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 guarantee of a single-valued, continuous displacement field. A new general compatibility condition, based on the theorem of strain-rotation decomposition (Chen[4]) is derived. The displacement compatible condition reduces to Saint-Venant's condition when strain and rotation are infinitesimal.
Similar content being viewed by others
References
Fung, Y.C.,Foundation of Solid Mechanics, Prentice-Hall, (1965), $4.6.
Chien, W.Z., and K.Y. Yeh,Elastic Mechanics, Science Press, (1956), 37–39. (in Chinese)
Chen, Z.D.,Lecture on Rational Mechanics, Graduate School, China Institute of Mining, (1980). (in Chinese)
Chen, Z.D.,Geometric Field Theory of Finite Deformation in Continuum, Acta Mechanica Sinica, No. 2, (1979), 107–117 (in Chinese)
Green, A.E. and W. Zerna,Theoretical Elasticity, Oxford, (1954), $2.3 2nd edition, Oxford, (1968).
Eringen, A.C.,Nonlinear Theory of Continuous Media, McGraw-Hill, (1962), $13.
Truesdell, C. and R. Toupin,The Classical Field Theories, in “Handbuch der Physik”, Vol. III/1, Springer-Verlag, (1960).
Murnaghan, F.D.,Finite Deformation of Elastic Solid, John Wiley, (1951), 38–42.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhi-da, C. On the compatibility condition of displacement field for finite deformation of continuum. Appl Math Mech 4, 849–854 (1983). https://doi.org/10.1007/BF01896171
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01896171