Elastic buckling analysis of perforated thin-walled structures by the isoparametric spline finite strip method

This paper presents the application of the isoparametric spline finite strip method to the elastic buckling analysis of perforated folded-plate structures. The general theory of the isoparametric spline finite strip method is introduced. The kinematics assumptions, strain–displacement and constitutive relations of the Mindlin plate theory are described and applied to the spline finite strip method. The corresponding matrix formulation is utilised in the equilibrium and stability equations to derive the stiffness and stability matrices. A number of numerical examples of flat and folded perforated plate structures illustrate the applicability and accuracy of the proposed method.     

Linear elastic isoparametric spline finite strip analysis of perforated thin-walled structures

This paper describes the application of the isoparametric spline finite strip method to the linear elastic analysis of tri-dimensional perforated folded plate structures. The general theory of the isoparametric spline finite strip method is introduced. Kinematics assumptions and the procedure for combining in-plane (membrane) and bending effects are set out. Particular attention is paid to the procedure for rotating the stiffness matrix and load vector from local to global coordinates. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square stiffened perforated plates in compression and bending are analysed.     

Free vibration and stability analysis of shells by the isoparametric spline finite strip method

The isoparametric spline finite strip method has been applied to the free vibration and stability analysis of shells. The convergence of the method is reviewed critically. Additional numerical examples on shells of different geometry are also employed to demonstrate the efficiency, accuracy and versatility of the method.     

Dynamic analysis of partially prismatic thin-walled structures

A mixed-mode method is investigated for the dynamic analysis of partially prismatic structures, such as box girders with intermediate diaphragms and supports, or with variable-depth webs. Thus the prismatic ‘main structure’ is discretised by finite strips, and the non-prismatic ‘sub-structure’ by finite elements. After dynamic reduction of the finite element degrees of freedom, advantage may be taken of the finite strip harmonic expansions in determining mode shapes. The method is tested by a variety of examples. Thus for structures with transverse substructures (e.g. diaphragms), the method is shown to be successful, being up to an order of magnitude faster than finite elements. However, for structures with longitudinal substructures (e.g. variable-depth webs) the method is shown to be unreliable. This is because for such structures, approximations in the dynamic reduction procedure are found to be significant.     

Analysis of shallow shells by spline finite strip method

A spline finite strip method is presented in this paper for the analysis of shallow shell structures. It makes use of β₃-splines and conventional shape functions to describe the displacement field of strips. Based on Vlasov's shallow shell theory, the stiffness and load matrices are derived in accordance with the standard finite element procedure. Numerical examples are given and compared with other available solutions. In all cases, good agreement is observed.     

Inelastic initial local buckling of skew thin thickness-tapered plates with and without intermediate supports using the isoparametric spline finite strip method

In this paper, skew isotropic plates subjected to in-plane loadings are analyzed using a stability analysis based on the isoparametric spline finite strip method, which includes inelasticity. Using this method, the initial inelastic local buckling of skew plates with or without intermediate line supports is studied based on Ramberg–Osgood representation of the stress–strain curve using the deformation theory of plasticity. Stiffness and stability matrices are formulated by energy expressions using the small deflection theory. The effect of tapered section on the local buckling of skew plates is taken into account. Finally, the inelastic local buckling loads of these plates are obtained and the results are compared with known solutions in the literature.     

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Numerical investigations

The theoretical developments of a material inelastic and geometric nonlinear analysis by use of the isoparametric spline finite strip method (ISFSM) are presented in a companion paper (Yao and Rasmussen (submitted) [1]). In the present paper, the numerical implementation of the analysis is reported, including nonlinear solution techniques, inelastic material models, selective reduced integration strategies, convergence criteria, and solution procedures. The reliability and efficiency of the method are demonstrated by a number of numerical examples, including analyses of flat plates with different material plasticity models, a classical nonlinear shell problem, perforated flat and stiffened plates, and perforated stiffened channel section storage rack uprights.     

