A study of the fundamental frequency characteristics of eccentrically and concentrically simply supported stiffened plates

The paper investigates the fundamental frequency characteristics of eccentrically and concentrically simply supported stiffened supported plates. As a first stage, a numerical procedure for the computation of the fundamental frequency is presented. The strain energy of the assembled plate/stiffener elements is derived in terms of generalized in- and out-of-plane displacement functions and Mathematical Programming is then used to determine the lowest natural frequency. The prediction of the described algorithm is verified with other numerical procedures like finite-element, finite-strip and finite-difference methods. Results are then presented showing the influence of the plate/stiffener geometric parameters on the fundamental frequency of the structure with various concentric and eccentric stiffening configurations.     

Vibration analysis of corrugated Reissner–Mindlin plates using a mesh-free Galerkin method

A mesh-free Galerkin method for the free vibration analysis of unstiffened and stiffened corrugated plates is introduced in this paper, in which the corrugated plates are simulated with an equivalent orthotropic plate model. To obtain the corresponding equivalent elastic properties for the model, a constant curvature state is applied to the corrugated sheet. The stiffened corrugated plates are treated as composite structures of equivalent orthotropic plates and beams, and the strain energies of the plates and beams are added up by the imposition of displacement compatible conditions between the plate and the beams. The stiffness matrix of the whole structure is then derived. The proposed method is superior to the finite element methods (FEMs) because no mesh is needed, and thus stiffeners (beams) do not need to be placed along the mesh lines and the necessity of remeshing when the positions of the stiffeners change is avoided. To demonstrate the accuracy and convergence of the proposed method, several numerical examples are analyzed both with the proposed method and the finite element commercial software ANSYS. Examples from other research are also employed. A good agreement between the results for the proposed method, the results of the ANSYS analysis, and the results from other research is observed. Both sinusoidally and trapezoidally corrugated plates are studied.     

Sound radiation from strip plates with longitudinal stiffeners using waveguide finite and boundary element methods

In this study, the vibration characteristics and sound radiation of strip plates with finite width and infinite length are investigated numerically in order to analyze the vibration and sound radiation of structures consisting of many stiffened and double-layered plates. The waveguide finite element approach, which is effective for waveguide structures, is applied as a numerical scheme. The sound power and radiation efficiencies for an unstiffened plate are calculated numerically via coupling boundary elements to the WFEs. Longitudinal stiffeners and additional upper plates are included in the plate model to investigate the effect of stiffeners and an upper plate on sound power and radiation efficiency. In this study, it is found that the stiffeners contribute differently to plate vibration and sound radiation, and that the radiation efficiencies of the stiffened and double plates are larger than those of the unstiffened plate due to the presence of the stiffeners.     

Adaptive finite element analysis of steel girder deck pavement

This paper shows a more exact and practical finite element model of the steel girder deck pavement. Based on Mindlin thick plate theory, a 12-node solid thick plate element was constituted to analyze the pavement. The computation result was compared with that by traditional 4-node and 8-node thick plate finite element, and is satisfactory. A combined plate beam element method is presented to investigate the stiffened plate. A 6-node solid thin plate element was constituted to analyze the top plate based on Kirchhoff thin plate theory. The stiffeners acting as the vertical supporting function mainly are taken as Euler beam elements. A method of using the linear interpolation to realize the longitudinal displacement and the cubic Hermite interpolation to the vertical displacement is presented to analyze the stiffeners. In addition, it is essential to consider the displacement coordination between the top plate and stiffeners. A node-to-node contact scheme, which is applicable for three-dimensional contact analyses involving large deformations, was used to treat the contact problem between pavement and stiffened plate by Lagrange multiplier methods.     

Free vibration and buckling response of hat-stiffened composite panels under general loading

The paper presents finite element free vibration and buckling analysis of laminated hat-stiffened shallow and deep shells using arbitrarily oriented stiffener formulation. Modified approach for modelling the curved stiffener is implemented using necessary transformations. A simplified stiffener formulation is presented to accommodate various shapes of stiffener shapes in developing the rigidity matrix for the finite element formulation. Investigation has been carried out on free vibration and buckling analyses of laminated composite stiffened shell structures with laminated open section (rectangular or ‘T’ shaped) and closed section (‘hat’ shaped) stiffeners. Parametric study on the hat-stiffened panels for the free vibration and buckling analyses confirms that the closed section stiffener being torsionally rigid is found to show better performance over open section stiffeners.     

