样条子域法计算折板问题

本文把样条子域法应用到折板结构中,采用三次B样条函数与满足边界条件的级数乘积作为折板的位移函数。应用最小势能原理,建立了折板结构分析的样条子域法。与通用有限元法及有限条法相比,本文方法具有精度高,未知数少,程序易于编制等优点,可在微型机及小型机上解决工程问题。文中给出数值例题,计算结果表明,该方法是十分有效的。     

Isoparametric spline finite strip method for the bending of perforated plates

The isoparametric spline finite strip method was recently applied by the authors to the linear elastic in‐plane stress analysis of perforated thin‐walled structures. In this paper, the application of the method is extended to the bending of perforated plates. The paper describes the theory of the isoparametric spline finite strip method in the context of Mindlin plate bending theory. It sets out the strain–displacement and stress–strain relationships and derives expressions for the local and global stiffness matrices. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square plates in bending containing openings of different shapes are analysed. Copyright © 2007 John Wiley & Sons, Ltd.     

条层法及其对板带轧制三维变形的仿真

提出一种模拟板带轧制过程三维变形的新的数值方法——条层法。首先沿高向将变形区均匀地划分为若干层,然后再沿着金属的流动轨迹将变形区内的每层带材划分为若干流线条元,为了方便分析和计算,又将流线条元映射为矩形条元。横向位移的纵向分布被构造为四次曲线,横向分布用三次样条插值函数表示,高向分布用二次曲线拟合。根据塑性力学流动理论,分析推导了变形区三维变形和应力的数学模型。与作者曾经提出的流线条元法相比,考虑了应力与变形沿高向的不均匀分布,实现了精确的三维分析和计算。关于热带钢连轧和厚板轧制的仿真实例表明,提出的方法和模型符合实际,为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。     

A spline strip kernel particle method and its application to two‐dimensional elasticity problems

In this paper we present a novel spline strip kernel particle method (SSKPM) that has been developed for solving a class of two‐dimensional (2D) elasticity problems. This new approach combines the concepts of the mesh‐free methods and the spline strip method. For the interpolation of the assumed displacement field, we employed the kernel particle shape functions in the transverse direction, and the B₃‐spline function in the longitudinal direction. The formulation is validated on several beam and semi‐infinite plate problems. The numerical results of these test problems are then compared with the existing solutions obtained by the exact or numerical methods. From this study we conclude that the SSKPM is a potential alternative to the classical finite strip method (FSM). Copyright © 2003 John Wiley & Sons, Ltd.     

Bending Analysis of Classical Symmetric Laminated Composite Plates by the Strip Element Method

A new formulation of strip element method based on classical laminated plate theory is derived for the bending analysis of laminated composite plates. In this method, an infinite-length plate is first considered and is discretized into a set of strip elements in the width direction. The principle of minimum potential energy is applied to obtain the ordinary differential equations, which are functions of only the coordinate in the length direction. These differential equations can then be solved analytically. The boundary conditions on the length coordinate direction are finally used to determine the deflection distribution in the plate. The strip element solutions are presented for a rectangular laminated composite plate with various boundary conditions and load cases. The solutions are compared with those of the Rayleigh-Ritz method, and very good agreement is obtained.     

Post-buckling behavior of composite laminated plates under end shortening and pressure loading, using two versions of finite strip method

Two different versions of finite strip method, namely spline and semi-analytical methods, are developed for analyzing the geometrically non-linear response of rectangular composite laminated plates of arbitrary lay-up to progressive end-shortening in their plane and to pressure loading. The plates are assumed to be thin so that the analysis can be carried out based on the classical plate theory. The in-plane lateral deflection υ is allowed at the loaded ends of the plate, whilst the lateral expansion of the unloaded edges is either free or completely prevented. Geometric non-linearity is introduced in the strain–displacement equations in the manner of the von Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the effects of pressure loading. The comparison between the two sets of results obtained by different finite strip methods is very good. The study of the results revealed that the response of the laminates is significantly influenced by the application of the normal pressure loading. Particularly, the response of unsymmetric laminates is strongly affected by the sign of the normal pressure loading.     

On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method

This paper augments bubble functions to the ordinary spline finite strip method in order to calculate the elastic local buckling coefficients of plates and plate structures. The results show that the use of bubble functions improves significantly the convergence of the spline finite strip method in terms of the strip subdivision, and therefore leads to smaller storage requirements for the global stiffness and stability matrices, and faster eigenvalue extraction. Benchmark numerical investigations are presented, including the study of plates with different boundary conditions under uniaxial and biaxial stresses, plates with different aspect ratios under shear, and a stiffened panel under combined shear and compression that has been studied elsewhere. These studies demonstrate that by implementation of the bubble functions, rapid convergence of the solution is obtained. The formulation is ideal for analysing local buckling under a variety of boundary and loading conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

Thin plate spline radial basis function for the free vibration analysis of laminated composite shells

In this paper, the free vibration characteristics of laminated composite cylindrical and spherical shells are analyzed by the first-order shear deformation theory and a meshless global collocation method based on thin plate spline radial basis function. The singularity of thin plate spline radial basis function is eliminated by adding infinitesimal to the zero distance. Several numerical examples are used to show convergence of the present method and choose the proper shape parameter. It is found that the natural frequencies computed by thin plate spline radial basis function with shape parameter m = 4 converge most rapidly. In the comparison study, the present results are in good agreement with the results of Reddy and Liu [8] and Ferreira et al. [21].     

