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C. Adam, W. Brunner:
"Comparison of beam and plane stress theories for inelastic structures";
in: "Computational Mechanics '95 - Proc. of International Conference on Computing Engineering Science 1995 (ICES'95)", S.N. Atluri, G. Yagawa, T.A. Cruse (ed.); Springer, Berlin, 1995, ISBN: 3-540-59114-1, 1199 - 1204.

Many theories have been developed in the analysis of moderately thick beams in order to avoid a plane stress computation. The range of validity of elastic Bernoulli-Euler and Timoshenko theory has been studied extensively in the literature for static and dynamic loading. In this contribution we study the validity of these theories for inelastic material behavior. Inelastic strains, e.g. plastic strains, are equivalent to eigenstrains in an identical but entirely elastic background structure. Since beam theories deal with stress and strain resultants, it is important to define proper resultants of these eigenstrains, i.e. inelastic curvatures and (in a Timoshenko theory) inelastic shear angles. Deformations and cross sectional stress resultants due to these eigenstrain resultants are obtained from proper dynamic Green's functions. Since the deformations of the background structure are assumed to be elastic, linear dynamic solution methods like modal analysis become applicable. During the last decade this elastic-inelastic analogy has been applied to various types of elastic-plastic structures like beams and plates. The goal of this paper is to show the range of validity of such an inelastic Bernoulli-Euler beam theory and a recently developed inelastic Timoshenko theory. These two theories are compared with plane stress Finite Element solutions. Ideal elastic-plastic material behavior is assumed. Furthermore, the computational efficiency of the described semi-analytical beam theories is demonstrated by means of comparison to Finite Element calculations.