Abstract

The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tensor is presented in the form of its expansion to the elasticity tensor and the additional terms tensor expressed the physical nonlinearity of the problem. The functions expressed the physical nonlinearity of the material are determined. The relations that allow to determine the range of elastic-plastic deformations on the surface of the present shell and their changing in shell thickness are presented. The examples of the calculation demonstrate the convergence of elastic-plastic deformations method and the range of elastic-plastic deformations in thickness in the spherical shell. Spherical shells with the angle of half-life regarding 90 degree vertical symmetry axis under the action of equally distributed ring loads are observed.

Highlights

  • The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit

  • In the present work the model of the numerical implementation of the calculation of thin isotropic shells the material of which works beyond the elastic limit is observed

  • The definition of stress-stain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method of A.A

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Summary

State of the problem

The constructions in the form of shells take a special place among the spatial structures. The theory of the calculation of stress-stain state of shells is presented in the works [1, 4] and in many other scientific works. The practical necessity of the calculation beyond the elastic material work is caused by the fact that the high tensions exceeded the limit of material proportionality appear in thin-walled constructions in the places of local influence. In the present work the model of the numerical implementation of the calculation of thin isotropic shells the material of which works beyond the elastic limit is observed. The definition of stress-stain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method of A.A. Ilyushin [2]. In the works of I.S. Tsurkov [3] the method got a theoretical justification and development for the calculation of thin shells. The usage of computers in the further calculation [4,5,6,7,8] allows to obtain the solutions distributed just on the surface of the loads, and distributed

The method of solution
A B u A
19 Eh3 2
19 Eh3 2n
Results
Conclusions

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