一类矩形中厚板弹性模型的Hamilton形式

The Hamiltonian Form for a Class of Elastic Models for the Rectangular and Moderately Thick Plates

通过分析矩形中厚板的一些具体力学问题,提出一类矩形中厚板模型,并从数学角度建立了该模型的两种Hamilton形式,得到两类Hamilton算子,这为辛体系方法的应用奠定了基础。最后从Lagrange密度函数和Legendre变换角度阐述了Hamilton形式导出过程。

A class of rectangular and moderately thick plate models has been proposed by analyzing some specific mechanical problems.Two kinds of Hamiltonian forms of the models are established from the mathematical point of view,and two kinds of Hamiltonian operators are provided.The corresponding results lay a foundation for the further application of the symplectic system method.Finally,the derivation of the Hamiltonian forms is described from the Lagrange density function and Legendre transform.