关键词: 广义变分原理, 双调和函数, Trefftz方法, 薄板弯曲

Abstract: From the generalized variational principles of plate bending problems, a variational equation is established in which the coordinate function satisfies the biharmonic equation within the region exactly. According to the functional theory of a complex variable, the trial function space is also constructed by using the series of biharmonic polynomials, thus the so-called Trefftz method for thin plate bending problems is proposed, whose feature is that the unknown parameters are evaluated in the manner that approximately satisfies the whole boundary conditions. Three examples for the rectangular plate are presented, which show the high convergence and accuracy of the solutions not only within the region but also on the boundaries and at the corners.

Key words: generalized variational principle, biharmonic function, trefftz method, thin plate bending problems