Abstract

A port-Hamiltonian formulation for general linear coupled thermoelasticity and for the thermoelastic bending of thin structures is presented. The construction exploits the intrinsic modularity of port-Hamiltonian systems to obtain a formulation of linear thermoelasticity as an interconnection of the elastodynamics and heat equations. The derived model can be readily discretized by using mixed finite elements. The discretization is structure-preserving, since the main features of the system are retained at a discrete level. The proposed model and discretization strategy are validated against a benchmark problem of thermoelasticity, the Danilovskaya problem.

摘要

提出了一般线性耦合热弹性和薄结构热弹性弯曲的哈密顿方程。该构造利用了哈密尔顿港系统的固有模块化，从而获得了线性热弹性公式，将其作为弹性动力学方程和热方程的相互联系。通过使用混合有限元可以很容易地离散导出的模型。离散化是保留结构的，因为系统的主要特征保持在离散的水平上。针对热弹性基准问题Danilovskaya问题验证了所提出的模型和离散化策略。