建议一个角应变的新定义
Suggestion of a New Definition of Angular Strain
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摘要: 本文建议了一个角应变的新定义.这个新定义和线应变的定义相类似,也是一种变化率(角位移的变化率).文中证明了这一新定义与原有定义是一致的,但在几何解释上却更为方便.文中还利用新的角应变定义证明了转轴公式,组成了应变张量和证明了剪切虎克定律.Abstract: A new definition of angular strain is put forward in this paper. Analogous to the definition of linear strain, angular strain is also defined as a rate of change(of angular displacement).It is verified that the new definition is equivalent to the original, but it is more convenient for geometrical interpretations. Using this new definition we deduce the transformation formulas for the rotation of coordinate axes, erect the strain tensor and verify the Hooke's law for shearing.
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[1] 钱伟长、叶开沅,《弹性力学》,科学出版社,(1980). [2] 杨桂通,《弹塑性力学》,人民教育出版社,(1981). [3] 徐芝纶,《弹性力学》上册,人民教育出版社,(1979). [4] Timoshenko,S,and J.N.Goodier,Theorg of Elasticity,(1951). [5] Warg Chi-teh,Applied Elasticity,(1953). -
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