论连续体有限变形的位移协调条件
On the Compatibility Condition of Displacement Field for Finite Deformation of Continuum
-
摘要: 有限变形的协凋条件在文献中常以Riemann-Christoffel张量等于零表达.水文应用Cesaro方法和作者的非线性应变-转动张量分解定理证明上述条件仅是必要的,尚不充分保证位移场的单值性与连续;文中导出新的一般有限变形的位移协调条件.当应变与转动微小时,它化为Saint-Venant方程.Abstract: The vanishing of Riemann-Christoffel tensor is usually adopted as the compatibility condition of finite deformation, However, we prove in this paper by the method of Cesaro that this condition is necessary but not sufficient for the guarantee of single-valued, continuous displacement field, A new general compatibility condition,based on theorem of strain-rotation decomposition (Chen[4])is derived, The displacement compatible condition reduces to Saint-Venants condition when strain and rotation are infinitesimal.
-
[1] Fung, Y C.,Foundation of Solid 1Llechanscs, Prentice-Hall, (1965),§4.6. [2] 钱伟长、叶开沅,《弹性力学》,科学出版社,(1956), 37-39. [3] 陈至达,《有理力学讲义》.中国矿院,(1980). [4] 陈至达、连续介质有限变形力学几何场论.力学学报,2(1979). 107-117 [5] Green, A.E.and W Zerna, Theoretical Elasticity, Oxford, (1954), 2.3. 2nd Edition, (1968). [6] Eringen, A, C.,Nonlinear Theory of Continuous BTedia, McGraw-Hill, (1962),§13. [7] Truesdell, C, and R.Toupin, The Classical Field Theories, in Handbuch der Physik,Vol Ⅲ/1,Springer-Verlag,(1960) [8] Muruaghan, F, D Fsnste Deformation of Elastic Solid, John Wiley, (1951).38-42. -
计量
- 文章访问数: 2166
- HTML全文浏览量: 133
- PDF下载量: 711
- 被引次数: 0
下载:
渝公网安备50010802005915号