Dynamic critical load based on different stability criteria for coupled buckling of columns with stiffened open cross-sections

The dynamic coupled buckling loads were determined for the columns with intermediate stiffener subjected to in-plane pulse loading. The pulse loading of a rectangular shape was concerned. Columns made of isotropic material were assumed to be simply supported at loaded ends. A plate model was adopted in the analysis. The discussed problem of interactive buckling is solved by the analytical–numerical method (ANM) using Koiter’s perturbations method. The differential equations of motion were obtained from Hamilton’s Principle, taking into account all components of inertia forces. In this study, the interactions of two global modes with two local ones were presented. The results obtained by the analytical–numerical method (ANM) were compared with finite element method (FEM)—ANSYS. The dynamic critical loads using the most popular Budiansky–Hutchinson’s criterion, the Kleiber–Kotula–Saran’s criterion with Kubiak’s modifications and the phase plane criterion were determined. New versions of criteria: Kleiber–Kotula–Saran’s quasi-bifurcation dynamic criterion and the phase plane criterion were proposed.     

Buckling of cracked functionally graded plates under tension

Buckling of functionally graded cracked plates under tension has not been investigated so far. In this paper critical buckling load of functionally graded plates containing a crack has been obtained using classical plate theory through the finite element method. Displacement in vicinity of crack tips has been approximated using previous solutions related to bending of cracked plates. Effect on buckling of plate under uni-axial and bi-axial tension of different parameters, such as plate dimensions and material properties, are studied. Results show that the critical load decreases as material gradient index increases, while bi-axial loading leads to higher critical loads compared to uni-axial case.     

Buckling analysis of skew laminate plates subjected to uniaxial inplane loads

Elastic stability of skew composite laminate plates subjected to uniaxial inplane compressive forces has been studied. The critical buckling loads of the skew laminate plates are carried out by the bifurication buckling analysis implemented in finite element program ABAQUS. The effects of skew angles, laminate layups, plate aspect ratios, plate thicknesses, central circular cutouts, and edge conditions on the buckling resistance of skew composite laminate plates are presented.     

Geometrically non-linear analysis including shear deformation of composite laminates

Geometrically non-linear deformations of composite laminated plates are computed using the perturbation finite element method (PFEM). The PFEM is more economic in terms of computational time than conventional finite element iterative procedure, and results in semi-analytic solutions because deformations are polynomial functions of external loads, and vice-versa. To account for the transverse shear effect on deformation of a laminated plate, a discrete-layer shear deformation theory is introduced. This approach predicts more accurately the distribution of displacements and stresses through the thickness than single-layer theories. Detailed derivation of the theory is presented in the paper. A three-node triangular element model and computer program have been developed and implemented as part of this study. Computed numerical results of several examples show that the perturbation finite element solutions are in good agreement with exact solution, experimental data and calculated numerical result from other investigators.     

Non-uniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections

In this paper, the analysis of the behavior of thin-wa lled beams, derived from Proki ’s work, is carried out by using beam theory with a single warping function valid for arbitrary form of cross sections, without any distinction between open and closed profiles and without using sectorial coordinates. The finite element method is used and numerical examples show the accuracy of the solution by comparison with other numerical or analytical results. For the stability analysis, analytical and numerical calculations of critical loads are given for beams submitted to bending moment and centrally applied forces. Equilibrium equations are established from the principle of virtual work. Critical loads are calculated by considering that a structure already in equilibrium reaches instability if there is one or more than one equilibrium position for the same loading. Results with this formulation are compared to those obtained with classical warping functions.     

Prediction of vehicle-induced local responses and application to a skewed girder bridge

This paper proposes an innovative and flexible simulation method that predicts the dynamic responses of bridges induced by passing vehicles. The decoupled equations of motion of the vehicle-bridge system are derived from Lagrange equations and include the effect of road surface roughness, while the interaction forces between the two systems are calculated step by step, using Newmark’s method. This algorithm does not require a special finite element (FE) code and can be implemented with standard FE software and general numerical software such as ABAQUS and MATLAB, respectively. In order to illustrate the practicability of the method, an extensive case study is then presented in which some aspects of the dynamic behaviour of a skewed bridge monitored under vehicle-induced loads are investigated. After adjustment of the boundary conditions and the spectral roughness coefficient, good agreement is obtained between the bridge vibrations predicted by the numerical model and the field measurements. The validated model is further used to analyse the distinctive dynamic effects caused by the skewness. For that purpose, a reference non-skewed bridge model is prepared according to the same design as the original skewed bridge. The obtuse corner of the skewed bridge located near the loading path is found to be a critical region where the slab-negative moments, the girder stress near the sole plate and the bearing force are significantly greater than those in the reference bridge.     