箱梁剪力滞分析的样条有限点法

主要采用样条有限点法分析箱梁剪力滞,并结合试验比较了样条有限点法和有限元法分析箱梁剪切滞的结果,表明采用样条有限点法分析箱型结构简洁有效。     

用三次B样条进行旋转壳有限元分析

本文成功地应用三次B样条对旋转壳进行了静力有限元分析。在本法中,壳体中面一点位移的三个分量及子午线方向的几何形状均用以三次B样条为基样条的样条函数来逼近。同一般的有限元分析相比较,本法具有多项式次数低、自由度少而连续性强、精确度高,计算速度快,内存小,方便经济等优点。     

非协调四结点平面等参位移元新列式方法

本文导出一种等参协调元位移函数的新的表示方法,在此基础上建立起了构造等参非协调元的新方法。作为实例,构造两个可以给出单刚显式的四结点平面非协调新单元。     

A study on the structural analysis for structural synthesis of substructures

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed–free and free–free end elements. The flexibility and stiffness matrices of the free–free end elements are the Moore–Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of a complete structure composed of two mixed types of substructures. This study provides a general form to express equilibrium equations of the entire structure by combining the equilibrium equation of each substructure and compatibility conditions. Applications demonstrate that the proposed method is effective and simple. Copyright © 2005 John Wiley & Sons, Ltd.     

Buckling optimization of variable thickness prismatic folded plates

This paper deals with the structural shape optimization of prismatic folded plates under buckling load consideration. Buckling loads are determined using linear, quadratic and cubic, variable thickness, C(0) continuity, Mindlin-Reissner finite strips. The whole structural optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, semi analytical sensitivity analysis and mathematical programming algorithm. The objective is either the maximization of the critical buckling load or minimization of the cross-section of the prismatic folded plate with constraints on the volume and buckling loads. Several examples are included to illustrate various features of the optimization algorithm, including plates and stiffened panels.     

Post-local-buckling of fiber-reinforced plastic composite structural shapes using discrete plate analysis

In this paper, post-buckling of rectangular composite plates rotationally restrained at the longitudinal unloaded edges and subjected to end shortening strain at the simply-supported loaded edges is analyzed using the first-order shear deformation plate theory-based spline finite strip method, and its application to post-local-buckling of fiber-reinforced plastic (FRP) composite structural shapes is illustrated with discrete plate analysis. Two cases of elastically- and rotationally-restrained plates are analyzed using the spline finite strip method: rotationally-restrained along both the unloaded boundary edges (RR) and one rotationally-restrained and the other free along the unloaded edges (RF). The two cases of rotationally-restrained plates (i.e., the RR and RF plates) are further treated as the discrete plates of closed and open section FRP shapes, and by considering the effect of elastic restraints at the joint connections of flanges and webs, post-local-buckling of various FRP shapes under end shortening is studied. The numerical comparisons with the finite element modeling demonstrate that the proposed discrete plate analysis technique and spline finite strip method can be used as an efficient and valid tool for post-local-buckling analysis of FRP shapes.     

板弹性自由振动的等参元分析

根据Mindlin板理论，推导了板的八结点等参单元的广义质量矩阵，采用有限元方法对弹性板的自由振动进行了数值分析，考察了板的边界条件及厚度对板的自振频率的影响，研究了板的振动模态，分析结果与P-里兹法的结果相当接近，证明了该方法的准确性和有效性。     

考虑翘曲变形的复合材料叠合梁几何非线性的有限元分析

提出了一个用于复合材料叠合梁结构分析的有限元模型,梁结构具有几何非线性性能,包括扭转翘曲变形。采用一个考虑了改进拉格朗日法和广义位移控制法的公式对结构的变形进行计算。采用二次等参有限单元对梁横截面进行离散化,以确定梁的弯扭特性。利用两结点的Hermitean三维有限梁元对结构进行离散化,其中每结点具有7个自由度。运用数个实例,分析了层的取向对结构性能的影响。     

Vibrational analysis of point-coupled structures

Vibration Analysis of systems with beam components is performed. A previously developed method called Internal Loading Decomposition is applied to this particular configuration. A beam is used as the master structure to which are added one or more substructures. The method is assessed for several variations of this configuration using finite element analysis. Numerical examples demonstrate how the method can be advantageously applied to analyze periodical structures. Finally, a sensitivity study is performed to illustrate the effect of compliance uncertainties on the vibrational response.     

