Otimização de forma aplicando B-splines sob critério integral de tensões

This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient

Sobre formas e processos: projeto de um condomínio de casas a partir de princípios da gramática da forma

With the intention of studying and developing the design process based on a specific methodology, the object of this work is to present the design of a gated condominium community in Natal based on the application of principles of shape grammar, used in their design process. The shape grammar is a design method developed in the 1970s by George Stiny and James Gips. It is used for the analysis of the project as well as for its synthesis, with the goal of creating a "formal vocabulary" through mathematical and/or geometrical operations. Here, the methodology was used in the synthesis of the design process, through the relationship between formal subtractions and the houses’ architectural planning. As a result, five dwellings configurations were proposed, each one different from the other with respect to their shape and architectural programming, distributed in three twin groups, which are repeated until the final total of nine architectural volumes. In addition to studies of the condominium’s ventilation and the buildings’ shading simulations, studies of spatial flexibility and acoustic performance were also performed. The mapping of the design process, one of the specific objectives of the dissertation, was composed not only by the record of formal constraints (the preparation and application of rules), but also by physical, environmental, legal and sustainability aspects in relation to, on one hand, the optimization of the shading and passive ventilation for hot and humid climates, and, on the other hand, the modulation and rationalization of the construction.