哈密顿体系下的弹性圆板热屈曲问题

以工程中由于温度引起的结构屈曲为研究背景,以最基本的结构之一的圆板热屈曲问题为研究对象,建立了由于温度引起的弹性圆板屈曲问题的哈密顿体系.在辛体系下将临界温度和屈曲模态归结为辛本征值和本征向量问题,印每一个辛本征值和本征向量对应一个临界温度和屈曲模态.这种辛方法克服了传统振型函数方法的局限性,并可直接得到轴对称和非轴对称的屈曲模态.本征解空间的完备性确保可得到所有的临界温度和对应的屈曲模态.数值结果显示了临界温度的变化规律和屈曲模态的特点.这种辛方法也为求解其他问题提供了一条路径.

Thermal buckling problem of elastic circular plates in Hamiltonian system

The buckling of structures, which is aroused by temperature, is discussed as the primary problem. The circular plate is as one of basal structures and its thermal buckling is studied with a new method. For researching, a Hamiltonian system is presented for the thermal buckling of elastic circular plates. In the symplectic system, critical temperatures and buckling modes are corresponding to eigenvalues and eigenvectors, namely, every symplectic eigenvalue and eigenvector correspond to a critical temperature and the respective buckling mode. In the symplectic method, the axisymmetric and non-axlsymmetric buckling modes can be obtained directly. Since the eigen solution space is complete, all critical temperatures and corresponding buckling modes are able to be obtained. Numerical results show the characteristics of critical temperatures and buckling modes. The symplectic method provides a way for solving other problems.