Plate bending analysis by unequally spaced splines

A cubic B-spline finite strip method (BFSM) is developed to analyze thin plates in bending. The basic mathematical relationships are derived for a direct stiffness formulation using a series type strip displacement function. Longitudinal behavior is modeled by a spline series in which unequal spline spacing is permitted. This feature allows local refinement of the discretization near patch and concentrated loads. Accuracy and convergence vis-à-vis alternative methods are compared. These include various finite element models, the conventional finite strip method and the BFSM with equally spaced splines. Comparisons show comparable accuracy with improved convergence. Oscillatory convergence due to Gibb's phenomenon, evident in some of the models, is avoided in the BFSM.     

Analysis of 2-D Steady Incompressible viscous Flow on Microcomputers Via Vorticity-Streamline Mixed Finite Elements

A mixed, isoparametric finite element model for analysis of two-dimensional, steady, incompressible Newtonian flows for a microcomputer has been developed. An ad hoc mixed variational principle, in terms of vorticity ω and streamline φ functions, has been used in the finite element formulation. The six-node, isoparametric element has been employed in the computer program VISFLOW-2D which uses the newton-Raphson method to perform the nonlinear analysis. Computed ω and φ functions over a given domain are then used by the computer program PRESS-2D, to calculate the pressure distribution. The unsymmetric frontal solver is used to solve the linearized equations in ω-φ formulation and the symmetric frontal solver in the pressure formulation. A postprocessor has also been developed to plot the contours for ω, φ, and p, called CONT. This program splits each deformed or undeformed six-node, isoparametric element into 16 three-node triangular elements and computes the nodal values for the resulting elements before a linear interpolation is employed for plotting a contour. The procedure for analysis of steady, two-dimensional, incompressible viscous flow was then used to solve the problem of flow around a cylinder on a microcomputer.     

建筑结构混合试验平台HyTest开发研究

拟动力试验是一种重要的结构抗震联机试验方法,近年来出现了网络化、有限元化和实时化的趋势,形成了混合试验方法。鉴于混合试验分支多样,涉及数值分析、加载设备与控制等多个学科,为了方便试验的实施与技术的发展,迫切需要使用混合试验平台。为此开发了建筑结构混合试验平台HyTest,能够实现全结构拟动力试验、传统子结构拟动力试验、本地及分布式的基于静力子结构的混合试验和基于动力子结构的P2P混合试验。试验平台采用MTS二次开发编程库VB-COM连接试验控制系统,还可以调用有限元软件OpenSEES和ABAQUS进行数值子结构的分析。为了开展分布式的混合试验,该平台采用Socket通讯机制实现子结构间的数据传输,并采用带中转服务器的通讯模式,解决不同局域网之间的数据传输问题。利用该平台完成了6自由度单层单跨钢框架混合试验,验证了该试验平台的有效性。     

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Analytical developments

This paper presents the analytical developments of the application of the Isoparametric Spline Finite Strip Method (ISFSM) to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures. The general theory of the ISFSM is briefly introduced. The formulations of the kinematics, strain–displacement and constitutive assumptions are presented, and the tangential stiffness matrix is derived by applying the incremental equilibrium condition. The requirements for strip continuity and boundary conditions are also discussed. In particular, the plasticity theory and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted. The present isoparametric spline finite strip analysis is verified against a number of analyses of perforated and non-perforated plates and plate assemblages, as described in the companion paper (Yao and Rasmussen, submitted for publication) [1], demonstrating its accuracy and efficiency for the predictions of the inelastic post-buckling behavior of perforated thin-walled steel structures.