| The objective of the optimization of structures is to obtain a design, that is to say, a group of values for some design variables that minimizes a function, and satisfy a series of constraints that depend on these variables. The optimization problems of structures can be divided in three categories: size, shape, and topology.; The development of methods to optimize structures has been quite lawless due to division of ideologies: mathematical programming (MP), optimality criteria (OC), evolutionary structural optimization (ESO), solid isotropic microstructure with penalization (SIMP), biological growth structural optimization (BGSO), level set method (LSM), evolutionary computation (EC), etc.; Different evolutionary methods exist: evolution strategies (ESs), evolutionary programming (EP), genetic programming (GP), and genetic algorithms (GAs); the last ones have a strong theoretical basis and are the most biologically adapted method.; Fixed grid method (FG) has been previously used in problems in which the geometry of the object or the physical properties of the body change with time. In this work is shown the feasibility of using FG as an alternative to conventional finite elements method (FEM) to solve elasticity problems.; The main objective of this thesis is to introduce a new procedure, called MFAG, for the shape and topology optimization of bidimensional continuum structures. The topology and shape of the design depend on a genetic algorithm, which, through the problem isolines defines the number, shape and distribution of the contours. The analysis of the structure is carried out by a fixed grid of finite elements. The procedure has been implemented in the programming language FORTRAN 95.; The versatility and flexibility of this procedure has been proven through several examples. The results have been compared with those obtained in the most recent bibliography (multi-GA, MMA, SIMP, PBO, ESO, etc.). The results demonstrate the effectiveness of the procedure, providing quality solutions with perfectly defined contours, without the need to interpretate the topology to obtain a final design. |
