弹性地基板的非线性分析

本文以路面工程为应用背景,针对弹性地基上承受横向载荷的板体进行了非线性有限元分析,采用考虑横向剪切变形的中厚板非协调单元模式,改进了数值性能,避免由于局部小面积受载时,剪切变形较大带来的误差,同时将地基刚度矩阵引入失衡力迭代格式中,保证解的收敛性.文中给出了载荷位于板中、板边、板角时的板体变形情况和破坏状况以及极限承载能力,并与塑性铰线理论、弹性薄板理论进行了比较和分析.     

Generation of higher-order subparametric bending elements

A family of high-order subparametric bending elements with up to 25 nodes are developed. These elements are conforming elements and by including the effect of transverse shear moderately thick plates can also be analysed. This is demonstrated in one of the numerical examples in which the contribution of the shear deformation to the central deflection of rhombic plates supported on two opposite sides is investigated.The elements, being subparametric, can model plates of different geometries, such as rhombic, trapezoidal and curved plates. Several examples are presented here and comparisons are made with results obtained by other methods. The versatility of these elements are clearly shown since only a few elements will normally give results of sufficient accuracy for design purposes.     

An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis

In this article, we investigate the vibration analysis of plates and shells, using an eight-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The natural frequencies of plates and shells are presented, and the forced vibration analysis of plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve the eight-node shell element for free and forced vibration analysis, a new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner–Mindlin theory, which directly addresses the transverse shear deformation without a shear correction factor, is adopted for the development of a new eight-node assumed strain shell element with rotary inertia effect. In order to validate the finite element numerical solutions, the reference solutions of plates based on the first-order shear deformation theory are presented. Results of the present theory show good agreement with the reference solutions. In addition, the effect of damping is investigated on the forced vibration analysis of plates and shells.     

Membrane forces acting on thin-walled box girders considering shear lag effect

A new method for the determination of membrane forces acting on box girder bridges considering shear lag effect is proposed in this paper. A box girder is divided into four thin plate elements: top plate, bottom plate, cantilever and web. Using the equilibrium conditions of the plates, the membrane force equation for each plate element is established. The analytical formulas for calculating the membrane normal, transverse and shear forces of each plate element considering shear lag effect are derived. The proposed method is easy to implement in the design of thin-walled box girders considering shear lag effect.Through examples using the high order finite strip element method and the experiment, the results obtained by the proposed method are examined and the accuracy of the proposed method is verified. The discussions on the shear lag effect on the membrane forces acting on cantilever box girders are given considering the variations of span to width ratio, width to height ratio and various loading conditions.     

A study into optimization of stiffeners in plates subjected to shear loading

A great deal of attention has been focused on plates subjected to shear loading over the past decades. One main fact in design of such elements, which fall in the category of thin-walled structures, is their buckling behavior. Plate girders and recently shear walls are being widely used by structural engineers, as well as ship and aircraft designers. The role of stiffeners is proved to be vital in design of such structures to minimize their weight and cost.In this work, by using ANSYS finite element method of analysis, some 1200 plates are analyzed in order to study the role of stiffeners and to come up with some limits for an optimized design procedure. This eigenvalue method of analysis is first validated with the theoretical calculations and known cases for a wide range of typical panel geometries.The results show that the number of panels produced by intermediate transverse stiffeners should not be less than the value of plate's aspect ratio. In other words, the transverse stiffeners should divide the length of the plate to portions equal or less than its width.It is also shown that the optimum geometric properties of the stiffeners correspond to the point when the buckling shape of a plate changes from the overall mode to local mode. Furthermore, all stiffened plates, with a similar aspect ratio and number of stiffeners, have a specific value of EI_s/aD, for which the critical shear stress is optimal. In addition, some expressions to predict these properties are presented.     

On the design of stiffeners in steel plate shear walls

This paper describes a numerical investigation to provide a practical design method for stiffening thin steel plate shear walls. The procedure considers one-sided transverse and longitudinal flat stiffeners located in various arrangements on shear plates which effectively divides the plate into subpanels and expands tension fields across the infill walls. The results obtained from several nonlinear static analyses are employed to draw applicable empirical relationships for evaluating optimal dimensions of stiffeners. The procedure also ascertains the effects of optimised stiffeners on the postbuckling behaviour and ultimate load bearing capacity of stiffened shear walls.     

