用无网格有限点方法对柔性板的大挠度分析

基于级数展开的经典差分法只适用于分析具有简单几何特性、加载和边界条件的板。相反,有限元法却可以广泛应用于分析柔性板(弯曲和平面内作用)。应力不连续以及网格划分复杂导致了无网格分析法的出现,如有限点法(FPM)。有限点法是结合了带插值的最小二乘法和不规则点分布的一种方法,可以采用其推导出系统的控制方程。研究中,采用耦合的4阶非线性偏微分方程,分析板在侧向和平面内加载作用下的大挠度性能。研究中同时也解决了板的其他一些问题,并且利用其他的数值分析结果对文中提出的方法进行了评估。     

Analysis of chloride diffusion in concrete structures for prediction of initiation time of corrosion using a new meshless approach

In this paper, a finite point method (FPM) is developed and adopted for solving the chloride diffusion equation for prediction of service life of concrete structures and initiation time of corrosion of reinforcements. Diffusion of chloride ions is generally assumed to follow the Fick’s second law. FPM is a truly meshless method which uses a moving least square approximation within a collocation strong form for solving the governing differential equation. Several 1D and 2D problems are solved using FPM and the results are compared with the analytical solution, classical finite element and finite difference methods, and weak form meshless based element free Galerkin method.     

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.     

Orthotropic von Karman plates using higher order elements

The nonlinear behaviour of orthotropic plates subject to transverse loading is studied in this paper using higher order finite elements. The formulation procedure for elements with up to 25 nodes is established and derivation of the tangential stiffness matrix based on the classical von Karman nonlinear theory is presented. These elements are derived by employing a high order polynomial displacement function to represent the in-plane and the bending displacements. By adopting separate variables for the transverse deflections and the rotations of the plate, the effect of transverse shear deformation can be included in modelling thin to moderately thick plates, thus enabling the effect of transverse shear on the nonlinear behaviour of plates to be included. The Newton-Raphson method for solving nonlinear equations is adopted to obtain the final state of equilibrium of the system. Several numerical examples are presented and the results are compared with available experimental data as well as analytical and numerical solutions obtaned by other conventional methods. Satisfactory agreement on the nonlinear performance of the plates as predicted by the present method is demonstrated.     

面内受弯玻璃板承载性能的有限元分析

面内受弯玻璃板经常被应用于玻璃承重结构中,这种板件在不同的支承情况下会有不同的力学响应,而且当缺少足够的侧向支承时,板件还会发生整体失稳而破坏,现有的玻璃幕墙规范对这种结构没有相关的规定。采用有限元方法分析了面内受弯玻璃板静力承载性能的两个主要影响因素——板厚和跨高比,并对不同荷载状况下两种常见类型玻璃板的稳定问题进行分析,得到了其屈曲荷载及屈曲模态。     

考虑畸变的开口薄壁构件变形方程及其应用

为简化考虑截面畸变的薄壁杆件力学分析,提出一种把薄壁杆件拆分为两个较简单的部分分别分析、按需综合的方法。该文重点探讨截面畸变变形的效应分析:首先基于薄板小挠度弯曲理论,建立矩形板条的面外弯曲变形方程,然后适当简化截面畸变的变形形式和平衡条件,实现反映开口薄壁杆件畸变和扭转性能的"板件面外弯曲综合抗力体系"分析,最后与另文探讨的薄壁杆件"板件面内拉弯综合抗力体系"的分析进行综合,建立考虑截面畸变的开口薄壁杆件常微分变形方程。与目前较为常用的广义梁理论及有线条法相比,该方法无需进行截面正交分析或假定变形沿杆长的分布。为提高方法的实用性,文中还基于该变形方程,探讨了薄壁杆件单元刚度方程等矩阵位移法诸实现要件,据此编制的通用程序计算结论与基于壳单元的ANSYS软件算例结论吻合良好。     

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.     

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.     

Bending and buckling of inflatable beams: Some new theoretical results

The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed.     

A parametric study on the longitudinal stiffeners of web panels

Optimum location and dimensions of longitudinal stiffeners in web plates under in-plane bending are investigated. This parametric study is performed by numerical simulation utilizing finite element method. Several plates having various aspect ratios are analyzed and an equation for minimum required second moment of area of stiffeners is presented and compared to that recommended by AASHTO. Also, it is shown that the optimum location of stiffener mainly depends on its relative flexural rigidity.     

