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.     

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.     

加劲板的计算方法研究

提出了一种板梁分开方法计算加劲板的理论模型，并用有限元法对该理论模型进行了几何非线性分析，与一些实验结果及一些解析解比较，得出了满意的结果。     

Bending analysis of folded plates by the FSDT meshless method

In this paper, a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT) will be introduced to analyse the elastic bending problem of stiffened and un-stiffened folded plates under different loadings and boundary conditions. Folded plates are regarded as assemblies of plates that lie in different planes. The stiffness matrices of the plates are given by the meshfree method. Employing the element concept, which is borrowed from the finite element method, and treating every plate as a big element, the global stiffness matrix of the whole folded plate is obtained by superposing the stiffness matrices of the plates. This is about the same for the analysis of stiffened folded plates. They are considered as assemblies of stiffened plates. The stiffness matrices of the stiffened plates are also given by the meshfree method. Superior to the finite element methods, no mesh is required in determining the stiffness matrices for the plates and the stiffened plates in this paper, which means time-consuming and accuracy-suffering remeshing is entirely avoided for problems such as large deformation or crack propagation in folded plates or stiffener position changes of stiffened folded plates. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated by it and the finite element commercial software ANSYS. Good agreement is observed between the two sets of results.     

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.     

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.     

The geometric non-linear analysis of thin-walled structures by finite strips

The geometric non-linear analysis of prismatic thin-walled structures is presented. The theory is based on the moderately large displacement assumption, giving non-linear strain-displacement relations, but linear curvature-displacement relations. The corresponding non-linear equilibrium equations are produced by the principle of stationary potential energy using the finite strip discretisation. The equilibrium equations are solved using incremental and incremental-iterative numerical methods. Thus for the simple case of the square plate in edge compression, the self-correcting incremental method gives satisfactory results. For more complex examples of loading and structural type, a variable load incremental-iterative method is adopted. It is shown that the finite strip method used in conjunction with this method can be applied in particular to problems containing load maxima.     

Determination of effective breadth and effective width of stiffened plates by finite strip analyses

A finite strip (FS) method is presented for the numerical investigation of two design parameters — effective breadth and effective width — of stiffened plates. For the effective breadth, stiffened plates under bending are studied. Due to the transverse bending loads there is shear transmission through the plate from the stiffener which leads to a non-uniform longitudinal stress distribution across the plate width. This phenomenon, termed as shear lag, can be represented by the ‘effective breadth concept’, and has been extensively studied by analytical methods. A linear FS method is presented which utilizes the advantages of decoupling of Fourier terms on the one hand and, on the other hand, allows the treatment of both webs and flanges using a plate model. A definitely different situation exists for estimating the effectiveness of the plate breadth (or width) of plates in the postbuckling range. The ‘concept of effect width’ is based on the fact that plates with supported longitudinal edges and/or stiffeners can accept additional load after buckling under longitudinal compression, and enables the designer to evaluate the postbuckling strength of plate structures simply by using the design parameter ‘effective width’. Several formulae (most of them empirically derived) exist for an approximative calculation of the load dependent value of the effective width. A nonlinear FS method is developed and applied to the investigation of the postcritical strength of locally buckled structures. An incremental successive iterative procedure is introduced for an effective numerical analysis.     

Iso-response Analysis of Blast Loaded Stiffened Plates

Abstract: An iso-response analysis is presented for the nonlinear dynamic response of blast loaded stiffened plates. This analysis is based on a new rigid-plastic grillage modelling of stiffened plates. The analysis provides iso-response curves in two-dimensional peak pressure versus total impulse space for particular structures which can be used directly for design purposes. Representative results are presented for several one- and two-way stiffened plates.     

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.     

Elasto-plastic large deflection response of pressure loaded circular plates stiffened by a single diametral stiffener

Equations for the elasto-plastic large deflection non-axisymmetric response of discretely stiffened circular plates are presented. Plastic strains within the plate and stiffener are modelled using the Ilyushin full-section and modified Von Mises yield criteria and the associated flow rule. The equations are discretised using finite differences for solution by the DR iterative procedure. The analysis is used to study the large deflection response of uniformly loaded plates stiffened by a diametral stiffener of rectangular cross-section. Dimensionless graphs of centre deflection, etc., versus pressure are presented for stocky and slender simply supported and clamped plates with shallow and deep stiffeners.     

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.     

Theoretical and numerical analysis and design of stiffened steel plate shear walls having unequal subpanels

Following the adequate seismic behavior, the steel plate shear walls have gained popularity among the designers worldwide, and many buildings have been designed employing such walls as their lateral load‐carrying system. Despite the fact that the steel shear walls using unstiffened thin plates outnumber the ones benefitting from stiffeners, it should be kept in mind that application of stiffeners prevents the buckling induced by lateral loads such earthquake or wind. On the other hand, the stiffeners enhance the stiffness and shear strength of the plate. Accordingly, this paper deals with an analytical and numerical investigation into the steel plates stiffened by unequaled vertical and horizontal stiffeners. The results obtained for the analyses led to the development of the analytical relations to compute the shear strength, stiffness, and displacement. To validate the proposed relations, analytical outputs were compared with those obtained from the numerical investigation indicating great accuracy of the proposed analytical relations. Moreover, in this paper, the design process of the stiffened steel plate shear walls has been presented based on the interaction between the plate and frame. The results indicate the addition of stiffeners to the steel plate, improves its shear strength by 6 to 15%.     