Developing an element free method for higher order shear deformation analysis of plates

A procedure is presented to eliminate transverse shear locking in analysis of laminated composite plates using Element Free Galerkin (EFG) method based on higher-order transverse shear deformation theory (HSDT). In the procedure, derivatives of the transverse displacement are introduced as independent variables. Thus, a formulation requiring C⁰ continuity shape functions for approximation is proposed for higher-order transverse shear deformation analysis of plates. Shear locking is avoided considering reduced integration for shear stiffness matrix; a method which is implemented in FEM. Moving Least Squares (MLS) method is utilized for shape functions and the penalty method is implemented to impose approximate boundary conditions. The present solutions are verified with other higher-order shear deformable studies. Moreover, a comparison between the present solutions with those obtained by EFG procedure based on First-order transverse Shear Deformation Theory (FSDT) is performed.     

Vibration of general triangular composite plates with elastically restrained edges

Triangular fibre reinforced composite plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration behaviour of anisotropic triangular plates with edges elastically restrained against rotation and translation. The approach developed is based on the Rayleigh–Ritz method and the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for single layer composite plates with different fibre orientations and combinations of boundary conditions. For some plates, mode shapes of free vibration are also shown. Selected new transverse vibration mode shapes are presented to illustrate the effects of boundary constraints, aspect ratio and fibre orientation.The method can be applied to a wide range of elastic restraint conditions, any aspect ratio and for higher modes. The effect of the fibre orientation on the natural frequencies for plates with these restraint conditions are also considered.     

Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 1: Finite strip formulation

This paper deals with the linear elastic analysis of prismatic folded plate and shell structures supported on diaphragms at two opposite edges with the other two edges arbitrarily restrained. The analysis is carried out using curved, variable thickness, Mindlin-Reissner finite strips. The theoretical formulation is presented for a family of C (0) strips and the accuracy and relative performance of the strips are examined for curved situations. Some variable thickness and elastically supported plates are considered and the interesting phenomenon of the occurence of boundary layers in the twisting moments and shear forces is highlighted for a common boundary condition. Other examples analysed include box girders and cylindrical shells. In all cases transverse shear deformation effects are included and the contributions to the strain energy from membrane, bending and transverse shear behaviour noted. In a companion paper these accurate and inexpensive finite strips are used for structural shape optimisation.     

Nonlinear stability of unsymmetrically laminated angle-ply shear-deformable plates in biaxial compression

The generalized Karman–Reissner equations governing large deflection of unsymmetrically laminated angle-ply shear-deformable rectangular plates are presented in this paper, based upon Karman and Reissner plate theories. Much effort has been concentrated on derivation of the Karman–Reissner equations for the laminates taking account of transverse shear effects so that only two unknown functions for nonlinear analysis need to be treated to gain a precise insight into the complexities; otherwise high-order refined plate theories must be applied. An asymptotic series solution is constructed according to the Karman-type refined theory for postbuckling behavior of the plates with the boundary condition of four edges simply supported. Typical numerical examples are presented for comparison with other nonlinear analytical and experimental results. The effects of shear deformation, lamination angle and geometrical imperfection on buckling and postbuckling behaviors of the laminates subjected to a combination of biaxial compressive loadings are examined for industrial application.     

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.     

Strength of perforated plates subjected to in-plane loading

Finite element solutions for the buckling and geometrically nonlinear elasto-plastic collapse of perforated plates are presented. Triangular elements are used to model the plates and the elasto-plastic stress-strain relationships are based on Ilyushin's approximate area yield function assuming full plastification of the entire thickness of the plate for stress states on the yield surface. Solutions are presented for square plates with central square and circular holes subjected to uniaxial compression, biaxial compression and pure shear, and are shown to be in close agreement with existing approximate and semi-empirical solutions which have been verified by test results.     

