Nonlinear dynamic thermal creep buckling and probabilistic failures of viscoelastic columns
by
Harry H. Hilton
University of Illinois at Urbana-Champaign
Coauthors: Dr. Cristina E. Beldica

ICNPAA 2004 Timisoara, Romania. June 2 – 4, 2004 NONLINEAR DYNAMIC THERMAL CREEP BUCKLING AND PROBABILISTIC FAILURES OF VISCOELASTIC COLUMNS CRISTINA E. BELDICA and HARRY H. HILTON Aerospace Engineering Department National Center for Supercomputing Applications University of Illinois at Urbana-Champaign 104 South Wright Street, MC-236 Urbana, IL 61801-2935 USA ABSTRACT Previous investigations of nonlinear isothermal quasi-static creep buckling (Hilton et al. 1996, 1997) indicate the significant contributions that geometric and material nonlinearities play. Equally important inertia effects have been observed in linear viscoelastic columns under static loads (Hilton 2002a, b). In the present paper the effects of inertia are examined for large deformation nonhomogeneous columns with nonlinear viscoelastic materials, initial imperfections and temperature distributions. The additional nonlinear contributions due to column end shortening due to both curvature and compressive loads are taken into account. Galerkin's method is used to eliminate spatial variations and the resulting nonlinear temporal governing relations are solved numerically using a fourth order Runge-Kutta approach. Column probabilities of failure and survival times due to creep buckling and/or material failure (delamination) are examined in detail including the influence of temperature.

Previously developed deterministic and stochastic combined load invariant failure criteria (Hilton & Ariaratnam 1994) are used to determine the onset of delamination in viscoelastic columns. Illustrative numerical examples are presented for elastic and viscoelastic columns with random combined failure stresses in bending, shear, compression and normal interlaminar stresses. Probabilities of delamination onset are established for various axial loads and initial imperfections and in the viscoelastic columns additionally as a function of lifetime.

PARTIAL LIST OF REFERENCES Hilton, H. H., & Ariaratnam, S. T. (1994) “Invariant anisotropic large deformation deterministic and stochastic combined load failure criteria,” International Journal of Solids and Structures 31:3285-3293.

Hilton, H. H., & Yi, S. (1996) “Stochastic delamination onset of large deformation elastic and viscoelastic columns with follower loads,” Proceedings Seventh International Conference on Applications of Statistics and Probability, (M. Lemaire, J. L. Favre and A. Mébarki, eds.) 3:1491-1495, A. A. Balkema, Rotterdam.

Hilton, H. H., Yi, S. & Danyluk, M. J. (1997) “Probabilistic analysis of delamina-tion onset in linear anisotropic elastic and viscoelastic composite columns,” International Journal of Reliability Engineering & System Safety 56:237-248.

Hilton, H. H. (2002a) “Dynamic creep buckling of linear viscoelastic columns in-cluding failure probabilities and survival times,” submitted to AIAA Journal. Tech-nical Report UILU-ENG 02-0503, 58 pp. University of Illinois at Urbana-Champaign.

Hilton, H. H. (2002b) “Probabilistic delamination onset analysis of nonlinear vis-coelastic composite columns with large deformations,” Proceedings 43rd AIAA/ASME/ASCE/AHS/ASC Structures. Structural Dynamics and Materials Conference, AIAA Paper 2002 – 1713, AIAA, Renton, VA.

Date received: February 26, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-75.