刚度分配图乘法的基本原理及应用
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摘要
在结构力学中,当采用常规图乘法计算变截面梁结构的位移时,通常会面临弯矩图分块面积多、图乘次数多、计算量大、计算效率低等困难。针对这些问题,从结构刚度的角度出发,提出变截面梁结构位移计算的刚度分配图乘法,推导了该方法的基本公式并建立其使用的基本操作原则。该方法概念清晰,容易理解,充分发挥了图乘法的优势。算例的应用与比较表明,采用该方法进行位移图乘计算简便合理,计算量非常小,计算效率高,值得推广。
When the regular diagram multiplication method is applied to compute the displacements of beam structures with variable cross-sections, many difficulties will be encountered, such as too much area blocks, excessive numbers of diagram multiplications, great amount of computation, and low computational efficiency. So a new stiffness-distribution diagram multiplication is proposed to solve these difficulties based on the structural stiffness. Basic formulas are derived with operation principles for their applications. The concept of the new method is very clear and can be understood easily, with the advantages of the diagram multiplication method taken fully. The application and the comparison of a numerical case show that the operation of the stiffness-distribution diagram multiplication method is very simple and reasonable.With the new method, small amount of computation is taken with high efficiency. So it is worth being recommended.
When the regular diagram multiplication method is applied to compute the displacements of beam structures with variable cross-sections, many difficulties will be encountered, such as too much area blocks, excessive numbers of diagram multiplications, great amount of computation, and low computational efficiency. So a new stiffness-distribution diagram multiplication is proposed to solve these difficulties based on the structural stiffness. Basic formulas are derived with operation principles for their applications. The concept of the new method is very clear and can be understood easily, with the advantages of the diagram multiplication method taken fully. The application and the comparison of a numerical case show that the operation of the stiffness-distribution diagram multiplication method is very simple and reasonable.With the new method, small amount of computation is taken with high efficiency. So it is worth being recommended.
引文
1包世华,辛克贵.结构力学.武汉:武汉理工大学出版社,2012
2金宝桢,杨式德,朱宝华.结构力学.北京:人民教育出版社,1979
3魏小文,张勇,陈红迁.对图乘法的发展.力学与实践,2006,28(6):76-79
4孙庆巍.谈结构力学图乘法应用中复杂图形的图乘技巧//田道全主编.土木建筑教育改革理论与实践(2009年第11卷).武汉:武汉理工大学出版社,2009:26-29
5黄亮,马捷,邓煜涵等.一种超静定变截面梁的力法计算技巧.力学与实践,2016,38(4):459-461Huang Liang,Ma Jie,Deng Yuhan,et al.Computing skills of force method for statically indeterminate beams with variable cross sections.Mechanics in Engineering,2016,38(4):459-461(in Chinese)
2金宝桢,杨式德,朱宝华.结构力学.北京:人民教育出版社,1979
3魏小文,张勇,陈红迁.对图乘法的发展.力学与实践,2006,28(6):76-79
4孙庆巍.谈结构力学图乘法应用中复杂图形的图乘技巧//田道全主编.土木建筑教育改革理论与实践(2009年第11卷).武汉:武汉理工大学出版社,2009:26-29
5黄亮,马捷,邓煜涵等.一种超静定变截面梁的力法计算技巧.力学与实践,2016,38(4):459-461Huang Liang,Ma Jie,Deng Yuhan,et al.Computing skills of force method for statically indeterminate beams with variable cross sections.Mechanics in Engineering,2016,38(4):459-461(in Chinese)