薄板哈密顿含参变分原理

将薄板哈密顿变分原理及其泛函),,,(xxxHVMwyP推广为含两个可选参数1h和2h的薄板哈密顿含参变分原理及其含参泛函),,,(21xxxHVMwyPhh。其推导过程为:首先将薄板Hellinger-Reissner变分原理及其泛函}){,(MwHRP推广为含可选参数1h的薄板Hellinger-Reissner含参变分原理及其含参泛函}){,(1MwHRhP。然后采用消元法(消去变量yM和xyM)和换元乘子法(增加变量xy和xV)由含参泛函}){,(1MwHRhP导出含两个可选参数的薄板哈密顿含参泛函),,,(21xxxHVMwyPhh。含参变分原理是多种变分原理的组合形式,并使多种变分原理之间得到沟通和融合。通过对参数1h和2h的合理选取和赋值,可以得到含参泛函的多种退化形式,为建立多种有限元模型创造条件。

HAMILTONIAN VARIATIONAL PRINCIPLE WITH ARBITRARY PARAMETERS FOR THIN PLATES

The Hamiltonian variational principle and its functional ),,,(xxxHVMwyP for thin plates are generalized and a new Hamiltonian variational principle with two optional parameters, 1h and 2h, and its functional ),,,(21xxxHVMwyPhh are developed. In the derivation process, the Hellinger-Reissner variational principle and functional }){,(MwHRP for thin plates are developed into a new Hellinger-Reissner variational principle with one optional parameter h1 and a functional }){,(1MwHRhP, respectively. With variable elimination method (variables yM and xyM are eliminated), variable substitution and multiplier method (variables xy and xV are added), the Hamiltonian functional with two optional parameters for thin plates,),,,(21xxxHVMwyPhh is derived from the functional }){,(1MwHRhP. The variational principle with parameters is the combined form of various variational principles, and it establishes close relationships among these variational principles. By rational selection and evaluation of the parameters 1h and 2h, many degenerative forms of the functional with parameters can be obtained. This provides an effective tool to develop various finite element models.