“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、虚应力原理三个概念的出现,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" is a distinctive chapter within the material mechanics curriculum. In teaching, to circumvent the concepts of dual variables (and space), external potential energy, and the principle of virtual stress, and given that no textbook positions the Principle of Virtual Displacement as a fundamental principle for application, the logical connections within its content are not clearly articulated. In view of this, this article summarizes and discusses the relationship of the Castigliano Theorem, the Complementary Energy Theorem, the Reciprocal Work Theorem, the Reciprocal Displacement Theorem, the Principle of Virtual Displacement, the Unit Load Method, the Graph Multiplication Method, and the Regularization Equation of the Force Method. The progressive hierarchy among these contents has been clarified, and the framework of the knowledge system has been presented.

     

/

返回文章
返回