Buckling and vibration of stiffened plates subjected to partial edge loading

The buckling and vibration characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element method. The initial stresses are obtained considering the pre-buckling conditions. Buckling loads and vibration frequencies are determined for different plate aspect ratios, edge conditions and different partial non-uniform edge loading cases. The non-uniform loading may also be caused due to the supports on the edges. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The vibration characteristics are discussed and the results are compared with those available in the literature. Buckling results show that the stiffened plate is less susceptible to buckling for position of loading near the supported edges and near the position of stiffeners as well.     

Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method

The elastic bending of unstiffened and stiffened corrugated plates is studied in this paper, and a mesh-free Galerkin method is presented for the analyses. A corrugated plate is treated as an orthotropic plate that has different flexure properties in two perpendicular directions. The equivalent flexure properties are estimated by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plate is considered as a composite structure of an orthotropic plate with beams. By superimposing the strain energy of the orthotropic plate and the beams, and imposing the displacement compatibility conditions between the plate and the beams, the stiffness matrix of the structure is obtained. Because no mesh is needed in the proposed method, there is no limitation to the position of the stiffeners (beams). Changes in the positions of the stiffeners do not require the re-meshing of the plate. Several numerical examples are employed to show the accuracy and convergence of the proposed method. The computation results demonstrate good agreement with the solutions given by ANSYS, and different profiles of corrugated plates are considered.     

The stacking sequence optimization of stiffened laminated curved panels with different loading and stiffener spacing

An efficient procedure to obtain the optimal stacking sequence and the minimum weight of stiffened laminated composite curved panels under several loading conditions and stiffener layouts has been developed based on the finite element method and the genetic algorithm that is powerful for the problem with integer variables. Often, designing composite laminates ends up with a stacking sequence optimization that may be formulated as an integer programming problem. This procedure is applied for a problem to find the stacking sequence having a maximum critical buckling load factor and the minimum weight. The object function in this case is the weight of a stiffened laminated composite shell. Three different types of stiffener layouts with different loading conditions are investigated to see how these parameters influence on the stacking sequence optimization of the panel and the stiffeners. It is noticed from the results that the optimal stacking sequence and lay-up angles vary depending on the types of loading and stiffener spacing.     

Influence of stiffener location on the stability of stiffened plates under compression and in-plane bending

The elastic behaviour of stiffened plates under non-uniform edge compression is investigated. As a first stage, an energy formulation, in which the structure is modelled as assembled plate and beam elements, is presented. A Sequential Quadratic Programming (SQP) algorithm is then used to evaluate the buckling load and the associated buckling mode for given plate/stiffener geometric properties. Results are presented showing the influence of the stiffener location on the stability of the structure under combined compression and bending. Then, a strategy is presented for optimum location of the stiffener. The proposed methodology can be used to develop an improved design procedure for efficient design of stiffened plates under this type of loading.     

有限加筋板宽度对应力强度因子的影响

基于线性累积损伤理论,分析了含裂纹损伤的加筋板加强筋宽度的不同对裂纹尖端应力强度因子的影响。然后根据分析得到裂纹尖端应力强度因子随加强筋宽度的变化规律。结果表明,随着加强筋宽度的增大,结构应力强度因子的下降幅度逐渐增大,当裂纹尖端离筋条越近时,这种现象越明显。     

Numerical analysis of static performance comparison of friction stir welded versus riveted 2024-T3 aluminum alloy stiffened panels

