基于数学物理方程预制密肋模板等效刚度拟板的分析法

预制密肋模板是装配整体式叠合楼盖永不拆除的结构构件,是由平板和密肋交叉梁组成.通过对其平板和密肋梁之间耦合作用的研究,建立了预制密肋模板.等效平板刚度的计算数学物理方程,并基于刚度最小的原则,确定了密肋模板等效平板的弯曲中心平面,将预制密肋板等效成平板,建立了简化的预制密肋模板竖向承载的理论计算方法.研究结果表明模板的跨度、肋梁间距、肋梁高度和模板的厚度对其力学响应具有明显的影响.     

复合多层介质在可变温度和集中荷载作用下的位移和应力

研究了多层介质中的热弹性位移和应力.多层介质具有不同厚度,各层又具有不同的弹性性质,最上层表面上作用热荷载和集中荷载.假设各层分别是均匀、各向同性弹性材料,各层相关的位移分量是轴对称的,对称轴为各层表面的垂线.因此,各层应力函数满足无体力的单一方程.利用积分变换法求解了该方程,对由任意多个层数构造的多层介质,给出了其相应层数基础热弹性位移和应力的解析表达式.并对3层介质和4层介质时的数值结果进行了比较.     

轴对称饱和地基竖向振动分析

基于Biot动力固结方程,考虑了土体和水体的惯性力以及水土之间的耦合作用,采用Laplace-Hankel积分变换求解耦联合方程组,得到动荷载下饱和地基振动问题的解答．根据下边界为不透水基岩的边界条件,获得了地基表面作用圆形轴对称任意荷载时土层应力、位移等的一般积分形式解．研究表明,激振频率对饱和地基的竖向振动有很大影响,地基表面的竖向位移与施加荷载之间存在相位差．此外,动力渗透系数在荷载施加的初期对结果有较大影响,随着荷载趋于稳定,其影响变得很小．     

偏心冲击荷载作用下薄圆板动力学响应的保结构分析

关注动力学系统的局部几何性质,采用多辛分析方法研究了偏心冲击荷载作用下薄圆板振动特性.在探索偏心冲击荷载作用下薄圆板振动问题动力学控制方程的对称性和守恒律的对应关系基础上,对动力学控制方程在多辛体系下重新描述,并采用显式中点差分离散方法构造其多辛格式,通过对存在不同相对偏心距冲击荷载作用下的薄圆板振动过程的数值模拟,研究了相对偏心距对薄圆板振动特性的影响,同时,数值模拟结果也充分体现了多辛算法的良好保结构性能.该研究结果不仅为由于荷载作用位置误差带来的动力学响应偏差估计提供了依据,而且为偏心冲击动力学问题的研究提供了新的途径.     

Synchronous/Asynchronous Buckling of Double-Layered Microplate Systems北大核心CSCD

采用修正的偶应力理论和双变量高阶剪切变形理论,发展了层间填充弹性介质的双层微板系统在面内压缩荷载作用下的屈曲模型.基于Euler-Lagrange方程推导了系统屈曲的控制微分方程,运用Navier法获得了上下层均为四边简支时系统同步/异步屈曲的解析解.通过数值算例讨论了系统各参数对其屈曲特性的影响.结果表明：系统的异步屈曲特性依赖于材料尺度参数、长宽比和弹性介质模量,而同步屈曲特性仅依赖于前两项,并且异步屈曲荷载高于同步屈曲荷载;弹性介质的Pasternak模量较之于Winkler模量对系统的屈曲特性影响更显著.     

折线强化弹塑性应力分析的有限元法

本文对材料的应力应变曲线用三段直线的折线拟合,按照弹塑性的简单加载理论,对以增量理论得出的完整应力应变关系进行简化,导出按位移求解的有限元的增量方程.其中弹塑性刚度矩阵可以从弹性刚度矩阵补充后得出,从而节省计算时间.根据von Mises屈服准则确定各次荷载的增量,引入迭代法进行求解,省去对弹塑性刚度矩阵的重复地三角分解,进一步减少计算时间.本文对于应用高次单元、偏离简单加载的荷载、卸载计算、曲线拟合以及荷载的估算问题,均作了说明.     

一类指定应力问题的变分原理与应用

针对有限元分析中对应力或内力有指定条件的问题,引入非弹性应变作为实现指定应力条件的附加未知量,在小变形条件下描述了指定应力条件应当满足的弹性力学控制方程;以位移和未知非弹性应变作为独立变量建立了具有指定应力条件问题的势能变分原理和虚功方程;以位移、弹性应变、未知非弹性应变和应力为独立变量,建立了一个含四类变量的广义变分原理.在基于变分原理得到的桁架单元和梁单元平衡方程中,指定轴力和需要的调整量以对偶形式出现,可实现调整量已知情况下的常规受力分析,又可在轴力指定条件下获得需要的调整量;同时考虑了材料刚度和内力对结构的影响,改进了目前预应力筋模拟的等效荷载法和实体力筋法,还可用于拉索结构的索力优化和调整算法.通过拉索结构位移优化和索力调整的数值算例,验证了该文理论与算法的可行性及精度.     

