限元软件ABAQUS对试件进行了数值模拟。结果表明:非加劲和槽钢竖向加劲墙板先屈曲后屈服,井字加劲墙板先屈服后屈曲,墙板屈服后连梁与钢板剪力墙边框梁相继屈服。方钢管混凝土柱脚屈服较早,屈服后仍具有良好的承载力和弹塑性变形能力。采用非加劲墙板的试件承载力最低,滞回环捏缩效应最严重,其次是采用槽钢竖向加劲墙板的试件。采用井字加劲墙板的试件滞回环较饱满。井字加劲和槽钢竖向加劲试件的峰值荷载分别比非加劲试件的峰值荷载提高了11.7%和6.9%,井字加劲和槽钢竖向加劲试件的等效黏滞阻尼系数分别比非加劲试件的等效黏滞阻尼系数提高了65.9%和19.9%。各试件的延性系数均大于4.5,表明不同加劲形式的联肢钢板剪力墙均具有良好的延性。数值分析与试验结果吻合较好,可充分地反映试件的滞回性能和破坏过程。加劲肋对连梁和边缘构件的内力影响较小,但可显著提高剪力墙板的抗剪承载力。相较于两片单肢钢板剪力墙,联肢钢板剪力墙的承载力和耗能能力均有大于20%的提高。     

平行四边形加肋板自由振动分析的无网格法

基于一阶剪切理论,提出一种求解平行四边形加肋板自由振动问题的无网格法,通过用一系列点来离散平板及肋条,得到加肋板的无网格模型。基于一阶剪切理论及移动最小二乘近似求出位移场,以梁模拟肋条,求出平行四边形加肋板总动能及总势能。再由Hamilton原理导出加肋板自由振动的控制方程,采用完全转换法引入边界条件,求解方程得出结构自振频率。以不同参数的加肋板为例,将该文解与ABAQUS有限元解进行比较分析。研究表明,该方法能有效地分析平行四边形加肋板自由振动问题,在肋条位置改变时,又避免了网格重构。     

Vibro-acoustic formulation of elastically restrained shear deformable stiffened rectangular plate

A method constructed on the basis of the Rayleigh–Ritz method and the first Rayleigh integral is presented for the vibro-acoustic analysis of elastically restrained shear deformable stiffened rectangular orthotropic plates. In the proposed method, the displacement fields of the plate and stiffeners are formulated on the basis of the first-order shear deformation theory. The theoretical sound pressure level (SPL) curve of the plate is constructed using the responses at different excitation frequencies and the first Rayleigh integral. The experimental SPL curve of an elastically restrained stiffened orthotropic plate was measured to verify the accuracy of the theoretical SPL curve of the plate. The effects of Young’s modulus ratio E₁/E₂ on the sound radiation characteristics of elastically restrained stiffened orthotropic plate with different aspect ratios are studied using the proposed method. It has been shown that the effects of Young’s modulus ratio become more prominent as the plate aspect ratio gets larger.     

Buckling Analysis of Plates Stiffened by Parallel Beams

In this paper a general solution for the elastic buckling analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section subjected to an arbitrary inplane loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. The unknown distribution of the aforementioned integrated tractions is established by applying continuity conditions in all directions at the two interface lines, while the analysis of both the plate and the beams is accomplished on their deformed shape. The method of analysis is based on the capability to establish the elastic and the corresponding geometric stiffness matrices of the stiffened plate with respect to a set of nodal points. Thus, the original eigenvalue problem for the differential equation of buckling is converted into a typical linear eigenvalue problem, from which the buckling loads are established numerically. For the calculation of the elastic and geometric stiffness matrices six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM-based method. Numerical examples with practical interest are presented. The accuracy of the results of the proposed model compared with those obtained from a 3-D FEM solution is remarkable.     

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.     

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。     

Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method

Based on the first-order shear deformation theory, a mesh-free Galerkin method for free vibration analysis of stiffened and un-stiffened folded plates and plate structures is presented in this paper. The folded plate or plate structure is modelled as a composite structure that consists of flat plates. The stiffness and mass matrices of the flat plates are derived based on the mesh-free formulation. To avoid the failure of direct superposition, a treatment is introduced to modify the stiffness and mass matrices. The global stiffness and mass matrices of the entire folded plate or plate structure are then obtained by superposing the modified stiffness and mass matrices of the flat plates. The analysis of the stiffened folded plates or plate structures proceeds in a similar fashion, as they are regarded as composite structures of stiffened and un-stiffened flat plates. The stiffness and mass matrices of the stiffened flat plates are also given by the mesh-free method. As no meshes are used in deriving the stiffness and mass matrices, the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. Several numerical examples are computed with the proposed method to demonstrate its accuracy and convergence. The results show good agreement with the solutions that have been given by other researchers and ANSYS.     

Boundary element analysis of shear deformable stiffened plates

In this paper a boundary element formulation for analysis of shear deformable stiffened plates is presented. The formulation is derived by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Both concentric and eccentric stiffeners have been considered. The interaction forces between stiffeners and the plate are treated as either line distribution or area distribution of body forces along the attachment. A rectangular stiffened plate and a circular stiffened plate under uniform load are analysed by the proposed method. Good agreement has been achieved compared with other published results.     

