Deformation of thin straight pipes under concentrated forces or prescribed edge displacements

•In the mixed formulation the vector of unknowns combines stresses and displacements.•The fundamental solution is achieved with a variational technique.•The analytical solution is obtained after evaluating eigenvalues and eigenvectors.•In one example a pipe is subjected to a prescribed edge displacement.•The final optimal solution is achieved by superposing weighted analytical solutions.

The purpose of this paper is to present an efficient analytic method for obtaining the deformation of thin straight pipes, subjected to prescribed edge displacements or concentrated loads.The approach uses the mixed formulation where unknown functions are combined with trigonometric terms. A variational procedure is used to obtain the system of ordinary differential equations. For the applied load a Fourier approach is used to represent the load as an analytical function. For the prescribed displacement, three solutions for the ovalization are evaluated and a method based on energy contribution of each term is used to obtain their superposition.In contrast to finite element method the proposed method is efficient and can be applied to other boundary condition problems leading to continuous displacement and stress fields with a low number of unknowns. Comparisons with experimental and finite element procedures show good agreement that enhances the merits of the analytical solutions proposed.The value of this method is based on solving the differential equations rather than using commercial codes. So far, the solution of prescribed edge displacements has been limited to one term. This paper discusses how to add further terms using the mixed formulation, thus, presenting a novel procedure.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slide