广义重调和算子及其在薄板弯曲中的应用

Generaliaed Biharmonic Operator and Its Application to the Bending of Elastic Thin Plates

本文用δ－函数具体构造出广义重调和算子，建立相应的二次泛函表达式，并将其应用于弹性薄板的弯曲问题．结果表明．当自变量函数为广义函数时，变分泛函中的自变量函数自然就允许某种程度的不连续性，用Ｌａｇｒａｎｇｅ乘子法所得的修正变分原理实际上是文中给出的变分原理的特殊形式．

In this paper,δ-fuuction is used to construct the generalized biharmonic opera-tors.the corresponding quadratic function is presented.and the latter is applied to the bending of elastic thin plates. The result shows that when the arguments in the variational functional are generalized functions.discontinuity to some degree is allowed,and the modified variational principle by using the Lagrange multipliers is merely a special form of the result mentioned above.