This paper aims to analyze the stress and strain states appearing in the elbow of a tube, such as those commonly used in a city’s water supply network. The stress field is characterized by the fact that there is a significant stress increase when compared to a straight tube. As a result, the strength of such an elbow must be investigated and guaranteed for such a network to be well designed. A practical solution used is to anchor the elbow in a massive concrete block. The paper compares the stress field that occurs in the elbow when it is free, buried in the ground, and when it is anchored in a massive concrete block. Furthermore, we investigate how a crack appears and propagates in the elbow. This happens especially for the elbow buried in the ground where the stress and strain are higher than when the elbow is anchored in concrete. The results obtained can be used in the current practice in the case of water supply networks made by high-density polyethylene pipes.
In our study, we consider the linear mixed initial boundary value problem for a porous elastic body having a dipolar structure. The equations that describe the elastic dipolar deformations are coupled with the equations which describe the evolution of the voids by means of certain coefficients. Our main result proves the continuous dependence of solutions for the mixed problem with regard to the coefficients which perform this coupling. Using an adequate measure, we can evaluate the continuous dependence by means of some estimate regarding the gradient of deformations and the gradient of the function that describes the evolution of the voids.