Dynamic buckling of thin isotropic plates subjected to in-plane impact

The dynamic stability behaviour of imperfect simply supported plates subjected to in-plane pulse loading is investigated. For the calculation of dynamic buckling loads a stress failure criterion is applied. The large-deflection plate equations are solved by a Galerkin method by using Navier's double Fourier series. In this paper the dynamic load factor (DLF) is redefined and plots that are useful for the design of plate structures are presented. Parametric studies are performed in which the influences of the pulse duration, shock function, imperfection, geometric dimensions and limit stress of the material are discussed. Comparison between the dynamic buckling loads, which are obtained by the commonly used criterion of Budiansky and Hutchinson [Proceedings of the 11th International Congress of Applied Mechanics (1964) 636], and the dynamic elastic limit loads, which are computed by the stress failure criterion, shows that the latter criterion is more useful for the design of lightweight structures.     

刚性路面在运动车辆作用下的动力响应

针对运动车辆引起的路面结构动力问题,采用移动荷载作用下Kelvin地基上无限大Kirchhoff薄板为力学分析模型,分析了运动车辆作用下刚性路面的动力响应。首先采用积分变换法推导了板挠度的Green函数,并通过Duhamel积分求得各种移动荷载模式作用下板稳态挠度的二维积分解析解,包括恒常和简谐移动点源、线源和面源荷载。然后采用自适应数值积分算法计算解析解中的二维无穷积分,得到了板稳态挠度的数值结果。最后对速度和阻尼等对板稳态挠度的最大值和空间分布的影响进行分析,得到了荷载临界速度,发现了板动力响应的特性和规律。     

Design of horizontally curved plate girder webs containing circular openings

A simple design method to predict the ultimate shear capacity of horizontally curved plate girder webs containing centrally placed circular openings, and subjected to shear is presented in this paper. The solution is obtained by incorporating the effects of curvature and opening size to an equilibrium equation for straight girders containing web openings. It is observed from a parametric study that ultimate load carrying capacity drops linearly with increasing degree of curvature for curved girders having smaller web openings. No significant drop in ultimate capacity is, however, observed when the web opening size exceeds half of the web depth. Accuracy of the proposed equation is assessed by comparing the results with the corresponding finite element values as well as with available experimental results. A satisfactorily correlation has been observed.     

复合材料杆塔压杆稳定计算方法研究

本文提出了适合于复合材料构件的"边缘破坏准则",按照"边缘破坏准则"给出了复合材料构件受压稳定承载力计算公式,并且进行了有限元分析。将"边缘破坏准则"理论计算值、有限元计算值、欧拉临界力和稳定承载力试验值进行比较,结果表明:对于长细比较大的构件,其欧拉临界力与试验值比较接近;对于长细比较小的构件,两者相差较大;对于所有长细比构件,"边缘破坏准则"理论计算值与有限元结果和试验值都非常吻合。     

Finite element analysis of linear plates buckling under in-plane patch loading

The elastic buckling load is physically important in design because it is actually the critical step in the changing plate configuration that will eventually lead to complete failure. The present work investigates the problem of linear buckling of simply supported thin plates subjected to patch compression. In order to satisfy the boundary conditions in a rigorous way, the authors chose the finite element method using the exact stress distribution throughout the plate.In the present paper, the stability problem treated using the total energy is briefly outlined. The plate modelling is made by means of an eight noded rectangular element and a reduction of variable strategy is applied to estimate the number of degrees of freedom leading to little or no loss in seeking solution accuracy.The buckling coefficient is determined for different load cases applied to a range of plate with various edge ratios. The achieved results are summarised through different graphs representing variation of the buckling coefficient against the plate ratio for each load case treated. A comparison with previous works is made. Finally, it is shown that the resolution of the plate buckling problem using true stress distribution with the finite element method leads to a good agreement with results previously obtained by means of analytical methods using an exact stress distribution.     

