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.     

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.     

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.     

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.     

Nonlinear vibration of thin plates with initial stress by spline finite strip method

The spline finite strip method and the incremental time–space finite element procedure are used to analyse large amplitude vibration of plates with initial stresses. Two improvements for the procedure are presented. The free vibration and the internal resonance of plates with initial stress as well as the forced vibration of plates with damping and initial stress are computed. The results compared favourably with those available in other publications.     

Inelastic buckling analyses of beams, columns and plates using the spline finite strip method

A method of inelastic buckling analysis of thin-walled structural members and plates is described. The method is based on the spline finite strip method of structural analysis. The analysis takes into account the non-linear material stress-strain properties, strain hardening and residual stresses. The plastic theories used in the study are the flow theory of plasticity and the deformation theory of plasticity. The method of inelastic buckling analysis is applied to a variety of instability problems including plates, cold-formed columns, hot-rolled columns and welded tee section beams. The buckling modes and loads computed are compared with theoretical values and test results.     

Geometric non-linear analysis of thin plate structures using the harmonic coupled finite strip method

The paper describes a modified finite strip method embracing the harmonic coupled Fourier series treatment. The well known uncoupled formulation, first developed in the context of thin plate bending analysis, represents a semi-analytical finite element process. As far as linear analysis is concerned, it takes advantage of the orthogonality properties of harmonic functions in the stiffness matrix formulation. However in the case of the geometric stiffness matrix calculation, the integral expressions contain the products of trigonometric functions with higher-order exponents, and here the orthogonality characteristics are no longer valid. All harmonics are coupled, and the stiffness matrix order and bandwidth are proportional to the number of harmonics used.     

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.     

Buckling analysis of thin-walled sections under localised loading using the semi-analytical finite strip method

Thin-walled sections under localised loading may lead to web crippling of the sections. This paper develops the Semi-Analytical Finite Strip Method (SAFSM) for thin-walled sections subject to localised loading to investigate web crippling phenomena. The method is benchmarked against analytical solutions, Finite Element Method (FEM) solutions, as well as Spline Finite Strip Method (SFSM) solutions. The paper summarises the SAFSM theory then applies it to the buckling of plates, and channel sections under localised loading. Multiple series terms in the longitudinal direction are used to compute the pre-buckling stresses in the plates and sections, and to perform the buckling analyses using these stresses. Solution convergence with increasing numbers of series terms is provided in the paper. The more localised the loading and buckling mode, the more series terms are required for accurate solutions. The loading cases of Interior One Flange (IOF) and Interior Two Flange (ITF) are investigated in this paper using simply supported boundary conditions.     

A general finite strip for the static and dynamic analyses of folded plates

In the conventional semi-analytical finite strip analysis of folded plates, the boundary conditions and the intermediate support conditions must be satisfied a priori. The admissible functions used as the longitudinal part of the displacement functions are sometimes difficult to find, and they are valid for specific conditions only. In this paper, a general finite strip is developed for the static and vibration analyses of folded plate structures. The geometric constraints of the folded plates, such as the conditions at the end and intermediate supports, are modelled by very stiff translational and rotational springs as appropriate. The complete Fourier series including the constant term are chosen as the longitudinal approximating functions for each of the displacements. As these displacement functions are more general in nature and independent of one another, they are capable of giving more accurate solutions. The potential problem of ill-conditioned matrices is investigated and the appropriate choice of the very stiff springs is also suggested. The formulation is done in such a way to obtain a unified approach, taking full advantage of the power of modern computers. A few numerical examples are presented for comparison with numerical results from published solutions or solutions obtained from the finite element method. The results show that this kind of strips is versatile, efficient and accurate for the static and vibration analyses of folded plates.     

The influence of bend–twist coupling on the shear buckling response of thin laminated composite plates

The finite strip method of analysis has been used in this paper to examine the effect of bend–twist coupling on the shear buckling behaviour of laminated composite constructions. The distorted nodal lines of the shear buckling mode and its complex deformation state in general are readily accounted for in the analysis procedure through the multi-term nature of the finite strip buckling displacement field and the appropriate level of structural modelling. The degree of bend–twist coupling in the laminated composite plates is varied by changing the level of anisotropy in the plies and by altering the lay-up configuration of the plies in the laminated stack. Symmetric laminates of a balanced and unbalanced nature are given consideration. It is shown that, for a given degree of anisotropy in the plies of a laminate and for a given laminate thickness, the stacking sequence of the plies significantly alters the degree of bend–twist coupling. The shear buckling performance of composite plates having the same dimensions and being made from the same material are therefore shown in the paper to be quite different. The preclusion of the bend–twist coupling coefficients in the solution procedure of the finite strip method allows the shear buckling orthotropic solution to be determined. Comparisons between the coupled and orthotropic solutions are shown in the paper to be markedly different.     

Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method

A new version differential quadrature method (DQM) has been proposed to obtain buckling loads of thin anisotropic rectangular and isotropic skew plates. The essential difference from the old version DQM is the introduction of two degrees of freedom for boundary points and from the existing differential quadrature element method (DQEM) is the determination of the weighting coefficients. The methodology is worked out in detail and a variety of buckling problems shown slow convergence earlier by Rayleigh-Ritz method with beam functions, including isotropic skew plates with various skew angles and anisotropic rectangular plates with simply supported or clamped boundary conditions, are solved by the proposed DQM. Numerical results indicate that fast convergence is achieved and excellent results are obtained by the proposed DQM.     

分块盖板屈曲约束钢板剪力墙受力性能与设计方法研究

为考察分块盖板屈曲约束钢板剪力墙的抗震性能,采用非线性有限元分析软件ABAQUS对其受力机理进行深入研究。将板墙的高宽比、盖板厚度比等参数作为变量,对屈曲约束钢板墙在水平往复荷载作用下的抗震性能进行分析,考察内嵌钢板面外变形与应力、盖板变形与钢筋应力。分析结果表明:采用非线性有限元数值模拟得到屈曲约束钢板剪力墙的滞回性能、内嵌钢板变形特性均与试验结果较为接近。分块盖板屈曲约束钢板剪力墙在层间位移角接近1/300时进入屈服;加载至层间位移角1/50时,滞回曲线接近于理想弹塑性。当盖板厚度比t_c/t_w不小于7时,可以形成对内嵌钢板面外变形的有效约束,钢板屈曲半波长度与钢板厚度之比λ/t_w基本保持不变。在此基础上,建立内嵌钢板与分块盖板简化计算模型,根据内嵌钢板主压应力推导出挤压应力计算公式,从而可以方便地确定对拉螺栓的内力与分块盖板的弯矩。简化计算方法与有限元数值模拟得到混凝土盖板弯矩的分布规律非常接近,简化计算方法偏于安全。     

A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution

An improved hybrid semi-analytical method for calculating elastic buckling load of a thin plate with a central straight through-thickness crack subject to axial compression is proposed. In the study, the actual non-uniform in-plane stress distribution is firstly conducted by using Muskhelishvili's complex variable formulation in conjunction with boundary collocation method. A deflection shape function, satisfying not only the outer boundary conditions but also the inner boundary conditions of the crack edges, is obtained by using domain decomposition method. Finally the buckling load of a cracked plate using Raleigh–Ritz energy method is calculated based on the actual in-plane stress distribution and the reasonable deflection shape function obtained. The effects of crack length, plate's aspect ratio are studied for thin plates with different boundary conditions. Results obtained from the proposed method are in good agreement with the existing numerical results and experimental ones. It is finally shown that the proposed method, based on a correct non-uniform in-plane stress distribution, is more accurate than the few existing analytical methods based on a uniform in-plane stress distribution.     

Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method

A nonlinear finite element (FE) model is developed to simulate two series of flexural tests, previously conducted by the authors, on industry standard cold-formed steel C- and Z-section beams. The previous tests focused on laterally braced beams with compression flange details that lead predominately to local buckling failures, in the first test series, and distortional buckling failures, in the second test series. The objectives of this paper are to (i) validate the FE model developed for simulation of the testing, (ii) perform parametric studies outside the bounds of the original tests with a particular focus on variation in yield stress and influence of moment gradient on failures, and (iii) apply the study results to examine and extend the Direct Strength Method of design. The developed FE model shows good agreement with the test data in terms of ultimate bending strength. Extension of the tested sections to cover yield stresses from 228 to 506 MPa indicates that the Direct Strength Method is applicable over this full range of yield stresses. The FE model is also applied to analyze the effect of moment gradient on distortional buckling. It is found that the distortional buckling strength of beams is increased due to the presence of moment gradient. Further, it is proposed and verified that the moment gradient effect on distortional buckling failures can be conservatively accounted for in the Direct Strength Method by using an elastic buckling moment that accounts for the moment gradient. An empirical equation, appropriate for use in design, to predict the increase in the elastic distortional buckling moment due to moment gradient, is developed.     

