A finite prism element for stability analysis of bulb flat stiffeners

For the purpose of analysing the effect of the bulb on the torsional buckling stress of panels with bulb flat stiffeners, an element in the form of a triangular prism has been developed. The bulb was divided up into a mesh of such prisms, whilst the web was treated according to classical thin plate theory. The elastic and geometric stiffness matrices of a typical prism are presented in explicit form, and the procedure for enforcing compatibility between the bulb and web plate, in order to connect them together, is explained.     

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.     

Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings

This paper describes the underlying theory, and a general-purpose computer program, VIPASA, for determining the critical buckling stresses or natural frequencies of vibration of thin prismatic structures, consisting of a series of plates rigidly connected together along longitudinal edges. Each plate may be either isotropic or anisotropic and may carry a basic stress system consisting of longitudinal and transverse direct stress combined with shear. The structure is assumed to be subjected to a “dead load” system which does not cause buckling; in addition a “live load” system, defined in magnitude by a single load factor, may be applied and the value of the load factor at buckling is determined. Alternatively the natural frequencies of vibration of the structure when subjected to the dead load system are determined. Any number of critical load factors or natural frequencies can be obtained. The theory is based upon the assumption that all modes are sinusoidal, in the sense that all three components of displacement vary sinusoidally along any longitudinal line, but phase differences are incorporated to allow for the effects of anisotropy and shear. Apart from this assumption no further approximations are made other than those inherent in thin plate theory.     

General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures

This paper is concerned with the derivation of stiffness matrices for the buckling or vibration analysis of any structure consisting of a series of long, thin, flat plates rigidly connected together at their longitudinal edges. Each plate is assumed to be subjected to a basic state of plane stress which is longitudinally invariant, and it is further assumed that the mode of buckling or vibration varies sinusoidally in the longitudinal direction. During buckling or vibration, the edges of any individual plate are subjected to additional systems of forces and moments which are sinusoidally distributed along the edges, and these give rise to sinusoidally varying edge displacements and rotations. Spatial phase differences between the forces and displacements are accounted for by defining them in terms of complex quantities. The sinusoidal edge forces and displacements are split into two uncoupled systems, corresponding to out-of-plane and in-plane displacements, and two stiffness matrices are defined. The out-of-plane stiffness matrix is shown to be in general complex, and Hermitian in form, but the inplane stiffness matrix is real and symmetrical. Explicit expressions are derived for the elements of the matrices, in which all the essential destabilizing effects of the basic stresses, as well as dynamic effects, are included. Finally, it is shown that buckling and vibration phenomena for any structure of this type are closely interrelated.     

Analytical models of sandwich plates with piezoelectric strip-stiffeners

A theory of sandwich plates with composite-material facings and piezoelectric strip-stiffeners bonded to the surface or embedded in the facings is developed. The stiffeners bonded to the surfaces are modeled using either the plane stress assumption or a first-order shear deformable theory. The former approach is appropriate if the stiffeners represent thin strips, while the latter method can be used in the case where the stiffeners are relatively deep. The stiffeners embedded in the facings in the form of piezoelectric strips are considered using the plane stress assumption.     

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     

薄板结构低噪声仿生拓扑优化方法

针对薄板结构的低噪声设计问题,以结构声辐射功率最小化为优化目标,借鉴植物脉序分枝结构的构型特征,提出了薄板结构加强筋布局的仿生拓扑优化方法。以结构应变能最小和释放局部最大剪应力作为加强筋主脉和次脉的生长准则,以广义Murray准则作为加强筋脉序的分歧准则,构造了具有脉序分级特征的加强筋自适应生长算法。以固支薄板结构的横向弯曲振动及声辐射问题为典型算例,对比分析了仿脉序分布加筋板结构的声辐射功率和振动功率流的分布特性。数值结果表明,与相同体积约束下的正交加筋布局方式相比,仿脉序分布加筋方法使薄板结构具有更优的声振特性,进而验证了薄板结构加强筋仿生布局降噪方法的有效性与可靠性。     

