Abstract
This paper has two main objectives. The first is to examine the influence of membrane stresses on postbuckled deformations of nonlinear elastic isotropic rectangular plates. The second is to further examine the accuracy of a new 3-D Cosserat eight noded brick element (Nadler and Rubin in Int J Solids Struct 40: 4585–4614, 2003) which was developed within the context of the theory of a Cosserat point. The equations of the Cosserat element include both material and geometric nonlinearities. A number of example problems are considered which examine predictions of the Cosserat element for beams and plates and comparison has been made with results from the commercial codes ANSYS and ADINA. Also, the approximate nonlinear postbuckling solution described in Timoshenko and Gere (Theory of elastic stability, Mc Graw-Hill, New York) is shown to be more limited than originally expected. These results suggest that the Cosserat element is robust, can perform well under extreme conditions and is capable of modeling combinations of three-dimensional bodies with attached thin structures.
Similar content being viewed by others
References
Bulson PS (1970) The stability of flat plates. Chatto and Windus, London
Bloom F, Coffin D (2000) Handbook of thin plate buckling and postbuckling. Chapman and Hall/CRC, Florida
Bodner SR (1955) The post buckling behavior of a clamped circular plate. Quart Appl Math 12:397–401
Flory P (1961) Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57:829–838
Friedrichs KO, Stoker JJ (1941) The non-linear boundary value problem of the buckled plate. Am J Math 63:839–888
Friedrichs KO, Stoker JJ (1942) Buckling of the circular plate beyond the critical thrust. J Appl Mech 9:7–14
Loehnert S, Boerner EFI, Rubin MB, Wriggers P (2005) Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing. Comput Mech 36:255–265
Nadler B, Rubin MB (2003) A new 3-D finite element for nonlinear elasticity using the theory of a Cosserat point. Int J Solids Struct 40:4585–4614
Naghdi PM (1972). The theory of plates and shells. In: Truesdell C (eds). S. Flugge’s Handbuch der Physik, vol VIa/2. Springer, Berlin Heidelberg New York, pp 425–640
Prescott J (1946) Applied elasticity. Dover, New York
Rubin MB (1985) On the theory of a Cosserat point and its application to the numerical solution of continuum problems. J Appl Mech 52:368–372
Rubin MB (1985) On the numerical solution of one-dimensional continuum problems using the theory of a Cosserat point. J Appl Mech 52:373–378
Rubin MB (2000) Cosserat theories: shells, rods and points Solid mechanics and its applications, vol 79, Kluwer, Dordrecht
Rubin MB (2005) Numerical solution of axisymmetric nonlinear elastic problems including shells using the theory of a Cosserat point. Comput Mech 36:266–288
Singer J, Arbbocz J, Weller T (1998) Buckling experiments: experimental methods in buckling of thin-walled structures. vol 1. Wiley, New York
Singer J, Arbbocz J, Weller T (2002) Buckling experiments: experimental methods in buckling of thin-walled structures. vol 2. Wiley, New York
Timoshenko SP (1940) Theory of plates and shells. McGraw-Hill, New York
Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Klepach, D., Rubin, M.B. Influence of Membrane Stresses on Postbuckling of Rectangular Plates Using a Nonlinear Elastic 3-D Cosserat brick Element. Comput Mech 39, 729–740 (2007). https://doi.org/10.1007/s00466-005-0023-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-005-0023-8