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One of the basic types of strength calculations is the calculation of limit equilibrium of constructions. This report describes new method for solving the problem of limit equilibrium. The rigid-plastic system in this method is substituted with an «equivalent» elastic system with specially constructed rigidities. This is why it is called the method of pseudorigidities. An iteration algorithm was developed for finding pseudorigidities. This algorithm is realized in a special software procedure. Conjunction of this procedure with any elastic calculation program (base program) creates a program solving rigid-plastic problems. It is proved, that iterations will be converge to the solution for the problem of limit equilibrium. The solution of tests show, that pseudorigidity method is universal. It allows the following: - to solve problems of limit equilibrium for various models (arch, beam, frame, plate, beam-wall, shell, solid); - to take into account both linearized and square-law fluidity conditions; - to solve problems for various kinds of loads (concentrated, distributed, given by a generalized vector); - to take into account the existing various of fluidity criteria in different sections etc. The iterative PRM process quickly converges. The accuracy of PRM is very high even in case of rough finite-element structuring. The author has used this method for design protection systems from extreme loads due to equipment of nuclear power stations, pipelines, cargo in any transportation.

Pseudorigidity method for solving the problem of limit equilibrium of rigid-plastic constructions
(1997)

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<.

Es wird gezeigt, daß zur Aufstellung eines korrekten Momentengleichgewichts nach Theorie zweiter Ordnung für Querkräfte die Hebelarme des unverformten Systems und für Normalkräfte Hebelarme des verformten Systems zu benutzen sind. Im Allgemeinen ist es aber nicht möglich, die Knotenverformungen eines Rahmens in relevante und nicht relevante Anteile zu zerlegen, so daß ein Momentengleichgewicht bei Berechnungen nach Theorie zweiter Ordnung im Allgemeinen nicht sinnvoll ist.