Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model

A four-noded quadrilateral (PBQ4) and an eight-noded quadrilateral (PBQ8) plate bending element based on Mindlin plate theory are adopted for the analysis of thin and thick plates resting on elastic foundation using modified Vlasov model. The terms of vertical deflection stiffness matrix and shear deformation stiffness matrix of the subsoil are evaluated using finite element method, and presented in explicit forms. Selective reduced integration technique is used in addition to full integration technique for both the types of the elements to avoid shear-locking problem that occurs under the thin plate limit. It has been demonstrated that the performance of the eight-noded quadrilateral element is excellent for thin and thick plates on elastic foundation when selective-reduced integration technique is used. General conclusion can be drawn from the results that the effect of the shear strain on the behavior of the plate resting on subsoil is always quite small for free plates compare to the supported ones.     

基于改进Vlasov模型的弹性地基上平板横向剪应变分析

运用Vlasov模型对弹性基础上的薄板和厚板进行分析,采用了基于Mindlin板理论的4结点四边形和8结点四边形弯曲单元。运用有限元法对底层土的竖向挠度刚度矩阵和剪切变形刚度矩阵进行推算。针对2种类型的板单元,采用完全积分方法和选择性简化积分方法进行分析,以避免极限状态下薄板的剪切闭锁问题。研究发现：在选择性简化积分方法中,8结点四边形板单元非常适用于分析弹性基础上的薄板和厚板。结果表明：相比有支撑的平板,剪应变对底层土上无支撑平板的影响非常小。     

Elastic modulus reduction method for limit analysis of thin plate and shell structures

The paper proposes an efficient numerical method, namely, the elastic modulus reduction method (EMRM) to calculate lower-bound limit loads of thin plate and shell structures. To determine the elastic modulus adjustment parameter q in a rational way, the precisions and convergent properties of four different strategies of elastic modulus adjustment (SEMAs) combined with the EMRM are investigated. Furthermore, to take into consideration the plastic resistances as well as the internal forces in the processes of elastic modulus adjustment, the element bearing ratio (EBR) of thin plate/shell element is defined as the governing parameter based on the generalised yield criterions. The flexibility and accuracy of the proposed EMRM combined with both the strain energy equilibrium principle (SEEP) and the fixed strain method (FSM) are demonstrated in the numerical example.     

Calculation of pure distortional elastic buckling loads of members subjected to compression via the finite element method

An analysis procedure is presented which allows to calculate pure distortional elastic buckling loads by means of the finite element method (FEM). The calculation is carried out using finite element models constrained according to uncoupled buckling deformation modes. The procedure consists of two steps: the first one is a generalised beam theory (GBT) analysis of the member cross-section, from which the constraints to apply to the finite element model are deduced; in the second step, a linear buckling analysis of the constrained FEM model is performed to determine the pure distortional loads. The proposed procedure is applied to thin-walled members with open cross-section, similar to those produced by cold-forming. The distortional loads obtained are rather accurate. They are in agreement with the loads given by GBT and the constrained finite strip method (cFSM).     

通过有限元法计算受压构件的纯畸变弹性屈曲荷载

基于有限元法,提出一个分析方法,可以计算纯畸变弹性屈曲荷载。计算中采用的有限元模型为非耦合屈曲变形模式。具体方法分为2步:第1步,采用一般梁理论(GBT)分析构件横截面,在此可以给有限元模型施加约束条件;第2步,对受约束有限元模型进行线性屈曲分析,确定纯畸变荷载。将此法应用于开口薄壁构件和冷弯构件,得到的畸变荷载非常准确,与一般梁理论和约束有限条法(cFSM)计算的荷载值一致。     

弹性支承厚板在局部载荷下的弯曲

在建筑结构设计中弹性支承板的计算一般采用有限元法和图表法。在理论上没有一般性的解析表达式,无论是薄板还是厚板,本文由边界积分法给出了一般封闭解析解的表达式。作为算例,求解了局部均布荷载作用的弹性支承四边简支厚板的弯曲问题,并相应地以图表的形式给出了计算结果,并与有限元结果进行了对照,证明本文给出的一般性的封闭解析解的表达式是正确的。     

Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes

The vibration of Mindlin plates with moving concentrated load is investigated using the finite element method (FEM). The use of Mindlin elements may, depending on the refinement of the mesh, yield poor results if the loads are located at off-nodal positions. A new strategy that is based on an adaptive mesh scheme and on the use of perturbation technique in the structural vibration simulation is proposed in this paper to overcome this problem. The strategy supports the use of the traditional finite elements and arbitrary geometry and boundary conditions for both plates and shells.     

