VARIATIONAL PRINCIPLES OF ASYMMETRIC ELASTICITY THEORY OF FINITE DEFORMATION

In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation energy is derived and the physical meaning is clarified. The power variational principle and the complementary power variational principle for finite deformation mechanics are supplemented and perfected.

Analytical solution to mapping rail deformation under bridge transverse deformation using energy variational principle

The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.

Elastoplastic 3D Deformation and Stress Analysis of Strip Rolling

An elastoplastic method for analyzing the 3D deformation, stress and transverse distribution of tension stress during cold strip rolling is developed. The analysis is based on the elastoplastic variational principle in which a kinematically admissible velocity field is constructed with the lateral flow function as an unknown function. The stress distribution and volume strain distribution are obtained by solving the simultaneous equations formed by the longitudinal differential equation of equilibrium and constitutive equations. The lateral flow function is determined by minimizing the total energy dissipation rate. Experimental investigation was carried out on a reversible cold mill. The front tension stress distributions in cold rolled strips were measured by a multi roll segmented tension sensing shapemeter. The calculated results are in good agreement with the measured ones.

The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material

In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.

ROLE OF UNDERGROUND STRUCTURE DEFORMATION VELOCITY IN THE ANALYSIS OF BLAST-RESISTANT STRUCTURES

The structural deformation velocity plays a significant role in the dynamic calculation of underground blast-resistant structures. The motion differentiating equation of a structure system taking into account the role of deformation velocity of the structure will truthfully describe the actual situation of structural vibration. With the one-dimensional plane wave theory, the expression of load on the structural periphery is developed, and the generalized variation principle for the dynamic analysis of underground arched-bar structures is given. At the same time, the results of the numerical calculation are compared.

Hybrid natural element method for large deformation elastoplasticity problems

We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system.Compared with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.

弹性参数变异下孔径变形法地应力测试实践

针对裂隙发育地区的弹性参数变异特点,推导了孔径变形法三维地应力计算模型,在工程实践和理论分析的基础上,提出3条裂隙发育区的孔径变形法测试数据筛选原则。利用三维地应力计算模型和测试数据筛选原则,结合实际工程进行了三维地应力测试,并将测试结果和工程区域地应力场特征、水压致裂测试数据、地形地貌进行综合对比分析,结果较为一致。采用下极点的全空间赤平投影技术,进一步分析了泊松比、弹性模量的偏离对三维地应力测试数据的影响。研究结果表明:建立的裂隙发育区孔径变形法地应力计算分析技术可以考虑弹性参数变异的特征,计算结果可靠;相较于泊松比,弹性模量的偏离则会明显影响地应力的量值、方位和倾角。

考虑全截面剪切变形的箱梁挠度简化计算方法

为进一步简化箱梁弯曲挠度计算方法,本文运用能量变分原理和铁摩辛柯梁理论推导了考虑全截面剪切变形的箱梁弯曲挠度计算公式,基于剪滞控制微分方程和现行公路桥规中翼缘有效宽度的折算办法,提出了全截面剪切变形的箱梁挠度简化计算方法。简支和连续箱梁算例分析表明:考虑全截面剪切影响的箱梁理论挠度、简化方法结果与ANSYS数值解吻合良好,且最大差值比基本在5%以内,验证了所提简化计算方法的正确性和适用性。

参变量变分原理求解土的变形模量与压缩模量间的关系

运用参变量最小势能原理推导了弹性及塑性状态下的土的变形模量与压缩模量间的关系 ,认为两者比值与土的内摩擦角、泊松比 μ及粘聚力c等土性指标有关 .提出了塑性影响因子α及临界应力p 的概念 ,指出当试验时土体应力大于土体的临界应力值时 ,变形模量与压缩模量的理论关系式应引入塑性影响因子α,从而克服了以往基于弹性理论得出的变形模量理论值远小于试验值的不足 .

薄壁箱梁剪滞效应的能量变分法

考虑了三个不同的剪滞纵向位移差函数以反映薄壁箱梁不同宽度翼板的剪滞变化幅度,提出了一种能对工程中常用的变高度梯形截面箱梁剪力滞及剪切变形效应进行分析的方法。应用能量变分原理,导出了箱梁受横向荷载作用下的剪滞控制微分方程和边界条件,获得相应的闭合解,并探讨了不同纵向位移差函数对剪力滞的影响。最后通过高阶有限条法计算验证了本文方法的正确性。所得的公式比以往剪滞理论有了发展,因此更具有一般性。

带悬臂板薄壁箱梁的扭转和畸变分析

为研究悬臂板对薄壁箱梁扭转和畸变效应的影响,本文基于广义坐标法建立位移模式和几何方程,采用混合变分原理,建立开闭口混合截面薄壁杆件扭转和畸变的分析理论,该理论能充分考虑剪切变形的影响。分析带悬臂板箱梁剪力流的分布和组成,对比统一剪力流的2种计算方法,研究悬臂板的内力状态及影响。结果表明:悬臂板对扭转和畸变效应的贡献主要体现在其扇形惯性矩所占的比例;悬臂板使闭口箱的翘曲正应力产生明显重分布;悬臂板使剪切变形影响增大,且这种影响随悬臂翼缘板的增长而增大;对于常规薄壁箱梁桥,悬臂板的贡献不可忽略。

