薄板的高阶振动

对薄板的高阶振动进行了讨论。应用模型基于Kirchhoff平板理论的假定和公差平均值的假定[Wo■ niak Cz,Wierzbicki E.Averaging techniques in thermomechanics of composite solids.Tolerance averaging versus homogenization.Poland,Czestochowa:Czestochowa University of Technology;2000],这使得模型可以考虑到周期单元对于整块板性能的影响。假设对周期单元振动的影响参数过多,可以对模型进行比基本振型更高阶的振动分析。这些函数是通过从边界条件中分离周期单元,对其自振时的特征值方程分析选取的近似值[JedrysiakJ.On vibrations of thin plates with one-dimensional periodic structure.Int J Eng Sci 2000;38:2023-2043]。通过应用平面板模型-正交各向异性模型、有限元模型和离散模型,对提议模型进行了论证。     

Tolerance modelling of vibrations of thin functionally graded plates

A problem of a modelling of vibrations of thin plates with a functionally graded macrostructure and a tolerance-periodic microstructure in planes parallel to the plate midplane is analysed. The proposed model, based on the Kirchhoff plate theory assumptions and additional hypothesis of the tolerance averaging technique [Wo?niak et al., editors. Thermomechanics of heterogeneous solids and structures. Tolerance averaging approach. ?ód?, University Press, Technical University of ?ód?; 2008], describes the effect of the microstructure size on dynamic behaviour of the plate. In this paper, as an example there are analysed free vibration frequencies of a functionally graded plate band. These frequencies are obtained in the framework of two proposed models—the tolerance model and the asymptotic model, using the known Ritz method.     

The tolerance averaging model of dynamic stability of thin plates with one-directional periodic structure

A dynamic stability of thin plates with one-directional periodic structure is investigated. An averaged non-asymptotic approach, called the tolerance averaging, is applied to derive governing equations of these plates. Obtained tolerance model equations of the Kirchhoff-type plate take into account the effect of the period lengths on the overall plate behaviour [Jędrysiak J. Dispersive models of thin periodic plates. Theory and applications. Sci. Bul. Łódź Tech. Univ., No. 872, series. Sci Trans 289, Łódź, 2001 [in Polish]]. It is shown that this effect plays a crucial role in some special cases of a dynamic stability of such plates.     

A non-asymptotic model for the stability analysis of thin biperiodic cylindrical shells

The object of considerations is a thin linear-elastic cylindrical shell with arbitrary cross-section having a periodic structure in both directions tangent to the shell midsurface. The aim of this paper is to propose a new averaged non-asymptotic model of dynamical stability problems for such shells. As a tool of modeling we shall apply the tolerance averaging technique, given for periodic structures in Woźniak and Wierzbicki [Averaging techniques in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, 2000]. In contrast with models obtained by means of asymptotic homogenization methods, the proposed one makes it possible to describe the effect of the period lengths on the global shell stability, called a length-scale effect.     

On the modelling of stability problems for thin plates with functionally graded structure

A conjunction of local apparent properties with a global design of structural elements is motivation for applying composites, which have space varying effective properties. This contribution deals with analysis of dynamics and stability problems for thin composite plates with a smooth and a slow gradation of macroscopic properties. The formulation of two mathematical models of these plates, based on a tolerance averaging technique, cf. Wo?niak et al. [18], is the aim of the paper. The general results are applied to the analysis of some special problems.     

Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model

A four-noded quadrilateral (PBQ4) and an eight-noded quadrilateral (PBQ8) plate bending element based on Mindlin plate theory are adopted for the analysis of thin and thick plates resting on elastic foundation using modified Vlasov model. The terms of vertical deflection stiffness matrix and shear deformation stiffness matrix of the subsoil are evaluated using finite element method, and presented in explicit forms. Selective reduced integration technique is used in addition to full integration technique for both the types of the elements to avoid shear-locking problem that occurs under the thin plate limit. It has been demonstrated that the performance of the eight-noded quadrilateral element is excellent for thin and thick plates on elastic foundation when selective-reduced integration technique is used. General conclusion can be drawn from the results that the effect of the shear strain on the behavior of the plate resting on subsoil is always quite small for free plates compare to the supported ones.     

