Pseudorigidity method for solving the problem of limit equilibrium of rigid-plastic constructions

Routmann, Y. L.

1.Design calculations , based upon the theory elasticity , cannot completely satisfy engineers and designers , because cannot answer to basic question about overload capability . Only design calculations of limit equilibrium of rigid-plastic constructions can answer to this question completely enough. As a rule , such design calculations are made issue from hypothesis, that material of construction has rigid-plastic diagram Prandtl .This scheme of calculation gives qualitatively more correct results, then usual calculation, based upon law Hooke’s , and allows more really estimate ultimate strength of construction due to different loads. Universal algorithms for solving the problem of limit equilibrium have been created since the middle of the 60’s.These algorithms are based upon two basic theorems about limit analysis - static and kinetics. It was found , that with the help of above-mentioned theorems the problem of limit equilibrium can be formulated as a problem of linear programming (for linear yield) or nonlinear programming (for yield Guber-Mizes). The method of linear programming conformably to calculation of rod systems got the most development in the reports Prager W. [1] and Chiras A. [ 2 ]. The method of linear programming conformably to plates and shells was widely used by Rganizin A.[3]. [3[ contains more full bibliography about this problem. Calculation of limit equilibrium with the help of linear and nonlinear programming has a few significant lacks: - complexity and laboriousness preliminary preparation of problem for PC; - necessity to use special program means , which are not in usual program packet for strength analysis. Author worked out a new method about design calculation of limit equilibrium without above-mentioned lacks . The method is based upon analogy of relations between internal generalized efforts and generalized deformations in elastic system and between generalized efforts and velocities of change generalized deformations in rigid-plastic system. Because later rigid-plastic deformation would be treated as an elastic deformation in the system with special constructed rigidities , this method could be called >pseudorigidity method<.

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Routmann, Y. L.: Pseudorigidity method for solving the problem of limit equilibrium of rigid-plastic constructions. 2005.

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