考虑非线性剪切效应的钢筋混凝土柱模型化方法及应用

采用纤维模型梁柱单元和与之串联的零长度单元,模拟柱的弯曲机制和剪切机制。利用OpenSees提供的Limit State Material和Shear Limit Curve材料模型,定义钢筋混凝土柱的非线性剪切效应及其与弯曲效应的耦合。通过与不同学者的试验结果比较,验证了该方法的可靠性。最后,对笔者完成的原位推覆试验的一榀平面框架进行了Pushover分析。结果表明,考虑非线性剪切效应的模型化方法能较好地模拟钢筋混凝土柱抗剪承载力和刚度的退化现象,传统的纤维模型梁柱单元难以反映配箍不足的钢筋混凝土柱的弯剪破坏机制。该方法可用于存在抗剪能力缺陷的框架结构的非线性分析。     

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

Web core panels, foam-filled sandwich panels with interior webs, are a structurally efficient option for transverse load bearing applications. In web core panels, the interaction between the webs and core material can have a substantial impact on web shear buckling strength and is a key element of lightweight structural design. The present work is an investigation of web buckling behavior in web core panels under a distributed load. To solve this problem, web shear buckling was analyzed for the case of pure shear loading with foam support, and this analytic model was extended to the case of panels with a transverse distributed load. The webs are modeled as simply supported plates resting on a Pasternak elastic foundation. To that end, a buckling model for plates on a Pasternak foundation is presented, along with closed-form approximations of the solution for square and infinitely long plates. An accurate model for the foundation constants is developed using energy methods. Applicability of the plate buckling model to web core panels with transverse loads is presented via a finite element study. In panels, the slenderness and spacing of the webs have a slight effect on the boundary conditions between the webs and face sheets. The effect is relatively small, however, and the model presented in this work underpredicts buckling strength by less than 25%. The model in this work is thus a reasonable approach to the practical design of web core panels.     

Effect of interfacial imperfection on bending behavior of composites and sandwich laminates by an efficient C0 FE model

The bending behavior of composites and sandwich plates having imperfections at the layer interfaces is investigated by a refined higher order shear deformation plate theory (RHSDT) and a Least Square Error (LSE) method. In this theory, the in-plane displacement field is obtained by superposing a globally varying cubic displacement field on a zig-zag linearly varying displacement field. This plate theory represents parabolic through thickness variation of transverse shear stresses which satisfy the inter-laminar continuity condition at the layer interfaces and zero transverse shear stress condition at the top and bottom of the plate. In this plate model, the interfacial imperfection is represented by a liner spring-layer model. Finite element method is adopted and an efficient C⁰ continuous 2D finite element (FE) model is developed based on the above mentioned plate theory for the static analysis of composites and sandwich laminates having imperfections at the layer interfaces. In this model, the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of C¹ continuity associated with the above plate theory (RHSDT). The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. The proposed model is implemented to analyze the laminated composites and sandwich plates having interfacial imperfection. Many new results are also presented which should be useful for the future research.     

Simplified nonlinear finite element analysis of buildings with CFS shear wall panels

The use of panelized cold-formed steel framing as the primary structural system has become increasingly popular for low- and mid-rise residential and commercial construction. The primary load-resistant elements in such framing are the structural panels built with uniformly spaced cold-formed steel studs and covered with structural sheathing. By taking advantage of in-line-framing, the framing members can be designed manually by using load tables published by manufacturers or spreadsheets developed in-house. In the case where the overall behaviour of the structure is needed, a finite element analysis has to be carried out. Conducting a finite element analysis for such types of buildings can be time consuming due to the large number of elements involved in modeling the framing member and structural sheathing. In this paper we present a simplified approach for analyzing cold-formed steel buildings by using finite element methods. In the proposed method, a typical 1.2 m wide wall panel which is built with cold-formed steel studs and structural sheathing is modeled by a 16-node shell element having equivalent material properties. In addition, the nonlinear behaviour of shear wall panels is simulated by a stiffness degradation factor. Compared to the conventional finite element method, a lesser number of elements will be used in the proposed method for modeling a building structure. The accuracy and efficiency of the proposed method are demonstrated through the comparison of results of the proposed and the conventional method on single shear wall panels. In addition, an example of nonlinear analysis for a three-storey building is presented.     

