Optimization Of Thick-walled Shells Based On
Solutions Of Inverse Problems Of The Elastic
Theory For Inhomogeneous Bodies
Author(s)
V. I. Andreev
Abstract
An inverse problem of elastic theory for inhomogeneous bodies is normally used
for identification of the dependencies of a material’s mechanical properties of
coordinates where the stress state of the body will be specified. It is known that
in thick-walled cylindrical or spherical shells under internal or external pressure
the highest stresses are close to the inner surface of the shell. Several solutions of
inverse problems (depending on the elastic modulus along the radius at which
the equivalent stress in the shell will be constant) are obtained in this paper with
the use of conventional strength theories. Corresponding shells could be called
equal stress shells. If an investigator changes the elastic modulus of the material
its mechanical properties change as well. It is shown that for some materials the
investigator can create a model of an equal strength shell with an equivalent
stress at each point, which is equal to the strength of the material. This paper is
devoted to creating multi-layered shells in which the elastic modulus in each
layer is determined by the results of solving inverse problems.
Keywords: elastic theory, inverse problem, thick-walled shells, inhomogeneous
bodies, stress state, strength, equivalent stress, multilayer shells, maximum shear
theory, maximum-strain-energy theory.
1 Introduction
The aim is to develop models of thick-walled shells which are close to equal
strength. The modulus of elasticity of the material, which depends on the radius
at which the corresponding equivalent stress will be constant at all points of the
shell [1], is determined with the use of solutions of inverse elasticity problems
Keywords
elastic theory, inverse problem, thick-walled shells, inhomogeneous
bodies, stress state, strength, equivalent stress, multilayer shells, maximum shear
theory, maximum-strain-energy theory.
Related Book
Other papers in this volume
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