腹板纵向加劲肋的参数研究

采用有限元数值模拟方法,对处于平面内弯曲的腹板纵向加劲肋的最佳位置和尺寸进行研究。分析对象为具有各种不同纵横比的平板,提出计算最小次弯矩的公式,并将其与AASHTO推荐的计算方法对比。结果显示,腹板加劲肋的最佳位置主要取决于其相对抗挠刚度。     

Inelastic buckling behavior of stocky plates under interactive shear and in-plane bending

Inelastic buckling and postbuckling behavior of stocky plates under combined shear and in-plane bending stresses are investigated and compared to slender plates. Aluminum and steel plates having various slenderness ratios are modeled and analyzed by means of (i) numerical nonlinear finite element method and (ii) theoretical p-Ritz energy method; and both results are compared to the classic interaction equation. It is observed that whereas in slender plates, elastic buckling occurs prior to the material's proportional limit load, stocky plates buckle in an inelastic way within the post-yield stage. In contrast to slender plates with considerable postbuckling reserves, the buckling of stocky plates is immediately followed by softening. In addition, it is shown that the classic interaction equation overestimates buckling loads; and therefore, a modified equation that can safely be applied to both stocky and slender plates is proposed.     

The static analysis of multi-bay coupled shear walls

The conventional continuum method for the analysis of multi-bay coupled shear walls is quite a complicated process. The shear forces in the lintel beams are taken as the basic unknowns and a set of ordinary differential equations has to be solved. A simple but general method for the analysis of multi-bay coupled shear walls is presented in this paper. The continuum technique is still adopted, however in this case the generalized axial forces in the walls are taken as basic unknowns, and the solutions are obtained in a form of finite series. The advantage of this approach is that simplified solution in closed form can be deduced by taking only the first few terms in the series. Comparison of the results with the finite strip method shows good agreement.     

Simulation of the dynamic response of transmission lines in strong winds

A numerical simulation procedure for predicting the response of a single span transmission line to strong turbulent winds is described. The wind velocities are generated using a ‘Monte Carlo’ technique based on an inverse fast Fourier transform; the equations of motion of the line are then solved numerically using a finite difference method. Results obtained using the method were compared with those from linearized random vibration theory. Effects due to the mean swing angle of the line, and due to the excitation of an in-plane mode of vibration were apparent.     

Buckling and postbuckling of shear-deformable rectangular plates of composite construction

Buckling and postbuckling behaviours of rectangular plates of composite construction are studied by means of the generalised von Karman equations counting for arbitrary lamination and material properties. In conjunction with four edges simply supported, higher order asymptotic solutions to the large deflection equations with incorporation of initial geometrical imperfection are constructed by the deflection type perturbation technique. Effects of initial imperfection, transverse shear deformation, shear-bending material interaction, and in-plane edge condition on buckling and post-buckling of the plates are examined through typical examples, and comparison of the present solution are made with other theoretical and numerical results. It is shown that the present predications are of fairly good accuracy.     

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.     

Static and dynamic interactive buckling of isotropic thin-walled closed columns with variable thickness

The present paper deals with static and dynamic analysis of interactive buckling of thin-walled closed columns with variable thickness subjected to in-plane constant and/or pulse loading. This investigation is concerned with thin-walled structures with corners bevelled at the angle of 45° under axial compression. The plate model is adopted for the structures. The material, all plates are made of, is subject to Hooke's law. The structures are assumed to be simply supported at the ends. The differential equations of motion have been obtained from Hamilton's principle. In this paper the static solution has been obtained by Koiter's asymptotic method in the second-order approximation. The study is based on the numerical method of the transition matrix using Godunov's orthogonalization. The interaction of an overall mode with two local modes having the same wavelength has been considered (i.e. three-mode approach). The nonlinear equations of dynamic stability are solved with the Runge–Kutta method. The calculations are carried out for settled imperfections.     

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.     

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.     

纵横向荷载作用下厚板问题的边界元分析

根据纵、横向荷载作用下厚板问题的受力特点, 引入等效荷载的概念［１］ , 以边界元法理论建立了该问题的边界元求解线性方程组。这为解决复杂荷戴作用下厚板问题,以及上部结构与基础及地基共同作用问题等提供了一种新的分析方法。