Optimal design of elasto-plastic steel frames loaded by normal and extreme loads and subjected to displacement, deformation and stress constraints

Kaliszky, Sándor and Lógó, János (2006) Optimal design of elasto-plastic steel frames loaded by normal and extreme loads and subjected to displacement, deformation and stress constraints. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 7 (2). pp. 201-212. ISSN 1586-2070

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Abstract

The paper presents a simple optimal elasto-plastic design method of steel frames and beams constructed of prismatic parts with I shape cross-sections in which the thicknesses of flanges are varying continuously. Two different loading conditions are considered. The normal load (dead load and live load) must be carried in elastic state while it is supposed that under the simultaneous action of an extreme load (explosion, impact, earthquake) and the dead load the structure is in fully plastic state. This state forms the basis of the optimal design. Using a quadratic weight function the determination of the optimal plastic moment distribution is reduced to the analysis of a fictitious linearly elastic structure of the same configuration as the one to be designed but with special bending stiffnesses [1,2,3]. In the knowledge of the optimal plastic moments the corresponding elastic bending stiffnesses and the elastic solution of the original structure subjected to the working load can be determined in which constraints on displacements and stresses are included. Besides, assuming that the complementary strain energy of the residual moments can be considered an average measure of plastic deformations, the plastic behaviour of the structure can also be controlled [4]. The proposed method is described in the form of two elastic solutions coupled in nonlinear form by the design variables. For the solution an iterative procedure and an approximate method are used. The application is illustrated by two numerical examples.

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