The Use of the Collocation Algorithm for Estimating the Deformations of Soil-Shell Objects Made of Corrugated Sheets

Abstract

Abstract The algorithm presented in this paper is intended for the analysis of deformations of shells in the construction phase of soil-shell objects when strain gauges and geodetic measurements are used. During the construction of such an object, large displacement values occur and the impact of axial forces on the displacement of a corrugated metal sheet is small. Internal forces (strain gauges), as well as the displacements of a selected circumferential band of the shell are determined directly from such observations. The paper presents two examples of the analysis of large span shell structures of constructed objects, as well as the assessment of the effectiveness of the finite difference method (FDM) in beam schemes. Good deformation mapping was indicated using the collocation algorithm and the differential approach to the solution when there is a dense mesh and regular distribution of measuring points. In the analysed examples, a significant divergence between the support conditions adopted in the FEM calculation models and the actual static conditions in the objects was indicated. The collocation algorithm is especially designed for such situations. Collocation points in such a solution are used to consider a beam – separated from a structure and without boundary constraints, but with specific changes in curvature – as a reference system, which is determined from the geodetic measurements of two collocation points.