雍华东. 基于卡氏第二定理求解细长螺旋杆件的位移. 力学与实践, xxxx, x(x): 1-4. doi: 10.6052/1000-0879-23-485
引用本文: 雍华东. 基于卡氏第二定理求解细长螺旋杆件的位移. 力学与实践, xxxx, x(x): 1-4. doi: 10.6052/1000-0879-23-485
Yong Huadong. Solution of the displacement of slender and helical rod based on the castigliano’s second theorem. Mechanics in Engineering, xxxx, x(x): 1-4. doi: 10.6052/1000-0879-23-485
Citation: Yong Huadong. Solution of the displacement of slender and helical rod based on the castigliano’s second theorem. Mechanics in Engineering, xxxx, x(x): 1-4. doi: 10.6052/1000-0879-23-485

基于卡氏第二定理求解细长螺旋杆件的位移

SOLUTION OF THE DISPLACEMENT OF SLENDER AND HELICAL ROD BASED ON THE CASTIGLIANO’S SECOND THEOREM

  • 摘要: 由于具有较为优异的力学性能,螺旋结构的细长杆件在工程中得到了广泛的应用。在拉伸及弯曲载荷作用下,螺旋杆件自身较为特殊的结构导致其变形规律较为复杂。本文基于螺旋杆件的应变能及材料力学的卡氏第二定理,得到了拉伸及横向载荷作用下螺旋杆件的位移,所得解析结果与有限元结果一致。螺旋杆件位移的求解可以作为材料力学基本内容的拓展,强化学生对相关知识点的理解和掌握。

     

    Abstract: Because of its excellent mechanical properties, slender rods with spiral structure have been widely used in engineering. Under the action of tensile and bending loads, the special structure of the twisted rods leads to the complicated deformation law. In this paper, based on the strain energy of slender rods and the Castigliano's second theorem in mechanics of materials, the displacements of the twisted rod under the action of tensile and lateral loads are obtained. The analytical results are in agreement with the finite element results. The calculation of displacement of twisted rod can be used as an extension of the basic content of mechanics of materials, which can strengthen students’ understanding and mastery of relevant knowledge points.

     

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