高强度等边角钢轴心受压局部稳定的有限元分析和设计方法研究

随着钢结构的发展,高强度热轧等边角钢在钢结构中的应用逐渐增多,如输电铁塔和大跨度桁架等。然而由于强度的提高,较多数量角钢截面的等效宽厚比超过规范的限值,不满足局部稳定的要求。我国现行规范尚未对这一问题给出明确规定。运用通用有限元软件ANSYS建立有限元模型,准确模拟构件的残余应力和几何初始缺陷,对15个高强度热轧等边角钢轴心受压构件的局部稳定受力性能进行有限元分析,并与相应的试验结果进行对比。比较结果表明,建立的有限元模型能够准确模拟几何初始缺陷和残余应力对构件局部稳定受力性能的影响,从而准确地分析计算高强度热轧等边角钢轴心受压构件的局部稳定受力性能。利用已验证的有限元模型,对高强度热轧等边角钢轴心受压构件的局部稳定受力性能进行有限元参数分析,并与美国规范和欧洲规范的设计方法进行对比。结果得到:几何初始缺陷和残余应力对于高强度热轧等边角钢轴心受压构件局部稳定承载力的影响比普通钢材受压构件小;美国钢结构设计规范能够更准确的计算Q420等边角钢轴心受压构件的局部稳定承载力。     

Application of the DSC-Element method to flexural vibration of skew plates with continuous and discontinuous boundaries

This paper generalizes the newly developed DSC-Element method for free vibration analysis of skew plates using the first-order shear deformable plate theory. Basically, the DSC-Element method not only embraces the discrete singular convolution (DSC) delta type wavelet kernel as a trial function with the Ritz principle, but also incorporates the concept of the finite element method. The current approach is novel and flexible as contrast to the global numerical methods in treating the complex kinematic supporting edges. The objective of this paper is to examine the efficiency and validity of the DSC-Element method for oblique plates having large skew angles. Parametric studies for the vibration analysis of skew plates with various skew angles, thickness ratios, aspect ratios and continuous or discontinuous periphery supports are presented as well. The natural frequencies are directly compared and discussed with those reported in the open literature. Some frequency solutions for skew plates with mixed edge conditions are also presented.     

The effects of bend–twist coupling on the post-buckling characteristics of composite laminated plates using semi-energy finite strip approach

In composite laminated plates various mechanical properties may be attained by changing the lay-up arrangement. The bent–twist coupling is one of the significant properties which dominate the mechanical performance of a laminated plate structure in large out-of-plane deformations. The effects of bend–twist coupling on the post-buckling behavior of composite laminated plates have been studied in this paper by implementing a finite strip approach based on the concept of a rigorous post-buckling solution for composite plates and plate structures, namely the semi-energy approach. All the plates are assumed to be symmetrically balanced laminates having uniform in-plane stiffness properties. As far as the out-of-plane stiffness properties are concerned, all the properties, except for the bend–twist coupling terms which are assumed to change from one laminate to another, are the same among different laminates. The orthotropic solutions have also been determined by precluding the bend–twist coupling terms. A comprehensive set of parametric studies have been carried out to investigate the effects of bend–twist coupling terms on the post-buckling load–displacement path, post-buckling deformations and stress distribution. The comparison between the results revealed markedly different behaviors among different laminates due to the bend–twist coupling effects. The outcome of the paper can help structural designers to have a better understanding of the effects of bend–twist coupling terms on the post-buckling behavior of laminated composite plates at the design stage.     

Finite strip method for the free vibration and buckling analysis of plates with abrupt changes in thickness and complex support conditions

The free vibration problem of a stepped plate supported on non-homogeneous Winkler elastic foundation with elastically mounted masses is formulated based on Hamilton's principle. The stepped plate is modelled by finite strip method. To overcome the problem of excessive continuity of common beam vibration functions at the location of abrupt change of plate thickness, a set of C¹ continuous functions have been chosen as the longitudinal interpolation functions in the finite strip analysis. The C¹ continuous functions are obtained by augmenting the relevant beam vibration modes with piecewise cubic polynomials. As these displacement functions are built up from beam vibration modes with appropriate corrections, they possess both the advantages of fast convergence of harmonic functions as well as the appropriate order of continuity. The method is further extended to the buckling analysis of rectangular stepped plates. Numerical results also show that the method is versatile, efficient and accurate.