复合材料层合板自由振动的薄板样条无网格解

无网格全局配点法分为多项式配点法和径向基函数配点法,国内外很多文献利用径向基函数配点法对复合材料层合板进行了分析。利用一阶剪切变形理论和基于薄板样条径向基函数的无网格配点法计算了复合材料层合板自由振动的固有频率和振型。研究了薄板样条径向基函数中形状参数的选取和本工作方法的收敛性。结果表明:形状参数m=3时收敛性最好,计算精度最高。将本工作计算结果与文献中的实验结果进行了对比,验证了本文方法的精度和效率。     

Buckling Analysis of Laminated Composite Plates Using Higher Order Semi—Analytical Finite Strip Method

Rectangular plates made of laminated composite material because of the advantageously high strength and stiffness to weight ratio are used frequently as structural component in various branches of engineering, chief of which are aerospace and marine engineering. Design concepts of these plates that lead to the increase in the buckling load can directly lower the structural cost and/or weight. The finite strip method is one of a number of procedures which can be used to solve the buckling problem of plate structures. In the present work the main concern is with the buckling behavior of plates with simply supported ends subjected to uni-axial pure compression loads. The solution is sought by implementing the higher order semi-analytical finite strip method which incorporates additional degrees of freedom for each nodal line by using Reddy’s higher order plate theory. Therefore the current method is more universal in dealing with different plate thicknesses. In addition, in this semi-analytical finite strip method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The solution is based on the concept of principle of minimum potential energy and an eigen-value analysis is subsequently carried out. From the presented results it can be concluded that the higher order semi-analytical finite strip method is very reliable for the preliminary design of composite plates especially in the case of buckling analysis of relatively thick plates.     

大宽厚比冷轧带材三维应力分布的样条有限条分析

本文在轧件宽厚比为６２５的条件下，用三次样条函数有限条法研究了冷轧带材三维应力的分布问题。获得了轧后边浪和中浪两种不同板形条件下的应力分布规律。对板形理论和板形控制技术的发展有指导意义。     

A method to correct coordinate distortion in EBSD maps

Drift during electron backscatter diffraction mapping leads to coordinate distortions in resulting orientation maps, which affects, in some cases significantly, the accuracy of analysis. A method, thin plate spline, is introduced and tested to correct such coordinate distortions in the maps after the electron backscatter diffraction measurements. The accuracy of the correction as well as theoretical and practical aspects of using the thin plate spline method is discussed in detail. By comparing with other correction methods, it is shown that the thin plate spline method is most efficient to correct different local distortions in the electron backscatter diffraction maps.     

Surface and internal cracks in a residually stressed plate

The problem of a surface or an internal crack in a plate which contains residual stresses is examined. The line spring model, which reduces a three-dimensional elasticity problem into a two-dimensional problem in plate theory, is used to model the crack. The Reissner plate theory, which takes into account transverse shear deformations, is used to model the plate. The formulation is based on Fourier Transforms which lead to a pair of singular integral equations that are solved numerically. The line spring method requires the plane strain solution to both the edge and internally cracked strip with crack surface loads representative of tension, bending, and the given residual stress distribution. For general use, plane strain solutions are presented for polynomial loading through the thickness up to the fifth order. Comparisons are made between the results given by the line spring model for the Reissner plate theory and the finite element method.     

Buckling and free vibration finite strip analysis of composite plates with cutout based on two different modeling approaches

A Reddy type, third order shear deformation theory of plates is applied to the development of two versions of finite strip method (FSM), namely semi-analytical and spline methods, to predict the behavior of the moderately thick plates containing cutouts. The internal cutouts are modeled based on two different modeling approaches, and the effects of cutouts on the buckling critical stresses as well as natural frequencies are investigated.     

Finite strip analysis of imperfect laminated plates under end shortening and normal pressure

The finite strip method is developed to predict the geometrically non-linear response of rectangular laminated plates subjected to progressive end shortening whilst initial imperfection and/or applied pressure loading are also present. The development is an extension of earlier work concerned with perfect, unpressurized laminates which have simply supported loaded ends at which lateral in-plane expansion is either allowed freely or is prevented completely. The analysis is conducted in the contexts of classical plate theory and first-order shear deformation plate theory, in turn. A number of applications involving both isotropic plates and laminated plates is described.     

The use of bubble functions for the post-local buckling of plate assemblies by the finite strip method

The finite strip displacement functions for post-local buckling are augmented with so-called bubble functions, which are extra modes associated with internal or nodeless degrees of freedom. A non-linear finite strip method of analysis including bubble functions is described for the post-local buckling of geometrically imperfect plate assemblies. It is shown that the use of bubble functions improves significantly the convergence of the method. The non-linear finite strip method is then used to study channel and I-section members in compression and bending.