“能量法求位移”教与学的思考材料力学教学札记

REFLECTIONS OF THE “ENERGY METHOD”: NOTES ON THE TEACHING OF MATERIAL MECHANICS

  • 摘要: “能量法求位移”是材料力学课程体系中独具特色的一章。在教学中,未涉及对偶变量(及空间)、外力势能、虚应力原理3个概念的出现,及未见有材料力学教材将虚位移原理置为第一性原理的位置予以应用,未能清晰体现内容上的关系。鉴于此,本文总结讨论了卡氏定理、余能定理、功与位移互等定理、虚位移原理、单位载荷法、图乘法及力法正则方程之间的逻辑关系,清晰化了各部分内容之间的递进层次,并给出了知识体系框架。

     

    Abstract: “The energy method for displacement calculation” stands out as a unique chapter in the material mechanics curriculum. In teaching practices, chanllenges arise from the need to navigate concepts such as dual variables (and space), external potential energy, and the principle of virtual stress. Additionally, since no textbook explicitly establishes the Principle of Virtual Displacement as a fundamental principle, the logical coherence within its content are not clearly articulated. To address this, this paper summarizes and discusses the interrelations among the Castigliano Theorem, Complementary Energy Theorem, Reciprocal Work Theorem, Reciprocal Displacement Theorem, Principle of Virtual Displacement, Unit Load Method, Graph Multiplication Method, and Regularization Equation of the Force Method. By clarifying the hierarchical progression of these concepts, the study delineartes a structured framework of the energy method's knowledge system.

     

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