| The complexity of solving elastostatic problems, defined by the Navier equation, usually requires numerical tools such as Finite Element. The main aim of the alternative formulations in terms of potential functions has been to get analytical solutions. Only certain cases, where straightforward functions as Airy and Prandtl can be applied, have been solved numerically in terms of potential.;The network simulation method is applied in this PhD Thesis on the numerical solution of 2D elastostatic problems based either in Navier formulation or in potential formulation, focusing on the Papkovich-Neuber potentials and derived solutions, by deleting some of the potential functions, for which no numerical solutions have been investigated up to day.;After exposing the theoretical bases of this memory (Chapter 2) and discussing the completeness and uniqueness conditions of the Papkovich-Neuber solution, the additional conditions required for the numerical solution are studied (Chapter 3). This question is still a matter of active interest in the research literature. In this sense, new additional conditions are proposed for some potential solutions applicable to 2D problems. In the case of the Boussinesq solution, the conditions proposed up to day, unique according to Tran-Cong, can be specified in alternative forms, even more simple.;The design of the network models as well as the implementation of the physical boundary conditions, for both Navier and potential formulations, is explained in Chapter 4. Software has been developed in Matlab programming language, with graphical interface, EPSNET_10. This contains the routines for the network design, simulation in PSpice and data treatment for the graphical result representation. Its performance and multiple user options are explained in Chapter 5.;Applications to problems defined by Navier and potential formulations are presented in Chapters 5 and 6, respectively. The reliability of the proposed models are verified by comparison between its results and analytical solutions, if they exist, or otherwise with standard numerical methods solutions, currently used in elasticity. |
