Elasto-plastic buckling of stiffener plates in beam-to-column flange connections

The problem of plastic buckling of steel plates is reviewed in relation to the load carrying capacity of stiffener plates in beam-to-column flange connections. Due to the non-uniformity of the stress distribution in these plates, the finite element method is used to compute the stresses in the elastic and plastic ranges. A bifurcation analysis is performed using both flow and deformation theory to evaluate the elasto-plastic buckling of the stiffener. A scaled inverse iterative version of the power method is employed to evaluate the bifurcation load. A parametric study is conducted on stiffeners and design curves are obtained showing the relationship between the critical stress and the slenderness ratio for different plate aspect ratios.     

Analysis of distortional stress in curved I girder bridges

A simplified means of determining more accurately the stress distribution in a curved girder system considering web distortion is presented. The distortional response of a single span curved plate girder bridge is determined utilizing a finite difference procedure. The analysis finds the maximum bending, warping and distortional stresses along each girder.

A UNIVAC 1108 computer was used in the development of the simplified equations which relate the bending and warping stresses to the induced distortional stress. The program written in FORTRAN V, calculates the stresses developed in a four plate girder system having any number of diaphragms along its span.     

Asymmetric thermal buckling of temperature dependent annular FGM plates on a partial elastic foundation

In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances.     

Elasto-plastic shear buckling of square plates with circular holes

With in-plane stresses calculated by finite element analysis, critical loads are obtained by the Rayleigh-Ritz method for a square plate subjected to uniform edge shear stress and containing centrally located circular holes. Elastic and elasto-plastic buckling is examined for clamped and simply supported plates, and results are compared with previous analyses and experiments for various sized holes. The range of hole sizes considered is extended to include larger holes than previously examined, and for small holes, the results suggest that the critical stress is higher than previously thought. For elasto-plastic buckling, critical shear stresses are given for the full range of appropriate slenderness. Experimental results for the cases of simply supported plates support the analytical results, whereas verification for clamped plates remains inconclusive on account of limited reliable test data.     

Analysis of plate resting on elastic supports and elastic foundation by finite strip method

A procedure incorporating the finite strip method together with spring systems is proposed in this paper for treating plates on elastic supports. The spring systems can simulate different elastic supports, such as elastic foundation, line and point elastic supports, and also mixed boundary conditions. To illustrate the application of this procedure, two numerical examples are presented. A three-span simply supported plate is first considered and the effects of support stiffness on the static and free vibration responses and on the critical buckling stress are discussed. A plate resting on Winkler elastic foundation is next studied and the effects of dimension ratio on the static and free vibration responses are discussed. Numerical results show that the spring system can successfully simulate different kinds of elastic supports.     

Lateral buckling of locally buckled beams using finite element techniques

This paper deals with lateral-torsional buckling of beams which have already buckled locally before the occurrence of overall buckling. Due to the weakening effects of local buckling, the stiffness of the beam is reduced. As a result, overall lateral buckling takes place at a lower load than the member would carry in the absence of local buckling. The effective width concept is used in this investigation to account for the post-buckling strength in the buckled compression plate elements of the beam section. A finite element formulation in conjunction with effective width concept is presented. Due to the nonlinearity involved because of local buckling, an iterative procedure is necessary. Search techniques are used to find the load factor. The method combined with an analysis on nonlinear bending moment distribution can be used to analyze the lateral stability problem of locally buckled continuous structure. In this case, both elastic stiffness matrix and geometric stiffness matrix must be revised at each load level. A computer program has been prepared for an IBM 370/165 computer.     

Finite element analysis of out-of-plane buckling of reinforced concrete walls

In this paper a FE model for the study of the out-of-plane buckling of reinforced concrete walls is derived. The concrete is modelled using non-linear orthotropic 16 d.f. plate bending elements; the reinforcing steel using elasto-plastic beam elements. In the plane of the structure stresses are calculated using either four or eight-node membrane elements with bar elements used for the reinforcing steel. The buckling load is calculated by determining when the determinant of the out-of-plane tangent stiffness becomes zero. Comparison of the FE model with available experimental results shows good agreement.     

Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. II: F. E. solutions and parametric study

In the companion paper, an improved formulation for spatial stability analysis of shear deformable thin-walled curved beams with non-symmetric cross-sections is presented based on the displacement field considering both constant curvature effects and the second-order terms of semi-tangential rotations. Thus the elastic strain energy and the potential energy due to initial stress resultants are consistently derived. Also closed-form solutions for in-plane and lateral-torsional buckling of curved beams subjected to uniform compression and pure bending are newly derived for mono-symmetric thin-walled curved beams under simply supported and clamped end conditions. In this paper, F. E. procedures are developed by using curved and straight beam elements with non-symmetric cross-sections. Analytical and numerical solutions for spatial buckling of shear deformable thin-walled circular beams are presented and compared in order to illustrate the accuracy and the practical usefulness of this study. In addition, the extensive parametric studies are performed on spatial stability behavior of curved beams. Particularly transition and crossover phenomena of buckling mode shapes with change in curvature and length of beam on buckling for curved beams are investigated for the first time.     

Application of dynamic relaxation to the large deflection elasto-plastic analysis of plates

The application of dynamic relaxation, a finite difference based iterative analysis, to the study of plates to date is reviewed. The extension of the method to include both geometrical and material non-linear effects in plates is then described in detail. Particular attention is paid to aspects of the iteration parameters which control convergence. The advantages of interlacing finite difference meshes is discussed and the mesh refinement necessary for the accurate analysis of plates in compression and in shear is considered. The usual elastic out-of-plane boundary conditions are generalised by the inclusion of terms applicable in the elasto-plastic range, and the role of in-plane boundary restraints is discussed in respect of plating in both bridge and ship structures. The scope of the method is demonstrated by examples of a long plate with patch loading normal to the undeflected plane of the plate and a panel of a box girder web. In both cases, the effects of initial out-of-plane geometric distortions and welding residual strains on behaviour up to and beyond collapse are considered.     

铝合金受压板件局部屈曲承载力设计方法

为考察现有铝合金设计规范预测非焊接受压板件承载力的准确性,采用壳单元建立单向受压四边简支板、方形截面管柱和十字形截面轴压柱有限元模型,使用ANSYS计算得到铝合金板件弹塑性屈曲临界应力和极限承载力。数值计算结果与理论分析结果对比发现：现有板件弹塑性屈曲应力理论能够给出铝合金板件屈曲临界应力的下限值,误差较小。中国规范非加劲板件有效厚度预测公式偏保守,因此给出修正的有效厚度预测公式。修正后的非加劲板件有效厚度公式可以提高板件利用率,增强经济性。     

基于塑性修正系数的矩形薄板屈曲计算方法

为探究薄板的屈曲破坏性能,以飞机机身设计中最常用的铝合金薄板结构为研究对象,利用金属材料塑性修正系数分析矩形薄板的屈曲失效,得到在均布压力和不同约束条件下矩形薄板的临界屈曲应力。数值仿真算例及其有限元计算结果对比,验证该方法的正确性。     

Stability and load-carrying capacity of three-dimensional long-span steel arch bridges

The behavior of several models of three-dimensional long-span steel arch bridges is investigated for evaluating the effects of various design parameters on both the strength and stability of these special structures. The major concerns in the design of a long-span steel arch bridge, from the structural safety point of view, are the yield and buckling failures. Different design parameters may affect the failure load for either type of failure in various ways. This study investigates how changes in certain design parameters would affect the behavior of steel arch bridges, which could lead to an optimum design of this type of bridge structures. The effects of the plate girder stiffness and arch bracing stiffness as well as the rise-to-span ratio and inclination of the arches towards each other are examined in this study. Both critical buckling load and the load-carrying capacity of each design alternative are investigated using the finite element method. All design alternatives are based on the latest AASHTO code for highway bridge design. It is concluded from this study that the inclined arch bridge using the maximum practical rise-to-span ratio (which is about 0.25) is the most favorable design. In addition, the increase in the stiffness of the plate girder does not reduce the bending moments in the arch ribs. However, providing a lateral bracing system with sufficient stiffness greatly reduces the out-of-plane bending moments and increases the load-carrying capacity and the critical buckling load of a long-span arch bridge.     

Thermal stress analysis of skew plates by finite element method

Thermal stresses are induced in general due to nonuniform temperature distribution or due to the boundary restriction. Most of the work reported so far deals with either plates with edges clamped in plane of the plate or plates with stress free edges. While studying buckling or post-buckling problems, one should ideally analyse the plates with mixed in-plane boundary conditions. Hence, in the present analysis, thermal stress analysis of skew plates with mixed in-plane boundary conditions using finite element approach is attempted. In addition, the effect of in-plane boundary conditions on the thermal stresses is also discussed.     

