力法中降维思想的应用

APPLICATION OF DIMENSION REDUCTION PHILOSOPHY IN THE FORCE METHOD

  • 摘要: 力法是分析超静定结构最原始、最基本的计算方法,也是结构力学课程学习的重点内容之一。但是,当前的教学基本要求仅是能熟练掌握超静定次数不超过3的结构受力变形分析,而当超静定结构复杂或超静定次数大于3时,采用目前力法教学内容将导致计算量大、计算难度高。为此,本文从“化繁为简、化未知为已知”的科学研究方法出发,提出用“降维思想”:包括结构降维、超静定次数降维、以及二者联合应用来求解。降维思想的应用,使得基本体系无论从结构形式,或是多余未知力个数均得以简化,既可以降低绘制复杂结构内力图的难度,又能够减少求解多元非齐次线性代数方程组的阶数及其系数、自由项的个数。灵活、熟练地掌握降维思想,可为力法求解提供新的思路,使仅仅用传统的力法知识来分析复杂超静定结构成为可能。

     

    Abstract: The force method is the most fundamental and classical method for analyzing statically indeterminate structures, and it is one of the key topics in the subject of structural mechanics. However, current teaching typically requires proficiency only in analyzing structures with up to three degrees of static indeterminacy. When the structure becomes more complex or the degree of indeterminacy exceeds three, applying the conventional force method results in heavy computational workload and high difficulty. To address this issue, this paper introduces the concept of dimension reduction, including structural dimension reduction, indeterminacy degree reduction, and their combined application, as an effective problem-solving strategy. The application of dimension reduction simplifies both the structural form and the number of redundant unknowns, thereby reducing the difficulty of constructing internal force diagrams and decreasing the size and complexity involved in solving multivariable nonhomogeneous linear equations. Mastery of this dimension reduction philosophy provides a new perspective for applying the force method and makes it feasible to analyze complex statically indeterminate structures using only traditional techniques.

     

/

返回文章
返回