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.     

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。     

Finite-Element Analysis of Laminated Stiffened Cylindrical Shallow Shell

A finite-element solution for a geometrically nonlinear fiber composite shallow shell with Stringer-type stiffeners is presented. A laminated, anisotropic thin/thick shallow stiffened shell finite element is developed and applied for the solution of several static problems. Geometrically, a nonlinear finite-element model is based on the nonlocking shear deformable theory. Stiffened composite cylinders are subjected to mechanical loading and the shallow shell theory is used for the geometric representation and formulation of the axially stiffened cylinders. A new, two-sided meshing system is generated to represent a cylindrical shell with stiffeners in a three-dimensional coordinate system.     

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.     

A new finite element for buckling analysis of laminated stiffened plates

A new stiffened plate element for stability analysis of laminated stiffened plates has been presented. The basic plate element is a combination of Allman's plane stress triangular element and a Discrete Kirchhoff–Mindlin plate bending element. The element includes transverse shear effects. The model accommodates any number of arbitrarily oriented stiffeners within the plate element and eliminates constraints on the mesh division of the plate. The element has no problem associated with shear locking – a phenomenon usually encountered in isoparametric elements. The stability analysis of laminated stiffened plates has been carried out under different loading conditions with the present element.     

Boundary element analysis of curved cracked panels with adhesively bonded patches

A new boundary element formulation for analysis of curved cracked panels with adhesively bonded patches is presented in this paper. The effect of the adhesive layer is modelled by distributed body forces (i.e. two in‐plane forces, two moments and one out‐of‐plane force). A coupled boundary integral formulation of a shear deformable plate and two‐dimensional plane stress elasticity is used to determine bending and membrane forces along the adhesive layer taking into consideration the compatibility conditions in the patch area. Two numerical examples are presented to demonstrate the efficiency of the proposed method. It is shown that the out‐of‐plane bending behaviour and panel curvature have significant influence on the magnitude of the stress intensity factors. Copyright © 2003 John Wiley & Sons, Ltd.     

A new boundary element formulation for shear deformable shells analysis

A new domain‐boundary element formulation to solve bending problems of shear deformable shallow shells having quadratic mid‐surface is presented. By regrouping all the terms containing shells curvature and external loads together in equilibrium equation, the formulation can be formed by coupling boundary element formulation of shear deformable plate and two‐dimensional plane stress elasticity. The boundary is discretized into quadratic isoparametric element and the domain is discretized using constant cells. Several examples are presented, and the results shows a good agreement with the finite element method. Copyright © 1999 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。     

竖向槽钢加劲钢板剪力墙剪切屈曲

对设置多道竖向闭口加劲肋的钢板剪力墙的剪切屈曲进行了有限元弹性屈曲分析,得到了剪切应力随加劲肋抗弯和加劲肋抗扭刚度变化曲线,以加劲板临界应力等于小区格按简支计算的剪切屈曲应力为条件,得到了双面加劲肋的门槛刚度。刚度小于门槛刚度时给出了剪切屈曲临界应力与加劲肋刚度的关系;将双面加劲同单面加劲、交错单面加劲两种情况进行比较,得出了后两者的门槛刚度放大系数。与数值结果比较表明:公式具有良好精度且偏安全。     

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。     

Buckling analysis of shear deformable shallow shells by the boundary element method

In this work a boundary element (BE) formulation for buckling problem of shear deformable shallow shells is presented. A set of five boundary integral equations are obtained by coupling two-dimensional plane stress elasticity with shear deformable plate bending (Reissner). The domain integrals appearing in the formulation (due to the curvature and due to the domain load) are transferred into equivalent boundary integrals. The BE formulation is presented as an eigenvalue problem, to provide direct evaluation of critical load factors and buckling modes. Several examples are presented. The BE results for a cylindrical shallow shell with different curvatures are compared with other numerical solutions and good agreements are obtained.     

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 shear deformable plates by boundary element method

In this paper, the derivation and numerical implementation of boundary integral equations for the buckling analysis of shear deformable plates are presented. Plate buckling equations are derived as a standard eigenvalue problem. The formulation is formed by coupling boundary element formulations of shear deformable plate and two dimensional plane stress elasticity. The eigenvalue problem of plate buckling yields the critical load factor and buckling modes. The domain integrals which appear in this formulation are treated in two different ways: initially the integrals are evaluated using constant cells, and next, they are transformed into equivalent boundary integrals using the dual reciprocity method (DRM). Several examples with different geometry, loading and boundary conditions are presented to demonstrate the accuracy of the formulation. Copyright © 2004 John Wiley & Sons, Ltd.     

