Development of methods for topology and shape optimization of mechanical structures

Abstract

The main contribution of the present Thesis is the following: • Introduction of new normalized indices for evaluating the performance of an optimization method. • Development of a new hybrid method for the weight minimization of skeletal structures and continua under any number of displacement and/or stress constraints. • Statement of a new Optimality Criterion for each of the following weight minimization cases: o 2D continua under a single compliance constraint. o skeletal structures under an extended single stress constraint. o skeletal structures under an extended single displacement constraint. • Statement of a new redesign procedure for the weight minimization of skeletal structures under an extended single stress constraint. • Development of a new optimization method for each of the following weight minimization cases: o 2D continua under stress constraints, implementing the concept of element-wise variable thickness and the use of nodes as control points for sculpturing the structural surface. o 3D continua under stress constraints. o skeletal structures under an extended single displacement constraint. o 2D continua under an extended single displacement constraint, implementing the concept of element-wise variable thickness and the use of nodes as control points for sculpturing the structural surface. • Investigation and comparison of applying the ESO and the FSD method in the weight minimization of 2D plates under stress constraints. • Development of a variation of the ESO method for minimizing the weight of 2D continua under a single displacement constraint. • Development of a new optimization method for minimizing the cost of: o skeletal structures, implementing a concept of grouping and elimination that aims at increasing the commonality of the active members of the structure. o oil storage tanks, using commercially available plates, taking into consideration the cost for the welds, and aiming at minimizing the scrap material. • Development of a: o weight minimization procedure for structures being considered as a single beam of standard profile. o new heuristic method for minimizing the weight of discrete structures, consisting of standard beams. o new ‘mixed-type’ heuristic method for minimizing the weight of plated structures. Solution of the weight minimization problem for a series of full-scale, real-life structures.