Rigid finite element and limit analysis

According to the lower bound theorem of limit analysis the Rigid Finite Element Method (RFEM) is applied to structural limit analysis and the linear programmings for limit analysis are deduced in this paper. Moreover, the Thermo-Parameter Method (TPM) and Parametric Variational principles (PVP) are used to reduce the computational effort while maintaining the accuracy of solutions. A better solution is also obtained in this paper. The project supported by National Natural Science Foundation of China  

基于参数变分原理的Cosserat连续体弹塑性分析

基于参数变分原理,提出了Cosserat模型弹塑性计算的算法,给出了基于Cosserat理论的参数最小势能原理,基于所提出的变分方程,建立了Cosserat理论弹塑性分析的参数二次规划模型,进一步将算法应用于平面应变软化问题计算中,获得的结果具有良好的非网格依赖性.  

用于弹性蠕变损伤问题的参变量变分原理

参变量变分原理是近年来发展的用于处理数学物理问题中边界待定边值问题的一种有效方法,本文建立起用于蠕变损伤问题结构分析的参变量变分原理,该原理将原问题化为求解带约束条件的泛函极值,其约束条件就是由蠕变损伤本构关系推导出的系统状态方程组;该原理物理意义明确、表达式简单并且规范,容易为计算机实现。本文给出原理的证明,并就2.25Cr-1Mo钢在550℃下的蠕变问题给出实例。  

岩土中弹塑性渗透固结问题的参变量变分原理

本文给出渗透固结过程的参变量变分原理,可以用来处理岩土弹塑性渗透固结问题,并不受 Drucker 假设的限制,对于关连或非关连塑性流动情形皆可。  

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Ф、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a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a，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。  

纤维增强复合材料层压板的失效过程分析——变参量变分方法

本文建立了关于具有逐层失效不连续本构关系的纤维增强复合材料层压板的参变量变分原理,所构造的受参变量控制的能量泛函的驻值问题可转化为一个拟二次规划问题.本文给出了一个求解此规则问题的有效算法.本文方法的优点在于避免了分析层压板强度的冗长迭代过程,可在一个加载步内求出对应各单层失效的一系列强度比值.  

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.  

材料弹塑性性能数值模拟的多尺度方法

将均匀化方法和渐近分析(Asymptotic Analysis)与参变量变分原理相结合提出了一种模拟复合材料非线性性能的多尺度数值方法.该方法用渐近分析建立宏-细观变量之间的联系,利用参变量变分原理计算非线性响应,求解过程采用迭代算法.为提高计算精度,针对Von-Mises准则和Tsai-Hill准则,提出了一个基于参变量变分原理的改进算法,算例表明该方法可以显著消除传统方法采用线性展开式构造线性互补条件所带来的误差.  

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF COSSERAT CONTINUUM

A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy principle of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.  

基于参变量变分原理的非均质多边形微结构材料弹塑性分析

为了更好地模拟复合材料及含夹杂非均质材料等的宏观弹塑性力学性能,简化有限元建模时间和减少有限元模拟计算量。本文基于参变量变分原理,提出了一种采用任意多边形弹塑性单元进行结构非线性分析的参数二次规划算法,给出了参变量最小势能原理以及最终的二次规划模型,并在有限元分析与优化设计软件系统JIFEX上进行了程序实现。数值算例证明了本文方法的正确与可行性。