Torsional buckling behaviour of stiffened cylinders under combined loading

In this study cylindrical boundary conditions for finite element analysis are formulated that allow torsional displacement and buckling of a sector of a cylinder of half axial height, and of a circumferential arc angle that will divide into 360°. Finite element tests are carried out on un-stiffened elastic cylinders to verify the method of analysis against classical elastic torsional buckling theory.Elastic–plastic limit point finite element tests are carried out on ring and stringer stiffened and stringer stiffened cylinders to investigate the effects of stiffeners on post-buckling behaviour in torsion.A stringer stiffened cylinder is subjected to many combinations of axial force and surface pressure in the elastic range of response and then tested to failure in torsion to investigate the effects of axial and surface pressure loads on the resistance to plastic collapse in torsion.     

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.     

基于非线性规划的岩质边坡有限元塑性极限分析下限法研究

结合塑性极限分析下限法理论、有限元离散技术以及非线性数学规划手段,将有限元塑性极限分析法运用于岩质边坡的稳定性分析。基于非线性Mohr-Coulomb屈服条件、平衡条件、边界条件以及间断面应力连续条件,提出塑性极限分析中无厚度节理单元、等厚度节理单元的有限元模式,建立带节理单元的有限元塑性极限分析非线性数学规划模型,并提出非线性规划的求解策略。最后对3个岩质边坡的稳定性进行分析,验证该方法的可行性。     

考虑恒荷载作用效应的弹性补偿有限元法

通过对弹性补偿有限元法的改进,提出可考虑恒荷载和活荷载同时作用的结构塑性极限分析方法。该方法利用弹性补偿有限元法采用迭代法进行极限分析的特点,在活荷载比例加载逼近极限荷载的同时,保持恒荷载作用效应不变,得到考虑恒荷载作用效应的工程结构极限承载力。典型算例的对比分析和影响因素研究表明,算法分析结果是收敛的、准确的和稳定的。     

高层建筑筏板基础分析的样条虚边界元法

基于Reissner厚板理论和Winkler弹性地基假定(非单一基床系数),提出了非均匀弹性支承厚板弯曲分析的样条虚边界元法,并将该法应用于高层建筑筏板基础的分析.本文方法计算量少、计算精度高,可以求解具有不同边界条件和任意域内支承的薄板和厚板在任意荷载作用下的挠度和内力,可用来对工程中各种板结构弯曲问题进行统一的分析.工程算例显示了本文方法在高层建筑筏板基础和桩基承台分析中的正确性和实用性.     

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.     

Natural frequencies of square plates with reinforced central holes subjected to inplane loads

The natural frequencies and the elastic buckling loads of square plates, containing reinforced square holes and subjected to inplane loads, are determined using the finite element method. The reinforcing beams which are located at the four edges of the hole are either square or rectangular in cross section.

To determine the appropriate out-of-plane stiffness and mass matrices, a rectangular non-conforming bending element is employed. This element has three degrees of freedom at each of its four corner nodes. The finite element method is also used to calculate the inplane stress distribution prior to buckling. This inplane element is rectangular and is based on strain assumptions. The element also includes the inplane rotation as well as the two translational displacements as the three degrees of freedom at each of its four corner nodes. To model the behaviour of the reinforcement, a three-dimensional exact beam element is used. For this element, the degrees of freedom for out-of-plane displacement are consistent with the non-conforming bending element, and the inplane degrees of freedom are consistent with the inplane strain-based element.

In the present paper the natural frequencies and the corresponding modes of vibration are investigated when the reinforced plates are subjected to uniform uniaxial, biaxial and shear loads. The variation of the natural frequencies with various sizes of reinforcement is obtained for plates subjected to a range of magnitude of inplane loading.     