波形钢腹板组合箱梁自振特性与试验研究

为了精确计算波形钢腹板组合箱梁的振动频率,根据能量变分原理,推导了振动频率公式,得到了考虑剪切变形及剪力滞效应的各阶自振频率的解析解。对一试验波形钢腹板组合箱梁进行了动力测试,得到了实际自振频率,并与简单梁理论、本文理论公式与三维有限元模型的计算频率进行对比。结果表明:剪力滞效应及剪切变形对波形钢腹板组合箱梁的振动频率影响较大,考虑剪力滞及剪切变形影响后的波形钢腹板组合箱梁的振动频率有所降低,且降低程度随着计算频率阶次的增加而迅速增加,因而在波形钢腹板组合箱梁振动频率的计算中须计其影响。

板带轧制在线控制模型的研究

为解决板带轧制高速高精度在线模型问题,文章基于能量变分原理,研究了一种快速数值算法。该法将变形区划分为有限离散单元,考虑剪切变形作用,建立了高速计算模型,在平面变形条件下实现了对轧制力的仿真。计算结果与实测值、Marc有限元计算结果有很好的吻合。通过对某厂五机架冷连轧的分析,模型可在0.3s内完成全部计算。该算法对深入研究冷热态连轧过程在线控制具有重要实际意义。

考虑剪切变形的薄壁箱梁畸变分析

采用广义坐标法,建立畸变位移模式和几何方程,推导出畸变剪应力;基于混合变分原理,建立了一种新的畸变理论和梁段单元模型,该理论充分考虑了剪切变形的影响。基于新理论,指出了在单箱室箱梁不存在布莱特纯畸变,明确了畸变中心的定义,研究了畸变剪应力成分对剪切变形的影响及其影响程度。结果表明,对于常见的箱梁是可以忽略剪切变形的对畸变效应的影响。

超弹性矩形板单向拉伸时微孔的增长

本文研究了含中心微孔的超弹性矩形板在单向拉伸时的有限变形和受力分析．为了考察微孔的存在对矩形板变形和应力的影响，将问题化成一个超弹性环形板的变形和受力分析，并用最小势能原理得到变分近似解．进行了数值计算，分析了微孔的增长情况．

有限变形弹性理论随机变量变分原理及有限元法

本文将材料、载荷、结构几何形状、力和位移边界条件的随机性，直接引入有限变形弹性理论的泛函变分表达式中，应用小参数摄动法，建立了统一的随机变量变分原理及非线性随机有限元法，并将其应用于结构可靠性分析。算例表明，应用此方法处理随机变量的力学问题，具有使程序实施简便，计算效率高等优点。

多体非连续变形系统的计算力学模型及其应用

针对由不同特性物体所组成的多体系统,探讨了能够涵盖各种变形状态和运动形式的广义有限单元模式及其插值函数形式。对于多体接触问题,发展了能够合理描述界面特性的接触力元模型,即采用某种应力插值函数将界面上的相互作用力由接触对上的接触应力来表达,并将接触对上的接触应力当作需满足界面上屈服准则与流动法则等状态控制条件的参变量,将其作为约束条件加入系统控制方程。根据非连续变形系统的分区参变量最小势能变分原理,联立变分驻值条件与参变量的状态控制条件建立了多体系统非连续变形计算力学分析的基本控制方程,将问题最终归结为一个含有自由变量和等式约束条件的线性互补问题,对此发展了数值解法,并进行了多个算例的数值分析。计算结果表明该模型不仅能够对多体系统进行静、动力耦合分析,而且还能够模拟多体系统的变形与应力及接触界面上的接触应力和相对运动等复杂的非线性过程。

能量变分原理推导考虑剪切变形的梁单元刚度矩阵

利用能量变分原理 ,导出了考虑剪切变形情形的梁段单元刚度矩阵和荷载列阵 。

摩擦约束不完全变分不等原理及其微粒群优化解法

利用不完全变分不等原理,将摩擦约束纳入问题的能量泛函,同时放松体积不可压缩的约束条件ε_(ii)=0,用罚因子处理体积应变。实际算例表明,不完全变分不等原理不但能计算速度场,而且能直接计算变形力,且所得到的变形力比滑移线场结合极值方法获得的解析解更接近试验结果。在有限变形情况下,仍能得到变形力的理想结果。同时,利用微粒群优化方法,直接求解变分问题的能量泛函,避开了变分不等式的求解困难问题。针对优化求解过程中出现解的随机性,利用求平均值方法,使求解过程稳定,有效地改善了求解结果,并由此扩展了微粒群算法的应用领域。

一种计入剪力滞及剪切变形效应的箱梁自振频率计算方法

由于剪力滞效应及剪切变形的存在,箱梁的弯曲振动频率按照初等梁理论计算往往存在较大的误差.综合考虑箱梁的剪切变形及剪力滞效应,利用能量变分原理分析简支箱梁的自由振动,推导出考虑剪力滞效应及剪切变形的简支箱梁的各阶自振频率的解析解,较以前只能计算振动基频有所推广.验证算例计算表明本文方法理论推导正确,计算精度较初等梁理论大大提高.最后对剪力滞效应及剪切变形对箱形梁自振特性的影响进行了讨论,发现考虑剪力滞效应以及考虑剪切变形均使简支箱梁的振动基频降低,且对于箱梁的高阶振动频率降低程度尤为明显;而箱梁的宽跨比是影响其降低程度的最重要因素.