STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.     

陀螺用超细径保偏光纤机械强度评估方法

针对陀螺应用场景下超细径保偏光纤机械强度评估需求,提出一种基于可拉伸骨架的超细径保偏光纤强度评估方法,超细径保偏光纤绕制于可拉伸骨架之上形成光纤环圈可模拟出成环应力过程,采用该光纤环圈构建光纤陀螺,环圈骨架内的压电堆栈可驱动骨架带动超细径保偏光纤周期性拉伸,对超细径保偏光纤起到应力激励施加效果可激发光纤疲劳以实现光纤强度快速评估与筛选,同时在超细径保偏光纤内形成相位调制功能以实现陀螺偏置调制,陀螺信号长期输出变化情况可表征超细径保偏光纤力学特性优劣。该方法能够体现出超细径保偏光纤成环应力施加的复杂性和陀螺应用光纤长期张紧、弯曲等条件下应力长期演变性,有助于陀螺用超细径保偏光纤强度评估与筛选。     

关于弹性力学广义变分原理的等价性定理的研究

利用场论中的不变性原理研究弹性力学广义变分原理的等价性定理,主要目的是研究弹性力学广义变分原理之间的关系;根据弹性力学广义变分原理的泛函在无穷小标度变换下的不变性,证明了这些泛函之间的等价性定理．如果这些泛函具有无穷小标度变换下的不变性,那么只有两类变量是独立的, 应力应变关系是这些泛函必须满足的变分约束条件．所得到的结果再一次证明了钱伟长教授关于所有的弹性力学广义变分原理都是等价的结论．