Periodicity in the response of nonlinear plate, under moving mass

The dynamics of nonlinear thin plates under influence of relatively heavy moving masses is considered. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development of vibration amplitude, which is Duffing's oscillator with time varying coefficients. Through the application of Banach's fixed-point theorem, the periodic solutions are predicted. The method presented in this paper is general so that the response of plate to moving force systems can also be considered.     

Inelastic local buckling of curved plates with or without thickness-tapered sections using finite strip method

This paper addresses the inelastic local buckling of the curved plates using finite strip method in which buckling modes and displacements of the curved plate are calculated using sinusoidal shape functions in the longitudinal direction and polynomial functions in the transverse direction. A virtual work formulation is employed to establish the stiffness and stability matrices of the curved plate whilst the governing equations are then solved using a matrix eigenvalue problem. The accuracy and efficiency of the proposed finite strip model is verified with finite element model using ABAQUS as well as the results reported elsewhere while a good agreement is achieved. In order to illustrate the proposed model, a comprehensive parametric study is performed on the steel and aluminium curved plates in which the effects of curvature, the length of the curved plate as well as circumferential boundary conditions on the critical buckling stress are investigated. The developed finite strip method is also used to determine the buckling loads of the curved plates with thickness-tapered sections as well as critical stresses of the aluminium cylindrical sectors that are subjected to uniform longitudinal stresses.     

基于改进Vlasov模型的弹性地基上平板横向剪应变分析

运用Vlasov模型对弹性基础上的薄板和厚板进行分析,采用了基于Mindlin板理论的4结点四边形和8结点四边形弯曲单元。运用有限元法对底层土的竖向挠度刚度矩阵和剪切变形刚度矩阵进行推算。针对2种类型的板单元,采用完全积分方法和选择性简化积分方法进行分析,以避免极限状态下薄板的剪切闭锁问题。研究发现：在选择性简化积分方法中,8结点四边形板单元非常适用于分析弹性基础上的薄板和厚板。结果表明：相比有支撑的平板,剪应变对底层土上无支撑平板的影响非常小。     

Free vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

The free vibration analysis of cracked thin plates via a quasi-convex coupled isogeometric-meshfree method is presented. This formulation employs the consistently coupled isogeometric-meshfree strategy where a mixed basis vector of the convex B-splines is used to impose the consistency conditions throughout the whole problem domain. Meanwhile, the rigid body modes related to the mixed basis vector and reproducing conditions are also discussed. The mixed basis vector simultaneously offers the consistent isogeometric-meshfree coupling in the coupled region and the quasi-convex property for the meshfree shape functions in the meshfree region, which is particularly attractive for the vibration analysis. The quasi-convex meshfree shape functions mimic the isogeometric basis function as well as offer the meshfree nodal arrangement flexibility. Subsequently, this approach is exploited to study the free vibration analysis of cracked plates, in which the plate geometry is exactly represented by the isogeometric basis functions, while the cracks are discretized by meshfree nodes and highly smoothing approximation is invoked in the rest of the problem domain. The efficacy of the present method is illustrated through several numerical examples.     

Static analysis of superelliptical clamped plates by Galerkin's method

In this study, clamped superelliptical plates under uniformly distributed surface load are statically analyzed. Linearly elastic, homogeneous, and isotropic material is considered. The classical thin plate model (Kirchhoff) is employed. The lack of contributions on the static behavior of this sort of plate shapes is the fundamental motivation of the current study. Galerkin's method is used to obtain solutions. The method is conducted for polynomial series at powers ranging from 2 to 8 in order to get converging solutions. Maximum deflections of the plates and mid-point moments are obtained and the results are arranged in tabular form. For purpose of understanding, the behavior trend of the structure with respect to the parameters, some of the solutions are organized in graphical form. The study is performed for a wide range of superelliptical plates. The results are also examined with respect to the parameters a/b ratios and n, which are the plate aspect ratio and the superelliptical power, respectively.     

