Extended limit design theorems for continuous media
TLDR
In this paper, the safe loads for a Prandtl-Reuss material subject to surface tractions or displacements which increase in ratio are extended to any perfectly plastic material and any history of loading.Abstract:
Earlier results [1,2]2 on safe loads for a Prandtl-Reuss material subject to surface tractions or displacements which increase in ratio are here extended to any perfectly plastic material and any history of loading.read more
Citations
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On discontinuous plastic states, with special reference to localized necking in thin sheets
TL;DR: In this article, the authors investigated the permitted discontinuities of stress, velocity, and surface slope in a plastic-rigid sheet deformed in its plane, and the necessary restrictions on the stress-state and rate of workhardening were obtained for any yield function and plastic potential.
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Geotechnical stability analysis
TL;DR: In this paper, the authors describe recent advances in stability analysis that combine the limit theorems of classical plasticity with finite elements to give rigorous upper and lower bounds on the failure load.
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The Theory of Plasticity: A Survey of Recent Achievements
TL;DR: In this article, a survey of recent achievements in the theory of plasticity is presented with emphasis on applications in mechanical engineering. But the authors do not discuss the theoretical foundations of limit analysis and their application to impact testing and blast damage.
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Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming
TL;DR: In this article, the authors present a method for obtaining strict lower bound solutions using second-order cone programming (SOCP), for which efficient primal-dual interior-point algorithms have been developed.
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Combining upper bound and strain path methods for evaluating penetration resistance
Itai Einav,Mark Randolph +1 more
TL;DR: In this article, a new generation of penetrometers, which have a much greater projected area than the cone shaft, and introduces a version of the strain path method based on classical upper bound solutions for the penetrationrometers.
References
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Recent Developments in the Mathematical Theory of Plasticity
TL;DR: In this article, the authors considered the case where the mechanical state is determined by the components of stress and permanent strain, and the conditions of continuity, uniqueness, irreversibility, and consistency can be used to extract rather far-reaching information regarding the structure of the stress-strain law.
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Some implications of work hardening and ideal plasticity
TL;DR: In this paper, the authors point out the severe restriction imposed on possible stress-strain relations by a mathematical formulation of the concepts of work hardening and ideal plasticity, and give an algebraic derivation and extension of Prager's extension of the Mises plastic potential function.
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The Safety Factor of an Elastic-Plastic Body in Plane Strain
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Limit Design of Beams and Frames
TL;DR: In this article, the limit design of statically indeterminate beams or frames under the action of given loads is studied and the limit moments under which individual sections act as yield hinges are defined.