U肋加劲板焊接残余应力的一种简化计算方法

基于焊接残余应力数值模拟方法, 分析了U 肋加劲板各组成板件的板宽、板厚对焊接残余应力分布的影响, 揭示了U 肋与母板残余应力合力的分配规律, 提出了针对不同构造尺寸的U 肋加劲板焊接残余应力分布简化计算方法。研究结果表明:各组成板件的板宽变化对焊接残余拉应力的分布影响较小, 但对焊接残余压应力的大小影响较大;U 肋与母板的板厚比对U 肋与母板残余应力的分配比例影响较大。U 肋加劲板受压承载力计算时, 焊接残余应力分布可以采用简化方法计算, 其结果与根据数值模拟得到的焊接残余应力分布计算的结果基本一致。     

Stiffened plate bending analysis in terms of refined triangular laminated plate element

Based on the higher-order global–local theories, a finite element model is proposed to study the bending behavior of stiffened laminated plates. The proposed model treats the embedded stiffeners as the part of laminated plate, so that the compatibility of displacements and stresses between the plate and the stiffeners can be automatically satisfied. Distributions of the displacements and stresses through the thickness of laminates were also given for the first time, which can serve as references for future investigations as such information is lacking in the published literature. In addition, the impact of the stiffeners on the bending response of the stiffened laminated plates is also studied in terms of the quantity, the collocation and the geometry of stiffeners. Numerical results showed that the higher-order global–local theories are more suitable for predicting the bending response of thick and moderately thick stiffened laminated plates compared to the first order theory commonly used in engineering. By varying the quantity, the collocation and the geometry of stiffeners, the stiffness and the strength of stiffened laminated plates can be remarkably improved.     

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。     

用耦合有限元／边界元方法研究加筋板的声传输

采用耦合的有限元／边界元方法,建立了考虑流体结构耦合的加筋板结构声传输计算模型,并利用该模型计算研究了加筋板的声传输特性。数值计算表明：结构的传声损失与结构的固有频率和激励频率密切相关,避免共振仍是产要的;改变板厚或肋骨惯性矩后,由于结构固有频率发生了变化会使得结构传声损失曲线上极小值的位置发生改变;当声波从空气经结构向空气中传递时,增大板厚或肋骨惯性矩可明显增大结构的传声损失;而当声波从空气经结构向水中传递时,增大板厚或肋骨惯性矩也增大了结构的传声损失,但效果明显不如当声波从空气经结构向空气中传递时显著。     

Asymptotic bounds on the globally optimal positions of orthogonal stiffeners for rectangular plates in elastostatic bending

The present paper treats the problem of finding the asymptotic bounds for the globally optimal locations of orthogonal stiffeners minimizing the compliance of a rectangular plate in elastostatic bending. The essence of the paper is the utilization of a method of analysis of orthogonally stiffened rectangular plates first presented by Mazurkiewicz in 1962, and obtained herein in a closed form for several special cases. Asymptotic expansions of the expressions for the deflection field of a stiffened plate are used to derive limit-case globally optimal stiffening layouts for highly flexible and highly rigid stiffeners. A central result obtained in this work is an analytical proof of the fact that an array of flexible enough orthogonal stiffeners of any number, stiffening a simply-supported rectangular plate subjected to any lateral loading, is best to be put in the form of exactly two orthogonal stiffeners, one in each direction.     

Analogies between Kirchhoff plates and Saint-Venant beams under torsion

Torsion of linearly elastic homogeneous and orthotropic Saint-Venant beams is based on the solution of a Neumann-like boundary value problem for the cross-sectional warping. Equivalence of differential conditions of elastic equilibrium for the beam twist stresses in terms of warping function and for the bending-twisting moments in a Kirchhoff plate is assessed. The analogy provides new exact solutions in the theory of thin plates. Examples are developed for composite plates with no kinematic boundary constraints. Elliptic and equilateral triangle shapes provide useful benchmarks for computational mechanics.     

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.     

Composite bonded systems for renovations of orthotropic steel bridge decks

The renovation solution for orthotropic steel bridge decks studied consists of bonding a second steel plate to the existing steel deck in order to reduce the stresses and increase the lifespan of the orthotropic bridge deck. A parametric study was carried out on the flexural behaviour of beams representing the renovation solution using experimental and analytical studies. The influence of different thicknesses, temperatures and spans was tested. The results obtained for the stress reduction factor show that it is independent of temperature. More efficient solutions can be achieved when minimizing the second steel plate thickness and maximizing the adhesive layer thickness reducing the weight and increasing the stiffness of the composite structure. Both elastic behaviour and yield load of the composite beams are dominated by the steel plate properties and therefore not affected significantly by temperature. However, the ultimate failure of the beams occurs by shear of the adhesive layer, the properties of which are affected by temperature.     

Analysis of functionally graded plates by meshless method: A purely analytical formulation

Functionally graded plates under static and dynamic loads are investigated by the local integral equation method (LIEM) in this paper. Plate bending problem is described by the Reissner moderate thick plate theory. The governing equations for the functionally graded material with respect to the neutral plane are presented in the Laplace transform domain and therefore the in-plane and bending problems are uncoupled. Both isotropic and orthotropic material properties are considered. The local integral equation method is developed with the locally supported radial basis function (RBF) interpolation. As the closed forms of the local boundary integrals are obtained, there are no domain or boundary integrals to be calculated numerically in this approach. The solutions of the nodal values for the entire plate are obtained by solving a set of linear algebraic equation system with certain boundary conditions. Details of numerical procedures are presented and the accuracy and convergence characteristics of the method are examined. Several examples are presented for the functionally graded plates under static and dynamic loads and the accuracy for proposed method has been observed compared with 3D analytical solutions.