Most researches on the static performance of stiffened panel joined by friction stir welding（FSW） mainly focus on the compression stability rather than shear stability. To evaluate the potential of FSW as a replacement for traditional rivet fastening for stiffened panel assembly in aviation application, finite element method（FEM） is applied to compare compression and shear stability performances of FSW stiffened panels with stability performances of riveted stiffened panels. FEMs of 2024-T3 aluminum alloy FSW and riveted stiffened panels are developed and nonlinear static analysis method is applied to obtain buckling pattern, buckling load and load carrying capability of each panel model. The accuracy of each FEM of FSW stiffened panel is evaluated by stability experiment of FSW stiffened panel specimens with identical geometry and boundary condition and the accuracy of each FEM of riveted stiffened panel is evaluated by semi-empirical calculation formulas. It is found that FEMs without considering weld-induced initial imperfections notably overestimate the static strengths of FSW stiffened panels. FEM results show that, buckling patterns of both FSW and riveted compression stiffened panels represent local buckling of plate between stiffeners. The initial buckling waves of FSW stiffened panel emerge uniformly in each plate between stiffeners while those of riveted panel mainly emerge in the mid-plate. Buckling patterns of both FSW and riveted shear stiffened panels represent local buckling of plate close to the loading corner. FEM results indicate that, shear buckling of FSW stiffened panel is less sensitive to the initial imperfections than compression buckling. Load carrying capability of FSW stiffened panel is less sensitive to the initial imperfections than initial buckling. It can be concluded that buckling loads of FSW panels are a bit lower than those of riveted panels whereas carrying capabilities of FSW panels are almost equivalent to those of riveted panels with identical geometries. Finite elem     

Rigid-plastic modelling of blast-loaded stiffened plates—Part II: Partial end fixity, rate effects and two-way stiffened plates

A new rigid-plastic analysis of stiffened plates subjected to uniformly distributed blast loads is developed. In this first part of a two-part paper, a uniform one-way stiffened plate with clamped ends is modelled as a singly symmetric beam, comprised of one stiffener and its tributary plating. Rigid-plastic analysis is then applied to this beam using an idealized piecewise linear bending moment-axial force capacity interaction relation or yield curve. Two solutions to the response are developed. The first solution is in closed form and is based on the solution of the resulting linearized differential equations. The second solution is obtained by approximating the response as a sequence of instantaneous mode responses, where the mode shapes are determined by an extremum principle which maximizes the rate of change of the kinetic energy. This latter solution may be extended to cases involving non-rigid boundaries and two-way stiffening and this is done in the second part of this paper. Here, the two solution methods are applied to several examples of one-way stiffened plates subjected to various blast-type pulses. Good agreement is obtained between the present results and those from elastic-plastic beam finite element and finite strip solutions.     

A plastic collapse mechanism for the tripping behaviour of flat-bar ring stiffeners in cylindrical shells subject to external pressure

A mechanism approach has been developed to predict the unloading response of a tripping failure of a ring stiffener in a cylindrical shell subject to external pressure. The work extends a previous mechanism developed by Murray [Struct. Engr. 51, 285 (1973)] on flat stiffened panels by modifying the approach to analyse the case of a curved panel and stiffener. An upper-bound failure load is also predicted from the intersection of the mechanism curve with a simplified elastic loading response. The predictions have been correlated with fully nonlinear finite element (FE) analyses. A brief parametric study has also been carried out, and the limitations and applicability of the mechanism are discussed.     

T形气缸盖罩垫密封性能的有限元分析

运用有限元软件对平型、加强筋型和凸台型T形缸垫的应力、应变以及接触应力分布规律进行研究,对比分析这几种T形缸垫的密封性能。结果表明,加强筋能提高缸垫的密封能力,但不同的加强筋结构对密封能力有着不同的影响,设计不合理的加强筋,还容易导致T形气缸盖罩垫过快失效和老化。平型气缸盖罩垫适用于密封周期长但密封力要求不高的情况;而加强筋型气缸盖罩垫则适用于密封力要求高但密封周长不长的情况;凸台型气缸盖罩垫的综合性能高,能满足密封周期长和密封力要求比较高的情况。     

Effect of fiber orientation on interfacial fracture toughness for adhesively bonded composite plates

In this study, interfacial fracture toughness was investigated experimentally and numerically in laminated composite plates with different fiber reinforcement angles bonded with adhesive. The composite plates are four-layered and the layer sequence is [0º/θ]_s. DCB test was applied to composite plates reinforced with epoxy resin matrix and unidirectional carbon fiber. The experimental sample model for the DCB test was made using the ANSYS finite element package program. In the numerical study, four layered composites were prepared in three dimensions. Under critical displacement value; mode I fracture toughness at the crack tip was calculated using VCC (virtual crack closure) technique. Numerical values consistent with experimental results have presented in graphical forms. At 60o and 75° the greatest fracture toughness was obtained. In addition, numerical results have shown that fiber orientation prevents the uniform distribution of stress on the interface crack tip and causes stress accumulation, especially at the edge of the plate.