Boundary element analysis of reinforced shear deformable shells

In this paper, stiffened shear‐deformable shells are analysed using the boundary element method. Coupled boundary integral equations are presented for describing curved shells under general loading conditions. The equations are based on boundary integral equations for plane stress and plate bending, with coupling terms arising from the curvature of the shell. Domain integrals are transformed into boundary integrals using the dual reciprocity technique. Stiffeners are modelled as curved beams, continuously attached to the shell. Numerical solutions calculated using the present method are compared with finite element results in two examples. Copyright © 2002 John Wiley & Sons, Ltd.     

Vibration of stiffened skew Mindlin plates

Summary This paper presents a formulation for the free vibration analysis of skew Mindlin plates with intermediate parallel stiffeners attached in two directions. The Mindlin theory is used to account for the effects of transverse shear deformations and rotary inertia of the plate while the Engesser theory associated with the consideration of torsion is employed for stiffeners. Based on these two theories, the energy functionals for the plate system have been derived. To obtain the vibration frequencies, these energy functionals are minimized with the shape functions assumed in a set of two-dimensional mathematically complete polynomials. This procedure has been implemented numerically to compute the vibration solutions. Convergence studies have been performed to verify the accuracy of this method. Sets of first known results have been presented for several stiffened plate structures.     

Buckling of open-section bead-stiffened composite panels

Stiffened panels are structures that can be designed to efficiently support in-plane compression, bending, and shear loads. Although the stiffeners are usually discrete elements which are fastened or bonded to a flat or continuously curved plate, manufacturing methods such as thermoforming allow integral formation of the stiffeners in a panel. Such a configuration offers potential advantages in terms of a reduced number of parts and manufacturing operations. For thermoplastic composite panels stiffened by integrally formed open-section beads, the effects of bead spacing and bend cross-section geometry on the initiation of buckling under uniaxial compression and uniform shear loading were investigated. Finite elements results for a range of stiffened panel sizes and bead geometries are presented and compared with approximate closed-form solutions based on an effective flat plate size. Experimental verification of analytical predictions for one of the shear panels and one of the compression panels is described. Compensation of the forming tool to reduce the degree of initial curvature of the panels was found to be necessary.     

Plane stress and plate bending coupling in BEM analysis of shallow shells

In this paper the shear deformable shallow shells are analysed by boundary element method. New boundary integral equations are derived utilizing the Betti's reciprocity principle and coupling boundary element formulation of shear deformable plate and two‐dimensional plane stress elasticity. Two techniques, direct integral method (DIM) and dual reciprocity method (DRM), are developed to transform domain integrals to boundary integrals. The force term is approximted by a set of radial basis functions. Several examples are presented to demonstrate the accuracy of the two methods. The accuracy of results obtained by using boundary element method are compared with exact solutions and the finite element method. Copyright © 2000 John Wiley & Sons, Ltd.     

Boundary element formulations for Mindlin plate on an elastic foundation with dynamic load

Boundary element method (BEM) for a shear deformable plate (Reissner/Mindline's theories) resting on an elastic foundation subjected to dynamic load is presented. Formulations for both Winkler and Pasternak foundations are presented. The boundary element formulation in Laplace domain is presented together with complete expressions for the internal point kernels (i.e. fundamental solutions). Quadratic isoparameteric boundary elements are used to discretise the boundary of plate domain. Time domain variables are obtained by the Durbin's inversion method from transform domain. Numerical examples are presented to demonstrate the accuracy of the boundary element method and the comparisons are made with other numerical technique.     

A Galerkin formulation for shear deformable plate bending dynamics

A Galerkin boundary element formulation for shear deformable plate bending dynamics is developed. The formulation makes use of the static fundamental solutions for the weighted residual integral equations. The domain integrals carrying the inertia terms and generic static loads are considered as body forces and approximated with boundary values using the dual reciprocity method. The load is modelled as a series of impact loads of time varying intensity and moving in space in a predetermined path. The formulation was implemented and tested solving a benchmark problem. The results are compared with finite element solutions. Copyright © 2004 John Wiley & Sons, Ltd.