Elastic small deflection analysis of annular sector Mindlin plates

An analytical method is developed for the bending response of annular sector Mindlin plates with two radial edges simply supported, and exact solutions are presented in the form of Levy-type series. Several different boundary conditions on the two circular edges are considered, viz. simply supported-simply supported, clamped-clamped and free-free. Numerical results for the case of uniform loading are presented to indicate the effect of shear deformation on the deflections and stress resultants at various points in the plate. Twisting stress couple and transverse shear stress resultant distributions along and near the edges of the plate are illustrated graphically, and the principal differences between the results predicted by Mindlin's plate theory and classical thin plate theory are discussed in detail. Results obtained with the present exact analysis may serve as references for approximate solutions and, especially, as a ‘shear locking’ test for thick plate finite element analysis.     

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.     

一种毫米波天线反射面板精密成形的数值模拟

天线反射面板的成形方法对面板精度有着重要的影响。根据具有大面积、主动反射面的毫米波天线对面板的成形要求,提出了一种基于高精度模具、蒙皮开缝、真空负压和胶粘背筋的成形方法。建立了该成形过程的有限元模型,并利用接触算法实现了该过程的数值仿真。研究发现蒙皮开缝后能有效降低蒙皮内的应力水平。面板回弹引起背筋的不均匀变形是面板成形误差产生的主因。分析了面板形面曲率、蒙皮开缝长度和背筋高度等面板结构参数对面板成形精度的影响规律,为合理设计该工艺过程和提高面板的成形质量提供了重要依据。     

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。     

A new approach for bending analysis of thin circular plates with large deflection

This paper is concerned with bending analysis of an axisymmetric simply supported circular plate with large deflection. Based on the linear theory of thin plates, the incremental load technique is developed for solving the bending problem of a thin circular plate with large deflection. In the proposed method, the total applied load is divided into various small load steps. In each load step, the plate stress behavior is simplified to be linear. The incremental formulations are presented for the deflection and stresses of the plate when external loads increase. A numerical example is given to show simplicity and accuracy of the present method. It is found that the proposed method can be an alternative useful tool for engineering applications.     

Analysis of reinforced or cellular panels and decks

A popular and efficient design for lightweight structural decks, floors, roofs and wall panels consists of a flat plate reinforced by and composite with one or two sets of ribs. A variation of the reinforced plate is the so-called cellular construction comprised of two membranes connected to ribs to from a discrete core sandwich structure. Until recently, no rational methods were available for the stress and deflection analysis of these structures. This paper presents formulas for the exact elastic analysis of late- tringer- iaphragm decks (composite stringers and non-composite diaphrams) and waffle decks (stringers and diaphrams both composite) which are rectangular with simple end and flexible side supports. Cellular construction is dealt with by creating a condition of anti-symmetry with respect to the middle plane. The formulas are derived by finding closed form solutions to the summation equation mathematical models which were written by use of a macro discrete field approach. The formulas are numerically illustrated through use of a simple programmable pocket calculator which is judged suitable for design office use and optimization studies. The examples permit comparisons between the single plate and cellular P-S-D panels and waffle plates.     

A composite view on Windenburg's problem: Buckling and minimum stiffness requirements of compressively loaded orthotropic plates with edge reinforcements

This paper discusses the buckling behaviour of orthotropic composite plates under uniform uniaxial compression with one free reinforced unloaded edge. A typical application example for use of such a mechanical model is the web of stiffeners and frames attached to the fuselage skin of an aircraft. The considered plates are rectangular and simply supported at the loaded transverse edges. One of the longitudinal unloaded edges is also simply supported, while the second unloaded edge is not supported at all but is reinforced by a flange of arbitrary cross-section. At first, an exact solution for the elastic buckling problem is derived from the governing differential equation by imposing the underlying boundary conditions. Thereafter, two approximate closed-form solutions for the buckling load are derived, which can be conveniently used for practical application purposes. Generic buckling curves using characteristic non-dimensional quantities are also presented. Finally, the question of the required bending stiffness EI_min of the flange is treated, to ensure that the flange withstands buckling and provides simply supported boundary conditions to the free reinforced plate edge.     

