Creep theory inverse problem for non-work-hardening body

Abstract

The body formation by constant external forces in the conditions of the steady-state creep during set time problem is formulated and solved so that after removal of loadings the movements of points of a surface accepted preset values. The case of small deformations is considered. At certain assumptions and restrictions the uniqueness theorem for the solution of this task is proved. Applied questions of a problem of finding the external influences which are necessary for receiving a demanded shape of a body for set time in the conditions of rheological deformation after removal of external forces (taking into account elastic unloading) are analyzed. The analysis of a thin-walled isotropic plate for a case of a flat tension is made in details. The solution for movements is searched in the form of an expansion in small parameter. The model solution for a round plate of single radius under the influence of constant external loadings which should have the set field of movements after creep and elastic unloading is provided.

Keywords

• steady-state creep
• inverse boundary problem
• shaping
• constant loadings
• small deformations
• drukker’s postulate for viscous deformations
• round thin plate