A robust and automatic elastic compensation method for collapse load determination of structures

Abstract

This thesis develops a general procedure for a robust and convenient collapse (limit) load determination of engineering structures using the elastic compensation method (ECM), which only involves a series of linear elastic analyses, and therefore is suitable for practical applications.

This research attempts to improve the robustness and automation of the traditional ECM and its modified versions. Two shortcomings of them reported in the literature are presented. Firstly, they use the number of iterations, input by the user, as the convergence criterion due to the presence of the sporadic oscillations with different amplitudes in the limit load curve. This criterion is baseless and might prevent a decent solution to be obtained. Secondly, they need a fine and high-quality mesh to produce acceptable results. Generation of such a mesh for complex structures is time-consuming and often requires tedious human interventions. The first shortcoming is overcome by developing a robust sensitivity-based ECM. It is shown theoretically and confirmed numerically that the use of the sensitivity-based ECM is robust in preventing the oscillations. This scheme provides accurate results by defining the convergence directly on limit loads. The second shortcoming is tackled through the use of the scaled boundary finite element method (SBFEM) and the automatic quadtree (in 2D) and octree (in 3D) mesh generation. Such technique automatically and efficiently handles structures with complex geometries and allows the SBFE discretizations to be constructed from an in-plane solid (2D) or of a solid 3D CAD model.

The combination of the sensitivity-based ECM with the SBFEM leads to an automatic scheme for the collapse load determination of structures. This scheme minimizes the required interference of the user in both mesh generation and analysis parts. However, it may be computationally demanding when uniformly refined meshes are used. To deal with this problem, an adaptive sensitivity-based ECM is proposed. The adaptive scheme generates non-uniform refinements efficiently by the ability of the SBFEM in handling the hanging nodes. This reduces the number of elements while still guaranteeing the required level of accuracy. Therefore, the size of the problem is significantly reduced and hence also the required computational resources.