THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD

IntroductionNumerical manifold method is a new numerical method established on the basis of finitecover of manifold[1,2].By using continuous and non-continuous finite cover system,thenumerical manifold method includes the continuous and non-continuous as …     

The applications of generalized variational principles in nonlinear structural analysis

This paper discusses the generalized variational principles founded by thetechnique of Lagrangian multipliers in structural mechanics and analyzes the nonlinearstatically indeterminate structures.It is assumed that the stress-strain relationship ofthe materials of structures has the form ofσ=Bε~(1/m)orτ=Cγ~(1/m),namely,thephysical equations of structures have the shape of exponential functions.Severalexamples are given to illustrate the statically indeterminate structures such as thetrusses,beams,frames and torsional bars.     

数值流形单元法数学网格自适应

基于数值流形方法和有限覆盖技术,将有限元法的后验误差估计理论及h型网格自适应技术推广应用到数值流形单元法中,提出了数值流形单元法的后验误差估计方法和数学网格自适应技术,并编制了相应的程序。数值算例表明,经过网格自适应,可以在粗糙的初始网格基础上得到质量比较理想的网格,计算结果可达到用户要求的精度。     

Zienkiewicz薄板单元的数值流形法实现

Zienkiewicz薄板单元是最早出现的板单元,因节点参数简单,所以在70年代之前曾起过重要作用;但同时它又是非协调的,仅对由三组间距相等的平行直线所形成的网格才能满足分片检验,这限制了这一单元的应用.因此,先后有不少学者对其进行过改进,使其能对任意形状的网格收敛.考虑到数值流形元法(NMM)总是用最佳质量的数学网格来进行逼近,本文尝试用NMM来解决Zienkiewicz单元的网格依赖问题.基于板的最小势能原理,提出了适用于NMM的混合变分提法,然后利用有解析解的椭圆板问题对方法进行了验证.本文所提出的方法,还可被用于其他类型的非协调单元的改造.     

数值流形方法的对象设计

研究了数值流形方法的对象设计方法和组织方式,为流形方法的理论研究和向三维问题的扩展打下良好的基础,研究发现数值流形方法具有编程和前后处理简单的特点,且仅用三角形流形单元和一阶近似的覆盖位移函数就可达到有限元多结点等参元的求解精度,具有深远的工程意义,计算结果表明,数值解与理论解吻合。     

The Variational Principle and Application of Numerical Manifold Method

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Semi-inverse method and generalized variational principles with multi-variables in elasticity

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The invariant manifold method and the controllability of nonlinear control system

The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A.M.Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics of rigid body to nonlinear control system for the first time and obtained a series of efficient results. Based on Kovalev’s oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition was discussed. At last, the motion of a rigid body with two rotors was investigated and the necessary condition which is satisfied by this system was proved.     

Region-wise variational principles and generalized variational principles on large strain for consolidation theory

Introduction Thedeformationofsaturatedsoftclayisoneofimportantquestionsingeotechnical engineering.Thenotablecharacteristicisthatthedegreeofitsstrainisgenerallylargerthan10percent.Oneofthecauses[1],Whichleadtoaquantitativedifferencebetweenthe numericalsimu…