Vol. 9, No. 5, 2014

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ISSN: 1559-3959
Buckling of two-phase inhomogeneous columns at arbitrary phase contrasts and volume fractions

Mohammed G. Aldadah, Shivakumar I. Ranganathan and Farid H. Abed

Vol. 9 (2014), No. 5, 465–474

Buckling is an instability encountered in a wide variety of problems, both in engineering and biology. Almost all engineering structures are designed with adequate safety factors to prevent failure due to buckling, yielding or dynamic loads. In a classical sense, design for buckling is done by carefully controlling the modulus of elasticity, moment of inertia and the length of the structure. Further, such an approach assumes the material to be homogeneous and does not generally account for the microstructural details of the column. In this paper, we study the buckling of inhomogeneous columns with a two-phase checkerboard microstructure. Monte Carlo simulations are used to generate microstructures with arbitrary volume fractions and phase contrasts (ratio of the modulus of individual phases). An analytical form is obtained for the ensemble averaged critical buckling load based on the results of over 18,000 eigenvalue problems at arbitrary volume fractions, phase contrasts and distributions. Further, microstructural realizations that correspond to the highest buckling load (best design) and the lowest buckling load (worst design) are identified and the corresponding distribution of individual phases is determined. Finally, the statistical nature of the critical buckling load is discussed by computing the statistical moments that include the mean and coefficient of variation.

buckling, microstructure, column, inhomogeneous materials
Received: 6 February 2014
Revised: 24 May 2014
Accepted: 1 June 2014
Published: 14 December 2014
Mohammed G. Aldadah
Department of Mechanical Engineering
American University of Sharjah
United Arab Emirates
Shivakumar I. Ranganathan
Department of Mechanical Engineering
Rowan University
201 Mullica Hill Road
Glassboro, NJ 08028
United States
Farid H. Abed
Department of Civil Engineering
American University of Sharjah
United Arab Emirates