结构的刚-热弹耦合稳定性问题研究

Investigation of structural stability of rigid-thermo-elastic coupling

对于刚-热弹耦合动力学这类学科交叉问题,尚无现成的控制方程可以利用.由于变分原理是从总体上把握事物,便于应用功能转化原理和能量守恒定律来研究问题.应用刚-热弹耦合动力学的变分原理,不仅可以建立刚-热弹耦合动力学的控制方程,而且可以为刚-热弹耦合动力学的有限元建模提供方便.本文根据功能转化原理和能量守恒定律,建立刚-热弹耦合动力学变分原理,给出刚-热弹耦合动力学变分原理的驻值条件,得到刚-热弹耦合动力学的控制方程,并且,将以上成果转化为非惯性坐标系中的静力学问题.作为该理论的应用,研究了结构的刚-热弹耦合稳定性问题.在非惯性坐标系中,给出两向应力状态刚-热弹耦合临界应力.最后,讨论了有关问题.

For rigid-thermo-elastic coupling dynamics, a subject crossing research, there are not available governing equations until now. Dealing with the problem from entirety angle, variational principles can apply the transformation theory between work and energy and the law of conservation of energy to solve the problem conveniently. As a result, the variational principle can be used not only to establish the governing equation but also to provide convenience for finite element models of rigid-thermo-elastic coupling dynamics In the paper, according to the transformation theory between work and energy and the law of conservation of energy, the variational principle of rigid-thermo-elastic coupling dynamics was established. Stationary value conditions of variational principle and the governing equations of rigid-elastic coupled dynamics were obtained. And then, conclusions presented above were transformed to statics expression in non-inertia coordinate system. As an application of variational principle of rigid-thermo-elastic coupling dynamics, investigation of structural stability of rigid-thermo-elastic coupling was carried out. Two-oriented critical stresses in case of rigid-elastic coupling state and rigid-thermo-elastic coupling state were presented. Finally, this paper discusses some problems.