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The Post-Buckling Equilibrium of Isostatic Hinge-Connected Space Structures Composed of Slender Members
Abstract
Elastic space structures, composed of pin-jointed slender members with symmetrical flexural properties, loaded centrally at the joints by conservative loads represent a class of symmetrical elastic systems discussed before.1 The behavior of such structures in the critical and post-critical statical equilibrium states is similar to that of plane pin-jointed frameworks, discussed in Chapter 1 and at length in Ref. 15. Also, the statements made in regard to the onset of unstable motion for plane isostatic frameworks, apply equally to space frameworks or lattices. In hyperstatic lattices the onset of unstable motion may take place only in certain restrained mechanisms. Hyperstatic systems are discussed later.
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This paper discusses the stability of quasi-static paths for a continuous elastic–plastic system with hardening in a one-dimensional (bar) domain. Mathematical formulations, as well as existence and uniqueness results for dynamic and quasi-static problems involving elastic–plastic systems with linear kinematic hardening are recalled in the paper. The concept of stability of quasi-static paths used here is essentially a continuity property of the system dynamic solutions relatively to the quasi-static ones, when (as in Lyapunov stability) the size of initial perturbations is decreased and the rate of application of the forces (which plays the role of the small parameter in singular perturbation problems) is also decreased to 0. The stability of the quasi-static paths of these elastic–plastic systems is the main result proved in the paper.