The effects of electro slag welding on material properties of box column plates

The effects of electro slag welding (ESW) on the material properties of box column plates, which is ASTM A572 Gr. 50 steel, were investigated experimentally and numerically. The material properties of the column plates before and after ESW were evaluated by macro-etching observation, micro-structural observation, and CVN impact tests. The temperature distribution of the column plates, with the ESW heat cycle as the heat input, was simulated by using the ANSYS FEM software. It was found that: (1) The CVN values in the through thickness direction of the base metal can be as low as 14J, 8.1J, and 8.1J at 0°C for plate thicknesses of 32, 40, and 50 mm respectively; (2) During the ESW process, the measured peak temperature for a 25×50 mm column plate surface was as high as 1033, 880 and 744°C for plate thicknesses of 32, 40 and, 50 mm respectively; (3) After the ESW heat cycle, the through thickness CVN value decreased by 68% for the coarse grain heat affected zone (HAZ) of the column pate; (4) The FEM thermal conduction model developed was able to simulate the temperature distribution of the steel plate during the ESW process with reasonable accuracy; (5) To avoid welding penetration due to ESW, a minimum plate thickness is suggested; (6) The impact of ESW heat cycle is more significant for thin column plates compared to thick ones.     

Seismic behavior of code designed steel plate shear walls

The AISC Seismic Design Provisions now include capacity design requirements for steel plate shear walls, which consist of thin web plates that infill frames of steel beams, denoted horizontal boundary elements (HBEs), and columns, denoted vertical boundary elements (VBEs). The thin unstiffened web plates are expected to buckle in shear at low load levels and develop tension field action, providing ductility and energy dissipation through tension yielding of the web plate. HBEs are designed for stiffness and strength requirements and are expected to anchor the tension field formation in the web plates. VBEs are designed for yielding of web plates and plastic hinge formation at the ends of the HBEs.This paper assesses the behavior of code designed SPSWs. A series of walls are designed and their behavior is evaluated using nonlinear response history analysis for ground motions representing different hazard levels. It is found that designs meeting current code requirements satisfy maximum interstory drift requirements considering design level earthquakes and have maximum interstory drifts of less than 5% for maximum considered earthquakes. Web plate ductility demands are found to be significantly larger for low rise walls than for high rise walls where higher modes of vibrations impact the response. The percentage of story shear resisted by the web plate relative to the boundary frame is found to be between 60% and 80% and is relatively independent of panel aspect ratio, wall height, or hazard level, but is affected by transitions in plate thickness. Maximum demands in VBEs in design level shaking are found to be considerably less than those found from capacity design for SPSWs with 9 or more stories.     

Behavior of thin gusset plates in compression

The use of cold-formed steel members for roof and floor truss applications is gaining widespread acceptance in the United States. However, there is little technical information regarding the behavior and design of thin gusset plates in compression. Thus, a study was initiated at the University of Missouri-Rolla aimed at investigating the behavior of thin steel gusset plates in compression. Key parameters that were considered in the experimental study were the thickness of the gusset plate, the width and length of the gusset plates, the fastener location, and the fastener pattern. Both a plate model and a column model were investigated for computing the strength of a thin plate in compression. Based on the findings of this study, design recommendations are proposed.     

Application of spline finite strip method in the analysis of space structures

The spline finite strip based on the thin plate theory has been demonstrated to be a versatile tool for the analysis of plates and shells. Applications of this method to the analysis of prismatic space structures have also been reported. This paper attempts to extend the method to the analysis of non-prismatic space structures. In the analysis, the plates that form the space structures are treated as flat shells. The Mindlin plate theory is adopted to model the bending action of the plate, and the in-plane action is modelled in the usual manner. The present formulation, which requires only C° continuity for the displacement interpolation functions, allows greater flexibility in the geometry of the structures. The accuracy and versatility of the method are also demonstrated by numerical examples.     