Curved box beam bridge analysis

A finite difference procedure is used to determine the response of a single and multi span curved single box beam bridge with any number of interior diaphragms. The bending and torsional distortions as well as cross-sectional distortions are determined throughout the box girder. The forces that are determined include bending moment and shear, pure torsion, warping torsion, and bimoment. These forces, in addition to distortional functions, yield resulting normal bending, normal warping, and normal distortional stresses.The entire analysis scheme has been programmed for use on an UNIVAC 1108 computer, FORTRAN IV language, as given herein.     

Design of shell shape using finite elements

A finite triangular facet element for the analysis of doubly curved thin shells is presented, the principal feature of which is a particularly simple resolution process. A simple iterative design procedure is developed, the optimality criteria of which are the elimination of bending and the minimization of the surface integral of the membrane stresses. The procedure is used to obtain numerical predictions of the optimal shapes for constant thickness arches and shells that are in good agreement with those expected. Finally, the procedure is extended to provide an optimal shape for a uniform thickness arch dam and an iterative procedure used to provide an optimal thickness variation.     

Hysteretic damping of structures vibrating at resonance: An iterative complex eigensolution method based on damping-stress relation

In this paper the damping is examined as an engineering property used in analysis and design of structures and machines. The design engineer needs to know not only the stresses of his structure or machine, under steady state conditions but also the stresses under resonance conditions. Then the material damping, as a function of the stress of the structure, has an important role to play and ignoring the damping the calculated stresses are far from reality. The nonlinearity here is due to the dependence of the hysteretic damping on the stress of the structure. Specifically here two problems are investigated in the following way:Firstly the direct problem is solved. The direct problem is to find the maximum bending stress at the resonance when the relation of the dissipating energy (or of the hysteretic damping) vs. the bending stress is known in advance. To perform this calculation, a useful tool for the design engineer, the structure is modelled using the continuum mechanics analytical approach or the finite elements (FE) method. Then the eigenvalues are calculated and using an iterative procedure the real stress. The procedure presented here is called iterative complex eigensolution method (ICEM). Secondly the inverse problem is solved. The inverse problem is to find the relation between the hysteretic damping and the bending stress. For this purpose the logarithmic decrement is experimentally measured, the eigenvalues and the maximum bending stress of the structure, excited at the eigenvalue, when the damping is the same as the measured one, are computed using the finite elements method. Once the bending stresses are found in each discrete element of the structure, then the mathematical expression of the relation of the dissipating energy and the stresses can be specified by minimizing a suitably formed objective function.     

板架结构复杂屈曲问题

利用Patran和MSC Nastran分析板的屈曲问题.明确利用有限元对板屈曲计算的方法,了解板架结构的长宽比和厚度对板架屈曲能力的影响程度.根据矩形板的中性平衡方程推导出板双轴向受压的临界压力公式,并利用有限元方法对其进行校核.     

Linear buckling analysis of thin-walled members combining the Generalised Beam Theory and the Finite Element Method

A finite element procedure to carry out linear buckling analysis of thin-walled members is developed on the basis of the existing Generalised Beam Theory (GBT) and constrained Finite Strip Method (cFSM). It allows designers to uncouple the buckling modes of a finite element model and, consequently, to calculate pure elastic buckling loads. The procedure can easily be applied to members with general boundary conditions subjected to compression or bending. The results obtained are rather accurate when compared to the values calculated via GBT and cFSM. As a consequence, it is demonstrated that linear buckling analyses can be performed with the Finite Element Method in a similar way as can be done with the existing GBT and cFSM procedures.     

Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures

In this paper we present a model and a fully implicit algorithm for large strain anisotropic elasto-plasticity with mixed hardening in which the elastic anisotropy is taken into account. The formulation is developed using hyperelasticity in terms of logarithmic strains, the multiplicative decomposition of the deformation gradient into an elastic and a plastic part, and the exponential mapping. The novelty in the computational procedure is that it retains the conceptual simplicity of the large strain isotropic elasto-plastic algorithms based on the same ingredients. The plastic correction is performed using a standard small strain procedure in which the stresses are interpreted as generalized Kirchhoff stresses and the strains as logarithmic strains, and the large strain kinematics is reduced to a geometric pre- and post-processor. The procedure is independent of the specified yield function and type of hardening used, and for isotropic elasticity, the algorithm of Eterovi? and Bathe is automatically recovered as a special case. The results of some illustrative finite element solutions are given in order to demonstrate the capabilities of the algorithm.