The inverse conditionally correct problem of determining the residual stresses in compound welded shells of revoltuion

Abstract

We solve the inverse conditionally correct problem of recovering the complete picture of the residual stressed state for a compound shell welded from two parts, one cylindrical and the other conical. We apply the partial values of the stresses obtained experimentally by the method of photoelasticity. We also apply the numerical method of spline-collocations.The numerical-experimental method of determining the residual stresses in compound welded shells of revolution is One of the nondestructive methods oL~ontrol of the level of'such stresses. It is: based on: solving)inverse conditionally correct problems of recovering the complete picture of the stress-strain state of the shell from some of the values of the stresses obtained experimentally [4,6].We consider a shell structure made of optically active materials for which the method of integral photoelasticity [7] is an effective experimental method. For such materials, especially for glass, we describe the residual strain field by the spherical tensor o =80.e 0, Thus we have a finite-parameter representation of the field (1), and we regard the inverse of the problem of creating it as the problem of finding the parameters of the model just constructed in a finite-dimensional space, where each closed bounded set is compact [8]. For parametric models the following assertion holds [8]: if there

Axisymmetric residual stresses in a solid cylinder of finite length

“…The most advanced way for predicting the actual levels of residual stresses corresponding to certain distribution profiles of incompatible strains combines both theoretical and experimental techniques [ 17 , 18 ]. One of such approaches is a non-destructive computational–experimental method [ 19 ] based on solving the inverse elastoplastic problems [ 20 ] and fitting the results with the experimental evidence obtained by non-destructive techniques in order to evaluate the effective stress distribution parameters. The formulation and solution of the inverse problems is based on the so-called conventional-plastic strain hypothesis [ 21 , 22 ] implying the base material of a solid to be elastic, while the expected zone of residual stress distribution exhibits specific elastic–plastic behavior so that the total strain can be represented in the following form: where is the total strain tensor, is the tensor of elastic strains occurring within the entire solid, and denotes the tensor of incompatible strain [ 23 ] distributed within the area affected by the impacts causing the residual stress–strain state.…”