摘要
在轴对称载流薄壳的几何方程、物理方程、运动方程和电动力学方程基础上,建立了载流薄壳热磁弹性耦合方程。考虑电磁场的焦耳热效应,引入热平衡方程及广义欧姆定律得到了薄壳的温度场。应用变量代换进行变形,整理成含有八个基本未知函数的标准柯西型方程式。通过差分及准线性化方法,变换成能用离散正交法编程求解的准线性微分方程组。对于载流球台薄壳,得到了洛仑兹力的表达式,并且推导得到了温度场积分特征值。讨论了载流球台薄壳应力、温度及变形随外加电磁参量的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对板壳的应力、应变、温度的控制。
In a symmetrical current-carrying thin shell, the magnetic-elasticity coupling equations were built according to geometrical equations, physical equations, motion equations and electrodynamics equations. The temperature field in the thin shell is obtained after considering the Joul’s heat effect and inducting the thermal equilibrium equation and generalized Ohm’s law. The normal Cauchy form nonlinear differential equations including eight basic unknown functions are obtained from a variable replacement method. Through the difference method and quasi-linearization method, the quasi-linearization difference equations which could be solved by the discrete orthogonalization method are gotten. The expression of Lorenz force and the temperature field eigenvalues of integral were derived. The variant regularity of the stress, temperature and deformation in the current-carrying spherical segment, and the varying law with loaded electromagnetic parameter are discussed. It is proved from an example that the deformation and stress can be controlled by means of changing the electromagnetic and mechanics parameters.
出处
《工程力学》
EI
CSCD
北大核心
2010年第10期224-229,240,共7页
Engineering Mechanics
基金
国家自然科学基金项目(50875230)
关键词
热磁弹性
载流球台薄壳
耦合
电磁场
温度场
thermal magneto-elastic
thin current-carrying spherical segment shell
coupling
electromagnetic field
temperature field