具有凸缘加劲肋圆孔的应力分析

本文讨论无限平面内具有凸缘加劲肋圆孔的应力分析问题。所谓凸缘加劲肋系指孔周用型钢或其他形状的构件加劲,进行应力分析时难以将其视为板的一部分来处理的加劲肋。文中讨论了两种荷载情形:一为薄板在无限远点处应力σ_X(∞),σ_Y(∞)及τ_XY(∞)的作用;另一为薄板受线性应力的作用。分析方法是:将加劲肋视为圆形杆件,把加劲肋与薄板间相互作用之径向力q₀(θ)及切向力t₀(θ)表示成三角级数,分别求出加劲肋轴线之位移与具有圆孔薄板孔周之位移,利用加劲肋与薄板孔周变形一致的变形协调条件,确定径向力q₀(θ)及切向力t₀(θ),从而得到加劲肋及薄板之位移和内力的算式。     

板梁组合结构可靠性分析的随机边界元法

本文用随机边界元法分析了随机荷载作用下具有随机边界条件的正交各向异性板、梁组合结构的可靠性.文中首先给出正交各向异性板、梁组合结构的边界积分方程,进而基于随机边界元法建立了随机结构可靠性分析方法和得到用于计算正交各向异性板、梁组合结构可靠性指标的公式.算例表明了本文方法的有效性.     

柱塞泵油膜压力分析的高效有限单元法

利用有限单元法,数值分析轴向柱塞泵缝隙高度可变时阀门板上油膜的压力分布.缝隙中油压变化的确定,通常是应用Pasynkow 润滑理论中的Reynolds方程.使用基于有限单元法的自编程序,数值地求解该方程.为了提高结果的精度,基于解的残差估计,应用了加密的自适应网格.给出了依赖于泵的几何条件和工作参数的计算结果.     

Efficient nonlinear finite element modeling of slab on steel stringer bridges

This paper conducts three-dimensional (3D), nonlinear finite element analyses (FEA) to predict ultimate load behavior of slab on steel stringer bridge superstructures. This is accomplished using the commercial finite element package ABAQUS to efficiently capture the behavior of such bridges; comprehensive details of the modeling procedure are presented herein. Two composite steel girders fabricated from high performance steel (HPS) and one four-span continuous composite steel bridge tested to failure have been used to validate the proposed FEA models. These FEA results indicate excellent agreement with the experimental data.     

Partial hybrid finite elements for composite laminates

Three types of partial hybrid finite elements are presented in order to set up a global/local finite element model for analysis of composite laminates. In the global/local model, a composite laminate is divided into three different regions: global, local, and transition regions. These are modeled using three different elements. In the global region, a 4-node degenerated plate/shell element is used to model the overall response of the composite laminate. In the local region, a multilayer element is used to predict detailed stress distribution. In the transition region, a multilayer transition element is used to smoothly connect the two previous elements. The global/local finite element model satisfies the compatibility of displacement at the boundary between the global region and the local region. It also satisfies the continuity of transverse stresses at interlaminar surfaces and traction conditions on the top and bottom surfaces of composite laminates. The global/local finite element model has high accuracy and efficiency for stress analysis of composite laminates. A numerical example of analysis of a laminated strip with free edge is presented to illustrate the accuracy and efficiency of the model.     

Micromechanical Approach of Martensitic Transformation Problem in Steels

To determine the mechanical behavior of material involving the martensitic phase transformation (for example, steels like 100Cr6), a representative volume element (RVE) model including phase transformation criterion is desireable at micromechanical approach. A framework combining the Eshelby's inclusion theory as well as continuum mechanics with phase-transformation (PT) critical condition at RVE model is presented briefly. And application of this model to estimate the critical aspect ratio of martensitic plate or lath inside homogeneneous stress field is also included, where the RVE can be under uniaxial tension/compression or pure shear loading case. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pseudoelasticity of Shape Memory Alloys - a 1D Material Model and Finite Element Implementation

This contribution is concerned with the formulation of a 1D-constitutive model accounting for the pseudoelastic behavior of shape memory alloys. The stress-strain-relationship is idealized by a hysteresis both in the compression as in the tension loading range. It is characterized by an upper loading path, which is to be ascribed to the transformation of the lattice to a martensitic structure. Unloading the material, a lower path is described, because of the reverse transformation into austenitic lattice. The constitutive model is based on a switching criterion which serves as a potential function for the evolution of the internal state variables. The model distinguishes between local and global variables to describe the hysteresis effects for the compression and tension range. A strain driven algorithm which captures the complete nonlinear material behavior is presented. The boundary value problem is solved for a truss element applying the finite element method. A consistent linearization of the nonlinear equations is derived. Simple examples will demonstrate the applicability of the proposed model. For future developments the usage of shape memory alloys within civil engineering structures is aimed. The advantage of the material is the very good damping behavior and the potential to overcome great strains. Both properties are distinguished to be of engineering interest. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear finite element reliability analysis of Concrete-Faced Rockfill (CFR) dams under static effects