     

Thermal buckling behavior of laminated composite plates: a finite-element study

In this paper, the thermal buckling behavior of composite laminated plates under a uniform temperature distribution is studied. A finite element of four nodes and 32 degrees of freedom (DOF), previously developed for the bending and mechanical buckling of laminated composite plates, is extended to investigate the thermal buckling behavior of laminated composite plates. Based upon the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical implementation of the present finite element allowed the comparison of the numerical obtained results with results obtained from the literature: 1) with element of the same order, 2) the first order shear deformation theory, 3) the high order shear deformation theory and 4) the three-dimensional solution. It was found that the obtained results were very close to the reference results and the proposed element offers a good convergence speed. Furthermore, a parametrical study was also conducted to investigate the effect of the anisotropy of composite materials on the critical buckling temperature of laminated plates. The study showed that: 1) the critical buckling temperature generally decreases with the increasing of the modulus ratio E _L/E _T and thermal expansion ratio α _T/α _L, and 2) the boundary conditions and the orientation angles significantly affect the critical buckling temperature of laminated plates.     

A point receptance array approach for stiffened panel structures

A point receptance array is proposed to study behaviors of panel structures with stiffeners. Although the overall objective is intended to develop a general algorithm for large structural members with stiffeners of arbitrary arrangements, the present study focus on an analytical evaluation of the accuracy of the approximation. To simplify the formulations, a thin plate with two diagonally connected beam stiffeners is selected. By solving governing differential equations for the plate and beam, point receptances that represent the interaction and compatibility conditions at the plate-beam interfaces are analytically obtained. Buckling modes of the stiffened plate are obtained by solving an eigenvalue problem. Accuracy of the approach is verified by a comparison of the analytical solution with data obtained from a direct finite element model. A parametric study was also performed. Good agreement indicates that the point receptance is a viable approach for general applications.     

弹性边界板结构拓扑优化声辐射

针对拓扑优化方法在减振降噪领域的应用以及板结构在实际应用中所处的环境,采用拓扑优化方法对不同弹性边界刚度的板结构进行拓扑优化分析,计算了不同边界刚度条件下板结构的声辐射情况。根据弹性边界板结构拓扑优化后的结构形式进行加强筋布置,对比于其他的加强筋布置形式进行板结构声学响应计算,得出了不同弹性边界刚度对于板结构拓扑优化结果的影响规律,以及不同板结构的边界刚度对于板结构声辐射情况的影响。板结构的声辐射响应计算结果验证了拓扑优化在减振降噪方面的应用价值。     

铝合金搅拌摩擦焊接加筋板剪切稳定性能研究

对2024-T3铝合金搅拌摩擦焊接加筋壁板的剪切稳定性能进行试验研究,得到该结构的剪切失稳形式及屈曲载荷、承载能力及破坏形式。应用有限元法对该焊接加筋壁板结构进行简化建模,对该结构的稳定性和承载能力进行计算,将计算结果与试验结果进行比较。试验及有限元计算结果表明,结构的剪切失稳形式表现为筋条间平板的局部屈曲;屈曲后结构进入张力场受力状态,破坏形式主要表现为平板的塑性变形和边缘撕裂、筋条的弯扭变形以及焊接区的局部脱焊;出现脱焊现象的试验件其承载能力较未出现脱焊现象的试验件下降7.7%;线性和非线性屈曲计算所得屈曲载荷分别比试验平均值高出18.4%和26.2%,而非线性计算所得承载能力比试验平均值高出5.7%,焊接引起的初始缺陷对结构承载能力的影响小于对屈曲载荷的影响;有限元分析得到的结构屈曲形式和失效形式与试验现象吻合,验证了有限元模型的合理性,但其仍需要进一步改进以考虑初始缺陷来减小计算误差。