多种材料结构体系塑性极限分析的弹性补偿有限元法

弹性补偿有限元法是一种简单、高效的结构塑性极限分析方法,目前仅用于采用单一材料的结构体系中。在经典弹性补偿有限元法中引入承载比概念,并据此对算法进行了改进,既保留了算法通过结构广义应力场不断平均化获得下限荷载的基本优化思想,又融入了平均化过程按各种材料的广义强度成比例调整的新思想,结构破坏时每种材料同时趋于各自的广义强度,使算法适用于对采用多种材料的结构体系做塑性极限分析。经典算例的对比分析表明,改进算法的分析结果是收敛的、准确的和稳定的。对复杂钢框架结构的极限荷载和破坏模式分析也表明,改进算法可用于采用多种材料的实际工程结构的安全评价中。     

Differential quadrature buckling analyses of rectangular plates subjected to non-uniform distributed in-plane loadings

The new version of differential quadrature method (DQM), proposed by the senior author recently, is used to obtain buckling loads of thin rectangular plates under non-uniform distributed in-plane loadings for the first time. Two steps are involved: (1) solve a problem in plane-stress elasticity to obtain the in-plane stress distributions and (2) solve the buckling problem under the loads obtained in step (1). The methodology and procedures are worked out in detail and buckling problems with loadings of non-uniform distributions are studied. Numerical studies are performed and the DQ results are compared well with analytical solutions and finite element results. This fact indicates that the DQ method can be employed for obtaining buckling loads of plates with other combinations of boundary conditions subjected to non-uniform distributed loadings.     

Finite Element Analysis of Track Structures

Abstract: A simple finite element method, based on the analogy with a beam on an elastic foundation, has been developed and applied to the analysis of track structures subjected to point or uniformly distributed loads, A technique for treating infinitely long tracks by using an equivalent model of finite length has also been developed and incorporated into the analysis. Variations in track and/or foundation properties along the Length of the track are easily handled in the proposed method. The entire analysis can be conveniently programmed to run on a microcomputer, and with a few elements gives fast and accurate results. Important parameters are identified and their effects on the results discussed.     

Stability of variable thickness shear deformable plates—first order and high order analyses

This work presents analysis of the buckling loads for thick elastic rectangular plates with variable thickness and various combinations of boundary conditions. Both the first order and high order shear deformation plate theories have been applied to the plate's analysis. The effects of higher order non-linear strain terms (curvature terms) are considered as well. The governing equations and the boundary conditions are derived using the principle of minimum of potential energy. The solution is obtained by the extended Kantorovich method. This approach is combined with the exact element method for the stability analysis of compressed members with variable cross-section, which provides for the derivation of the exact stiffness matrix of tapered strips including the effect of in-plane forces. The results from the two shear deformation theories are compared with those obtained by the classical thin plate's theory and with published results.     

Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements

Buckling of plates with arbitrarily oriented, sniped stiffeners is studied. The main objective is to present and validate an approximate, semi-analytical computational model for such plates subjected to in-plane loading. Estimation of the buckling strength is made using the von Mises’ yield criterion for the membrane stress as the strength limit. The formulations derived are implemented in a Fortran computer code, and numerical results are obtained for a variety of plate and stiffener geometries. The model may handle complex plate geometries, by using inclined stiffeners to enclose irregular plate shapes. The method allows for a very efficient analysis. Relatively high numerical accuracy is achieved with low computational efforts. The results are, in most cases, found to be conservative compared to fully nonlinear finite element analysis results.     

Post-local-buckling of fiber-reinforced plastic composite structural shapes using discrete plate analysis

In this paper, post-buckling of rectangular composite plates rotationally restrained at the longitudinal unloaded edges and subjected to end shortening strain at the simply-supported loaded edges is analyzed using the first-order shear deformation plate theory-based spline finite strip method, and its application to post-local-buckling of fiber-reinforced plastic (FRP) composite structural shapes is illustrated with discrete plate analysis. Two cases of elastically- and rotationally-restrained plates are analyzed using the spline finite strip method: rotationally-restrained along both the unloaded boundary edges (RR) and one rotationally-restrained and the other free along the unloaded edges (RF). The two cases of rotationally-restrained plates (i.e., the RR and RF plates) are further treated as the discrete plates of closed and open section FRP shapes, and by considering the effect of elastic restraints at the joint connections of flanges and webs, post-local-buckling of various FRP shapes under end shortening is studied. The numerical comparisons with the finite element modeling demonstrate that the proposed discrete plate analysis technique and spline finite strip method can be used as an efficient and valid tool for post-local-buckling analysis of FRP shapes.