粘弹性悬臂梁弯曲变形的哈密顿体系方法

Hamiltonian system approach to bending problem of viscoelastic cantilever-beams

利用对应原理和变分法,提出一种求解粘弹性悬臂梁问题的哈密顿体系方法,得到对偶方程的基本解向量,即零本征向量和非零本征向量.具体问题的解可表示为这些本征向量的线性组合,组合系数取决于边界条件.通过算例描述粘弹性悬臂梁弯曲变形的应力分布规律、由端部的位移约束带来的应力集中现象以及弯曲变形的蠕变特征,表明了这种方法的有效性.

The correspondence principle and variational method were employed to introduce a Hamiltonian system method for dealing with the bending problem of viscoelastic cantilever-beams, so that fundamental eigenvectors of dual equations, i.e. the zero eigenvectors and nonzero eigenvectors, were obtained. For a specific problem, its solution could be expressed by linear combination of these eigenvectors, and the coefficients of the combination were determined by boundary conditions. By means of an illustrative numerical computation, the stress distribution of bending deformation of cantilever-beam, the stress concentration phenomena caused by the restraint of displacement conditions, and the creep character of bending deformation were described, showing the efficiency of the Hamiltonian system approach.