The response of concrete slab on Concrete-Faced Rockfill (CFR) dams is very important. This study investigates the reliability of the concrete slab on a CFR dam by the improved Rackwitz–Fiessler method under static loads. For this purpose, ANSYS finite element analysis software and FERUM reliability analysis program are combined with direct coupled method and response surface method. Reliability index and probability of failure of the concrete are computed in the all critical points of the concrete slab by dam height. This study is also expanded for the reliability of CFR dams including different concrete slab thickness. In addition to the linear behavior, geometrically and materially non-linear responses of the dam are considered in the finite element analysis which is performed with reliability analysis. The Drucker–Prager method and the multi linear kinematic hardening method are, respectively, used for concrete slab and for rockfill and foundation rock. Finite element model used in the analyses includes dam–reservoir–foundation interaction. Reservoir water is modeled by the Lagrangian approach. Welded and friction contact based on the Coulomb’s friction law are considered in the joints of the dam. One-dimensional two noded contact elements are used to define friction. The self-weight of the dam and the hydrostatic pressure of the reservoir water are considered in the numerical solutions. According to this study, hydrostatic pressure, nonlinear response of the rockfill and the decrease in the concrete slab thickness reduce the reliability of the concrete slab of the CFR dam. Besides, the CFR dam models including friction are safer than the models including welded contact in the joints.     

Buckling Instability of a Thick Rectangular Plate of a Composite Material with a Spatially Periodically Curved Structure

Within the framework of the continuum approach for composite materials with a spatially curved structure developed by Akbarov and Guz', with the use of the three-dimensional linearized theory of stability, the buckling instability of a rectangular plate made of a composite material is investigated. Various edge conditions are considered, and, for obtaining a numerical result, a three-dimensional FEM modelling is developed. Uniaxial and biaxial precritical compression of the plate is analyzed. The numerical results presented illustrate the influence of problem parameters on the critical relative shortening of the plate.     

Formulation and evaluation of a finite element model for the linear analysis of stiffened composite cylindrical panels

A finite element model for linear static and free vibration analysis of composite cylindrical panels with composite stiffeners is presented. The proposed model is based on a cylindrical shell finite element, which uses a first-roder shear deformation theory. The stiffeners are curved beam elements based on Timoshenko and Saint-Venant assumptions for bending and torsion respectively. The two elements are developed in a cylindrical coordinate system and their stiffness matrices result from a hybrid-mixed formulation where the element assumed stress field is such that exact equilibrium equations are satisfied. The elements are free of membrane and shear locking with correct satisfaction of rigid body motions. Several examples dealing with stiffened isotropic and laminated plates and shells with eccentric as well as concentric stiffeners are analyzed showing the validity of the models.     

A comparison of two microplane constitutive models for quasi-brittle materials

This article presents a comparison of two microplane constitutive models. The basis of the microplane constitutive models are described and the adopted assumptions for the conception of these models are discussed, with regard to: decomposition of the macroscopic strains into the microplanes, definition of the microplane material laws, including the choice of variables that control the material degradation, and homogenization process to obtain the macroscopic quantities. The differences between the two models, with respect to the employed assumptions, are emphasized and expressions to calculate the macroscopic stresses are presented. The models are then used to describe the behavior of quasi-brittle materials by finite element simulations of uniaxial tension and compression and pure share stress tests. The results of the simulations permit to compare the capability of the models in describing the post critical strain-softening behavior, without numerically induced strain localization.     

Special finite elements including stress concentration effects of a hole

Special finite elements are developed for efficient evaluation of stress concentration around a hole in complex structures. The complex variable formulation is used to derive a special set of stress functions which embody the stress concentration effects of a hole. The stress functions in combination with an independent displacement field assumed along the element boundary are used to construct the special elements with the hybrid displacement finite element method. Several numerical examples are presented to show that the used of special finite elements to model critical regions around a hole, together with conventional finite elements to model other regions away from the hole, is not only very convenient but also highly accurate.     

New variational-asymptotic formulations for 3-D stress analyses of laminated composite shells with a circular hole

A new approach for three-dimensional stress analyses in composite cylindrical shells is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. Classical assumptions have been justified and new approximations have been established. These formulations are directed especially towards, new high integrity mixed-hybrid finite element schemes. The expository examples chosen are of cross-ply and angle-ply laminated shells. The circumferential location of the delamination failure initiation, for angle-ply laminates containing a circular hole, is within a sector located symmetrically around the perpendicular direction to the applied load.