Nonlinear dynamic stability of composite plates with piezoelectric layers subjected to periodic in-plane load

Nonlinear dynamic stability characteristics of composite plates subjected to periodic in-plane load are investigated via the finite element method with dynamic response analysis. Piezoelectric actuator layers are embedded at the top and bottom of the laminated composite plate. The theoretical formulation is based on the modified first order shear deformation theory (MFSDT) incorporating the von Kármán type nonlinear strains. The structural system is considered to be undamped. The nonlinear governing equations obtained are solved using the Newmark's direct integration method coupled with the direct iteration method. The boundaries of dynamic instability regions are obtained using Bolotin's approach. Effects of in-plane forcing frequency and applied voltage on the characteristic features of dynamic stability behaviour are investigated using both linear and nonlinear dynamic response analyses.     

Influence of weld stiffness on buckling strength of laser-welded web-core sandwich plates

This paper investigates the influence of weld rotation stiffness on the global bifurcation buckling strength of laser-welded web-core sandwich plates. The study is carried out using two methods, the first is the equivalent single-layer theory approach solved analytically for simply supported plates and numerically for clamped plates. First-order shear deformation theory is used. The second method is the three-dimensional model of a sandwich plate solved with finite element method. Both approaches consider the weld through its rotation stiffness. The weld rotation stiffness affects the transverse shear stiffness. Plates are loaded in the web plate direction. Four different cross-sections are considered. Weld stiffness is taken from experimental results presented in the literature. The results show a maximum of 24% decrease in buckling strength. The strength was affected more in plates with high reduction of transverse shear stiffness and high bending stiffness. Furthermore, clamped plates were influenced more than simply supported. The intersection between buckling modes shifted towards higher aspect ratios, in the maximum case by 24%. The results show the importance of considering the deforming weld in buckling analysis.     

Mechanical and thermal post-buckling analysis of FGM rectangular plates with various supported boundaries resting on nonlinear elastic foundations

Mechanical and thermal post-buckling analysis is presented for FGM rectangular plates resting on nonlinear elastic foundations using the concept of physical neutral surface and high-order shear deformation theory, and investigations on post-buckling behavior of FGM rectangular plates with two opposite simply supported edges and other two opposite clamped edges are also new. Approximate solutions of FGM rectangular plates are given out using multi-term Ritz method, and influences played by different supported boundaries, foundation stiffnesses, thermal environmental conditions and volume fraction index are discussed in detail. It is worth noting that the effect of nonlinear elastic foundation is small at the pre-buckling and initial post-buckling state and is significant with increasing deflection at the deep post-buckling state. Especially, comparisons of post-buckling for FGM rectangular plates resting on nonlinear elastic foundations with movable simply supported edge subjected to compression acting on the geometric middle surface and the physical neutral surface are innovative, and may be helpful to clarify typical mistakes in literature.     

Semi-analytical models for the post-buckling analysis and ultimate strength prediction of isotropic and orthotropic plates under uniaxial compression with the unloaded edges free from stresses

This paper introduces two semi-analytical models developed for the nonlinear analysis of stability of isotropic and orthotropic plates under uniaxial compression. The possibility of considering fully free in-plane displacements at longitudinal edges (or unloaded edges) is the innovation of these models over existing models, where these displacements are always assumed constrained to remain straight. Contributions for the large deflection theory of plates related to the derivation of analytical solutions for the Airy stress function which satisfy Marguerre׳s equations for isotropic and orthotropic plates are presented. Namely, the extension of the Coan and Urbana solution for isotropic plates in order to consider all the terms of the unknown amplitudes of the out-of-plane displacements and the derivation of a solution for orthotropic plates. Comparisons between the semi-analytical model and nonlinear finite element model results are presented in order to discuss the effect of in-plane displacement boundary conditions on behaviour and strength of plates similar to bottom flanges used in steel box girder bridges. This study shows that the semi-analytical models have a clear potential to provide accurate solutions, requiring only a short computer time. It is also shown that the in-plane displacement boundary conditions for the unloaded edges significantly influence the behaviour and strength of plates and this problem cannot be neglected in the definition of the design rules.