Elastic local buckling of perforated webs of steel cellular beam-column elements

In this study, the finite element method is employed to determine the critical in-plane longitudinal load at which elastic local buckling of the web of cellular beam-column elements occurs. To simplify the simulation of the problem, the interaction between the flanges and perforated web is approximated by modelling the web only as a long plate having aspect ratio (L/h_w≥10) with multiple circular perforations. The utilized model incorporates restrained out-of-plane displacements along the four edges of the plate. Analyzed plates are subjected to linearly varying in-plane loads to simulate various combinations of axial and flexural stresses. The effect of different geometrical parameters on the elastic buckling load of perforated web plate is investigated. These geometrical parameters include the plate’s length and width, and the perforations’ diameter and spacing. Comprehensive finite element analyses are conducted to identify the behaviour of wide spectrum of perforated web plates at buckling under various combinations of axial compressive load and bending moment. Outcomes of the study are expected to enhance the understanding of the elastic local buckling of web plates of cellular beam-column elements.     

Postbuckling analysis of cross-ply laminated cylindrical shell panels under parabolic mechanical edge loading

Postbuckling equilibrium paths of simply supported cross-ply laminated cylindrical shell panels subjected to non-uniform (parabolic) inplane loads are traced in this paper. Love's shell theory with higher order shear deformation theory and von Kármán nonlinear strain–displacement relations are used in the mathematical formulation of the problem. In the first step, the plate membrane problem is solved to evaluate the stress distribution within the prebuckling range as the applied inplane edge load is non-uniform. The governing shell panel postbuckling equations are derived from the principle of minimum total potential energy using the above stress distributions. Adopting multi-term Galerkin's approximation, the governing equations are reduced into a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to plot the postbuckling paths through limit points. Numerical results are presented for symmetric (0/90/0) crossply laminated cylindrical shell panels under parabolic inplane load, lateral distributed load and initial imperfections. Limit loads and snap-through behavior of shell panels are studied.     

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.     

单调加载方式下桥墩的有限元建模方法研究

基于钢筋混凝土桥墩低周反复荷载试验结果,利用ANSYS软件,建立了单调加载方式下桥墩的有限元计算模型,讨论了不同的混凝土本构关系和有限元求解方法对计算结果的影响,并将模拟得到的桥墩屈服荷载、极限荷载以及荷载-位移曲线与试验结果进行了对比。结果发现,采用约束混凝土的本构关系可得到更好的收敛效果,但弧长法求解对收敛性影响不大;所建立的有限元模型可以较好的模拟桥墩的屈服荷载和极限荷载。     

Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria

In this paper a simple method of deriving lower bound limit loads for thin plates is presented. This method is based on the method of elastic compensation, an iterative elastic technique, which has recently been extended to allow the analysis of structures using thin shell finite element analysis using generalised yield criteria. Here the method is modified to allow analysis of plates, including the effects of transverse shear. The elastic compensation method, combined with generalised yield criteria, is implemented using the finite element numerical analysis technique. Convergence studies are carried out and limit loads are obtained for a range of geometries, boundary conditions and loading. The calculated limit loads are compared with results available in the literature and with new elasto-plastic results and show that the method can be used to quickly obtain practical results.     

基于矢量和方法的边坡动力稳定性分析

 边坡矢量和方法是基于力的矢量特性和边坡体真实应力场的分析方法,动力有限元法可模拟得到边坡体在天然地震动荷载作用下每一时刻的应力状态,在此基础上采用边坡矢量和法进行动力稳定性分析,可得到边坡体在地震动过程中的安全系数时程曲线,进而对其动力稳定性进行评价。针对一高陡边坡,在静力稳定性分析的基础上,针对软弱结构面控制的深层滑移面采用矢量和法进行动力稳定性分析,计算中考虑小震(50 a超越概率63%)和大震(50 a超越概率2%)作用下的动力响应。计算结果表明,在小震和大震作用下的动力安全系数分别为1.86,1.66。矢量和法能够较真实地模拟边坡在地震动过程中的动力特征和稳定性状态,为边坡动力稳定性分析提供一种切实可行的分析途径。     

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.     

Large deflection analysis of flexible plates by the meshless finite point method

The classical finite difference technique and methods based on series expansions can only be adopted for solving plates with simple geometry, loading and boundary conditions. In contrast, the finite element method has been widely used for general analysis of bending and flexible plates (coupled bending and in-plane effects). Lack of stress continuity and relatively expensive mesh generation and remeshing schemes have led to the emergence of meshless methods, such as the finite point method (FPM). FPM is a strong form solution which combines the moving least square interpolation technique on a domain of irregularly distributed points with a point collocation scheme to derive system governing equations. In this study, coupled nonlinear partial differential equations of fourth order are solved to analyse large deflection behaviour of plates subjected to lateral and in-plane loadings. Several plate problems are solved and compared with analytical solution and other available numerical results to assess the performance of the proposed approach.     

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.