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.     

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.     

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.     

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.     

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.     

Static and free vibration analysis of variable-depth bridges of arbitrary alignments using the isoparametric spline finite strip method

The isoparametric spline finite strips for shells are employed to solve static and free vibration problems of variable-depth bridges of arbitrary alignments. Using this approach, a continuous bridge is first split up into substructures. Each substructure is modelled as an assemblage of isoparametric spline finite strips. Compatibility between substructures is ensured by suitable transformation at the interface. The presence of support diaphragms and bearings can also be accounted for. This method retains the computational efficiency of the spline finite strip method while it is much more flexible in geometric modelling. Solutions of this method are compared with other available solutions, and good agreement is observed.     

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.     

Buckling of thin flat-walled structures by a spline finite strip method

A method of buckling analysis of thin flat-walled structures of finite length subjected to longitudinal compression and bending, transverse compression as well as shear is described. The analysis uses the spline finite strip method and allows for boundary conditions other than simply supported ends as required in the semi-analytical finite strip method of buckling analysis.Convergence studies with increasing numbers of section knots are described for plates in compression, bending and shear, and for long columns with different support conditions subjected to compression. A buckling analysis of a stiffened plate subjected to compression and shear is compared with results from a finite element analysis.     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

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.     

Spline FSM postbuckling analysis of shear-deformable rectangular laminates

A spline finite strip method is developed for the prediction of the geometrically non-linear response of rectangular, composite laminated plates to progressive in-plane loading. The development takes place within the context of the use of the first-order shear deformation plate theory and the non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumption. A number of applications of the new capability is described, involving laminates subjected to progressive uniform end shortening and to progressive in-plane shearing. In all the applications a close comparison of the finite strip results with independent finite element results is demonstrated.     

Inelastic restrained distortional buckling of continuous composite T-beams

This paper develops a method of inelastic buckling analysis of thin-walled sections to study buckling characteristics of single span and two-span composite T-section beams in the inelastic range of structural response. The method is based on a bubble-augmented spline finite strip method, developed elsewhere by the authors, and confirmed as both accurate and efficient for the elastic buckling analysis of thin-walled structural members and plates. The method admits both flexural and membrane buckling deformations and it allows for consideration of structures with intermediate supports and a variety of boundary conditions that may be prescribed at the ends of plate assembly. The analysis includes the so-called Tendon Force Concept developed at Cambridge University for residual stresses caused by the process of fabrication, and the non-linear stress-strain properties of the structural steel from which the joist section is made. The inelastic restrained distortional buckling (RDB) of continuous composite T-section beams under transverse loading and moment gradient is investigated, and conclusions are drawn that address the influence of geometry, residual stresses, member length, the rigid restraint provided by the concrete and the degree of reinforcement in the concrete element.     

基于扁壳理论的半解析有限条法用于冷弯构件的屈曲分析

提出了一种基于Marguerre的扁壳理论的有限条法。现有的大多数半解析有限条法都是基于基尔霍夫和Mindlin的板理论。在本文中,该板理论可以被视为扁壳理论的特殊情况。数值分析结果证实了基于扁壳理论的有限条法的有效性。     

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.     

样条有限条子结构法在板式结构分析中的应用

将样条有限条法与子结构法相结合，构造成样条有限条子结构法，并将板式结构中几种放线连结方式统一表示．使之适用于各种连结条件的板式结构．通过对薄板和装配式桥梁的数值计算表明．本法可灵活处理各种边界条件、集中荷载及突变荷载情况．能大幅度降低内存．提高运算速度．     

Elastic local buckling of perforated webs of steel cellular beam-column elements

In this study, the finite element method is employed to determine the critical in-plane longitudinal load at which elastic local buckling of the web of cellular beam-column elements occurs. To simplify the simulation of the problem, the interaction between the flanges and perforated web is approximated by modelling the web only as a long plate having aspect ratio (L/h_w≥10) with multiple circular perforations. The utilized model incorporates restrained out-of-plane displacements along the four edges of the plate. Analyzed plates are subjected to linearly varying in-plane loads to simulate various combinations of axial and flexural stresses. The effect of different geometrical parameters on the elastic buckling load of perforated web plate is investigated. These geometrical parameters include the plate’s length and width, and the perforations’ diameter and spacing. Comprehensive finite element analyses are conducted to identify the behaviour of wide spectrum of perforated web plates at buckling under various combinations of axial compressive load and bending moment. Outcomes of the study are expected to enhance the understanding of the elastic local buckling of web plates of cellular beam-column elements.     

Ultimate strength of perforated steel plates under edge shear loading

The aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under edge shear loading, which is a primary action type arising from cargo weight and water pressure in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges and kept straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the cutout size (diameter) as well as plate dimensions (plate aspect ratio and thickness). By the regression analysis of the FEA results obtained, a closed-form empirical formula for predicting the ultimate shear strength of perforated plates, which can be useful for first-cut strength estimations in reliability analyses or code calibrations, is derived. The accuracy of the ultimate strength formula developed is verified by a comparison with more refined nonlinear FEA results.     

Ultimate strength of perforated steel plates under combined biaxial compression and edge shear loads

The present paper is a sequel to the author's papers [Paik JK, Ultimate strength of perforated steel plates under edge shear loading. Thin-Walled Structures 2007; 45: 301–6, Paik JK Ultimate strength of perforated steel plates under axial compressive loading along short edges. Ships Offshore Struct, 2007; 2(3): (in press)]. In contrast to the previous papers with the focus on edge shear or uniaxial compressive loads, the aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under combined biaxial compression and edge shear loads, which is a typical action pattern of steel plates arising from cargo weight and water pressure together with hull girder motions in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges, keeping them straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the plate dimension (thickness). Based on the FEA results obtained, closed-form empirical formulae of the ultimate strength interaction relationships of perforated plates between combined loads, which can be useful for first-cut estimations of the ultimate strength in reliability analyses or code calibrations, are derived.     

绕弱轴纯弯的冷弯薄壁型钢构件畸变屈曲性能研究

采用有限条软件CUFSM对不同截面几何参数的冷弯薄壁卷边槽钢绕弱轴纯弯进行畸变屈曲应力计算,并根据经典板件屈曲应力公式计算构件翼缘畸变屈曲系数,分析构件截面几何参数的变化对畸变屈曲系数的影响,在此基础上,提出适用于求解直卷边槽钢绕弱轴纯弯畸变屈曲应力的简化公式。与有限条法和基于广义梁理论的横向弯曲铰支计算模型的计算公式进行对比,所提出的公式具有较高精度,且简单实用、便于手算,建议公式可供工程设计和修订规范参考。