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Abstract
Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.
Highlights
The elastic perfectly plastic structure is considered, the configuration, material, sandwich cross-section dimension of the structure and external load are prescribed
The structure adapted to the cyclic loading satisfies the constraints on strength and it is not likely to undergo cyclic plastic failure [1]
Residual force vector S r for structure at shakedown. is obtained by solving static analysis problem formulation. This formulation is made on the basis of the minimum complementary deformation energy principle [7,8,9]: of all statically admissible residual forces of structure at shakedown is the minimum complementary energy corresponding one
Summary
The elastic perfectly plastic structure is considered, the configuration, material, sandwich cross-section dimension of the structure and external load are prescribed. For a structure under plastic behaviour prior to a cyclic-plastic failure it is necessary to know actual stresses and strains and displacements (structural analysis problem) [15]. Applying the Rozen criterion [18] for incremental analysis problem solution, a new technique is created to determine unloading phenomenon in cross-sections during adaptation to quasi-static load process (Fig I, incremental stress-strain structure analysis at shakedown). Using this method more exact equilibrium equations are obtained to compare with other finite element methods In company with it statically possible elastic S, (subscript e) and residual S, forces (total forces are denoted by S = S, + S,, displacements- u = u, + u,) are defined more exactly.
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