摘要:
本文提出一类新的固体的离散型变分原理.它是从有限元离散分析的实际出发,考虑到元素的边界为可动边界,并且由于分片构造待解函数,使待解函数在元素的交界处具有各种间断性.由此,我们利用数学中的具有各种间断性的可动边界的变分方法,基于一阶变分为零的驻值条件上,建立了固体的离散型变分原理.离散型变分原理消除了元素交界处所导入的误差.它概括了古典与非古典变分原理.本文得到的待解函数应满足的交界方程,是有限元的收敛性(包括非保形元素在内)的必要条件,它开拓了待解函数应满足协调性的收敛性要求.
Abstract:
This paper suggests a new solid variations, principle of discrete form. Basing on the true case of the discrete analysis by the finite element method and considering the variable boundaries of the elements and the unknown functions of piecewise approximation, the unknown functions have various discontinuities at the interfaces between successive elements.Thus, we have used mathematical technique of variable boundary with discontinuity of the unknown functions, based on the conditions that the first variation vanishes immediately, to establish the solid variation principles of discrete form. It generalizes the classical and non-classical variational principles.Successive equations that have to be satisfied by the unknown functions are the convergency necessary conditions for the finite elements method (including conforming and non-conforming). They expand that convergency necessary conditions of the compatibility conditions in the internal interfaces.
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