FE analysis of unstiffened and stiffened corrugated panels subjected to blast loading

This paper presents the results of a dynamic analysis on unstiffened and stiffened corrugated panels subjected to hydrocarbon explosion. A parametric study is also conducted on simplified models of the stiffened corrugated panels considering the effect of stiffeners on the compressive flange under different loading levels. The 1/2 symmetry of corrugated panels is modeled. This numerical study is performed using NX Nastran version 7.5. The unstiffened panel produces localized buckling at the center of corrugation and large permanent deformation by increasing the peak pressure. The stiffened panels suppress the structural response, and the vee stiffeners are structurally more effective than the round ones.     

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.     

Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates

This paper presents analytical solutions of deflection and stress for orthotropic plates using a two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor. Additional features of the theory are that it has strong similarity with classical plate theory in many aspects, and the number of involved variables is only two as against three in case of other shear deformation theories. The Levy-type solution procedure in conjunction with the state space concept is used to determine the closed-form solutions for orthotropic rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are performed to verify the validity of the present results. Finally, the effects of thickness ratio, modulus ratio and aspect ratio on the deflection and stress of orthotropic plates are investigated and discussed.     

不同螺栓预紧力的水轮机顶盖及螺栓的静应力分析

使用ANSYS有限元软件建立了某电站轴流式水轮机顶盖及螺栓的模型,研究了不同预紧力工况下顶盖及螺栓的变形和应力分布。结果表明:顶盖应力梯度较大处主要存在于于内顶盖上盖板、内外顶盖法兰螺栓把合处以及开孔两端,螺栓同时承受轴向荷载和弯矩的作用,螺栓横截面应力存在不均匀性;顶盖局部应力与预紧力敏感性比较弱,螺栓应力变化敏感,螺栓预紧力的敏感性依次为变化相对短筋板、上盖板、长筋板。     

Elastic tripping analysis of corroded stiffeners in stiffened plate with irregular surfaces

Tripping of stiffeners is one of the buckling modes of stiffened panels which could rapidly lead to its catastrophic failure. Loss of thickness in the web and flange of stiffeners due to corrosion reduces elastic buckling strength. It is common practice to assume a uniform thickness reduction for corroded surfaces. To estimate the remaining strength of a corroded structure, a much higher level of accuracy is required since corroded surfaces are irregular. Finite element method is employed to analyze elastic tripping stress of corroded stiffeners with irregular surfaces. Comparing the results with elastic tripping stress of un-corroded stiffener, a reduction factor is introduced. It is found that for flat-bars and angle-bars the reduction factor increases by increasing corrosion loss; however, for tee-bars remains almost unchanged. Surface roughness has no significant effect on reduction of tripping Euler stress of angle-bars and flat-bars; however, it has an effect on reduction of tripping Euler stress of small flat-bars. For high values of corrosion loss, reduction of tripping Euler stress is higher in flat-bars than angle-bars. Corrosion at the mid-length or ends of flat-bars is more detrimental than full length. Corrosion at the ends of angle-bars is more detrimental than full length and mid-length.     

A post-buckling analysis for isotropic prismatic plate assemblies under axial compression

This paper presents a post-buckling analysis for prismatic plate assemblies made of isotropic materials. The structures are assumed to consist of a series of long flat strips rigidly connected together at their edges, subjected to longitudinal in-plane compressive load. The buckling load and corresponding buckling mode of the structure are first obtained as the results of transcendental eigenvalue problems, which arise when exact solutions to the member differential equations are used to form the stiffness matrix of the plate assemblies. The other post-buckling field functions are also obtained analytically as exact solutions to the member differential equations. Results for the load end-shortening and load–deflection relationships for long prismatic plate assembly examples are obtained and compared with results obtained by other authors.