Free vibration analysis of circular thin plates with stepped thickness by the DSC element method

Novel formulation is presented by using the discrete singular convolution (DSC) for free vibration analysis of circular thin plates with uniform and stepped thickness. Different from the commonly used ones in literature, regularity conditions are not needed at the circular plate center point to avoid singularity. DSC circular and annular thin plate elements are established. For the DSC circular plate element with radius of R₁, the stiffness equation is first formulated in region [−R₁, R₁] with even number of nodes and then reduced to region [0, R₁] by using either symmetric or anti-symmetric conditions. The proposed DSC circular and annular plate elements are used for obtaining frequencies of uniform/stepped circular thin plates or annular thin plates with different boundary conditions. Comparison of the present DSC results to existing analytic and numerical solutions verifies the proposed formulations. The present research extends the DSC method to free vibration of circular thin plates with stepped thicknesses.     

两边连接薄钢板剪力墙加固损伤RC框架结构抗震性能

为了提高损伤RC框架的抗震性能,采用两边连接薄钢板剪力墙对其进行加固.通过2个1/3缩尺比单跨2层两边连接薄钢板加固损伤RC框架的低周往复加载试验,对其抗震性能进行了研究,并与未损伤RC框架试验结果进行对比分析.结果 表明:设置两边连接钢板剪力墙,可显著提高损伤RC框架的承载力、抗侧刚度和延性;加固后的结构钢板剪力墙屈...     

Modified continuity conditions of plates in beam-column using the Mindlin plate theory

In the present paper, two independent functions of displacements along the z axis direction, i.e., the total lateral displacement w and the bending deflection φ, have been introduced within the first order shear deformation plate theory FSDT. The differential equations of motion and boundary conditions have been derived from Hamilton's principle employing the classical Mindlin approach. Modified conditions of two adjacent component plate interactions have been formulated. A plate model of the plate structure has been adopted to describe all possible buckling modes. The obtained equations are approximate since the shear locking is not ignored but the boundary layer effect is neglected. A method of the modal solution to the buckling problem within Koiter's asymptotic theory has been used. The calculations have been conducted for a few beam-columns of various shapes of cross-sections. The obtained results that account for transverse shear deformation have been compared to the results attained for the classical thin plate theory.     

Buckling and post-buckling behaviour of rectangular plates under linearly varying compression and shear: part 1 — Theoretical analysis

The buckling and post-buckling behaviour of thin, rectangular, simply supported flat plates subjected to end compression which varies linearly in the direction of loading and simultaneously loaded in shear is the subject of this paper. Part 1 presents a theoretical analysis of the problem. In this analysis the Rayleigh-Ritz energy method is utilised, and numerical minimisation of the total potential energy is applied to obtain the magnitude of the parameters of the assumed deflection functions. These are then used to define and describe other post-buckling characteristics of the plate. A simplified imperfection analysis is used to examine certain cases. The wide range of results presented covers many aspects of plate post-buckling behaviour.     

Thin steel plate shear walls behavior and analysis

Steel plate shear walls have been used in buildings in North America and Japan. Until recently, the design practice has been to limit the strength of the wall to the buckling strength of the plate. The post-buckling strength of thin plates subjected to shear has been recognized for more than 60 years, since it was outlined by Wagner in the early 1930s. Tests of a quarter and one third scale specimens of thin steel plate shear walls under cyclic loading were performed; the tests are described and the results are summarized. An analytical model to determine the behavior of thin steel plate shear walls was developed and is given. The model is capable of depicting the behavior of walls with plates welded or bolted to the surrounding beams and columns of the building frame. Comparisons between the analytical and experimental results are made.