The compressive post-local bucking behaviour of thin plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-local-buckling analysis of geometrically perfect thin-walled prismatic structures under uniform end shortening is developed in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the principle of minimum potential energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyse the post-local-buckling behaviour of thin flat plates. The results are discussed in detail and compared with those available from published works, wherever possible. This has provided confidence in the validity and capability of the developed finite strip in handling the post-local-buckling problem of plate structures.     

Ultimate shear strength of intact and cracked stiffened panels

The present paper focuses on the ultimate shear strength analysis of intact and cracked stiffened panels. Several potential parameters influencing the ultimate shear strength of intact panels are discussed, including the patterns and amplitudes of initial deflection, the slenderness and aspect ratios of the plates, and the boundary conditions defined by the torsional stiffness of support members. An empirical formula for the ultimate shear strength of intact stiffened panels is proposed based on parametric nonlinear finite element analyses in ANSYS. Furthermore, the ultimate shear strength characteristics of cracked stiffened panels are investigated in LS-DYNA with the implicit method. Three types of cracks are considered, namely vertical crack, horizontal crack and angular crack. A simplified method is put forward to calculate the equivalent crack length. And the formula for the ultimate shear strength of cracked stiffened panels is derived on the basis of the formula for intact stiffened panels.     

基于块体集上限法的砂土中条形锚板抗拔承载力分析

运用块体集上限法详细分析了砂土中条形锚板的抗拔承载特性。首先分析了砂土中水平条形锚板的抗拔承载力，并与已有文献中的极限分析上限解、极限平衡解和模型试验结果等进行了详细对比，验证了本文分析的有效性。对比结果表明本文块体集上限分析的求解精度要高于多块体上限法和极限分析有限元法，具有较大的优越性。运用块体集上限法分析了条形锚板的破坏面特性，对不同土体内摩擦角和不同锚板埋深比（H/B）条件下砂土中条形锚板的破坏模式及其变化规律进行了详细的分析研究。     

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.     

Eigenvalue analysis of flexural-torsional buckling of angle-bar stiffened plates

Equilibrium method is employed to analyze interaction of flexural and torsional buckling of angle-bar stiffened plates. The cross sectional areas of the angle-bar stiffened plate for these two modes are different (hybrid beam). In flexural buckling mode, angle-bar and attached plate buckle together, however in torsional buckling mode only angle-bar would be buckled. Basic equations of equilibrium for flexural and torsional buckling modes of angle-bar stiffened plates are deduced based on hybrid beam concept and new strain distribution assumption for sideway bending of stiffeners. Elastic buckling stress of different angle-bar stiffened plates are calculated and compared with finite element method and those available in the literature. It is shown that present method has very good agreements with finite element method for isolated rigid angle-bar and isolated rigid angle-bar with rigid attached plate. For isolated rigid angle-bar with pin connected to rigid attached plates it has better agreement than previously proposed method.     

U型加劲肋加固的高强钢面板体系的面内极限抗压强度

通过非线性有限元分析(FEA)研究使用U型加固件纵向加劲的面板的极限抗压强度。对112个由各种细长参数的面板和柱以及加固件组成的模型进行分析。模型包括了普通钢材和高强钢的弹塑性应变硬化本构关系。有限元分析中也包括了初始几何缺陷和残余应力。将有限元分析得出的结果与欧洲规范3EN1993-1-5、FHWA-TS-80–205和其他可用公式计算出的强度进行比较。基于分析结果,可得出一个针对使用普通钢材或高强钢(HPS)加劲板系统的新的强度预测公式。结果表明:当柱的长细比较大时,使用欧盟规范3EN1993-1-5和FHWA-TS-80–205可能导致设计过于保守;而采用所提出简化形式的公式可更精确地预测强度,从而得出更经济的设计。     

Impact response of rectangular and square stiffened plates supported on two opposite edges

Experimental drop weight impact tests have been performed to examine the dynamic response of small-scale stiffened plates struck laterally by a mass with a spherical indenter. The laboratory results are compared with numerical simulations. The plates stiffened with a flat bar or L profile are supported at two opposite edges and impacted at different velocities and locations along the span. The impact scenarios could represent incidents in marine structures, such as load actions due to dropped objects on decks. The experiments are conducted using a fully instrumented impact testing machine. The obtained force–displacement responses show a good agreement with the simulations performed by the LS-DYNA finite element solver. The finite element model includes defining the experimental boundary conditions so as to simulate small axial displacements of the specimen at the supports. This representation can be used to analyze the structural crashworthiness of similar marine structures under collision scenarios. The strain hardening of the material is defined using experimental data of quasi-static tension tests and the strain rate sensitivity is evaluated using standard coefficients of the Cowper–Symonds constitutive model. The results show that the plastic response of the specimens is highly sensitive to the amount of restraint provided at the supports. Furthermore, it is found that in most of the specimens the contribution of the stiffeners to the impact response is insignificant, since the ends of the stiffener are free at the unsupported edges and the specimens experience small axial displacements at the supports.