中文摘要：

变形体力学的广义变分原理在有限元素法和其他近似计算方法的应用方面取得重大成功，但将广义变分原理推广到分析力学中去的研究进展缓慢，难度很大．针对该问题，首先明确了非保守分析力学问题的控制方程，并按照广义力和广义位移之间的对应关系，将各控制方程乘上相应的虚量积分并代数相加，考虑到系统的非保守特性，建立了非保守分析力学问题的拟变分原理和广义拟变分原理．进而建立了非完整非保守分析力学问题的拟变分原理和广义拟变分原理，并给出合适的算例．

英文摘要：

The generalized variational principle in the mechanics of deformable solids achieved great success in the finite element method and other approximate calculation methods. In spite of this, efforts to popularize generalized variational principles in analytical mechanics experienced many difficulties. To resolve them, the governing equations of non-conservative analytical mechanics were refined. According to corresponding relations between generalized forces and generalized displacements, the governing equations were multiplied by corresponding virtual quantities, integrated and then added algebraically. Considering the non-conservative characteristic of the system, the quasi-variational principles and generalized quasi-variational principles of non-conservative analytical mechanics were established. Then the quasi-variational principles and generalized quasi-variational principles of nonholonomic non-conservative analytical mechanics were established. Finally, an appropriate example was discussed.