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.     

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.     

Buckling analysis of trapezoidally corrugated panels using spline finite strip method

Buckling of trapezoidally corrugated panels under in-plane loading is analyzed by a spline finite strip method. The influence on the elastic buckling load of various parameters, such as geometry. loading forms and boundary conditions, etc., is studied. It is found that: (1) for longitudinal compression the buckling load increases with the corrugation angle α, and for a given α the highest buckling load is achieved when the ‘proportion parameter’ γ = 1; (2) for shear loading the buckling load increases as α increases, and for a given α the highest buckling load is obtained when γ = 2; and (3) for a combined loading of compression and shear, interactive curves can be approximated by unit circles when α = 15°, 30°, 45°, 60° and 90°. However, when α = 75° a parabola seems to be a better approximation. Based on the numerical experiments, simplified formulae and interactive curves are suggested for practical design.     

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.     

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.     

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.     

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.     

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.     

A simplified method for free vibration analysis of cable-stayed bridges

A simplified method for the accurate prediction of the natural frequencies of cable-stayed bridges is proposed in this paper. In the proposed method artificial neural network (ANN) is applied to derive a simple formula to predict the natural frequencies of cable-stayed bridges based on existing natural frequency data. Unlike in the existing empirical methods, no functional relationship among the variables is assumed before we can develop an ANN model. ANN automatically constructs the relationships and adapts based on the training data presented to them. Also, the proposed method takes into account the wide range of parameters which may have a significant effect on the natural frequencies of cable-stayed bridges. The proposed method is particularly useful for the preliminary design stage of cable-stayed bridges where free vibration analysis needs to be carried out. The proposed method is compared with two existing empirical methods. It is found that the simplified method proposed in this study can produce a more accurate prediction of the natural frequencies of cable-stayed bridges than the existing empirical methods.     

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 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.     

Spline finite strip analysis of prestressed concrete box-girder bridges

The analysis of prestressed box-girder bridges using the spline finite strip method is presented. In the present study, the spline finite strip method is modified by using the non-periodic B-spline interpolation. In the analysis of the prestressed box-girder bridges, the short-term losses of prestressing are considered and each tendon force at the tendon point is evaluated by summation of the adjacent segment forces. Once the equivalent forces acting on the structure at the tendon points are found, they are transformed into statically equivalent forces at the adjacent node of nodal line. Several examples were analyzed to verify the performance of present method. Good agreements were obtained when compared with the previous studies.     

悬臂梁的静力分析及自由振动分析

大跨度及高层空间结构是目前发展最快的结构类型。大跨度建筑及作为其核心的高层空间结构技术的发展状况是代表一个国家建筑科技水平的重要标志之一。本文主要研究变截面均质悬臂梁的结构体系在水平均布荷载作用下的静力分析,以及EULER悬臂梁的自由振动分析。根据哈密顿原理推导出控制方程和边界条件,然后用常微分求解器COLSYS进行求解。     

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.     

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 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.     

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.     

冻融损伤对桥墩力学性能影响分析

为研究冻融损伤对桥墩力学性能的影响,以某矩形重力式桥墩为工程背景,利用ANSYS软件建立三维有限元模型,分别计算比较了不同桥墩损伤层厚度下桥墩的静动力特性,通过分析得出了一些有益的结论。     

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。