Abstract

This work proposes the use of the MSAA stochastic optimization technique to replace the optimality criterion used in the topology optimization method proposed by Andreassen. To evaluate and validate the MSAA performance we studied three plane elasticity problems reported in the literature. Each problem was analyzed with three different finite element mesh types in order to compare the results obtained in terms of topology, strain energy value and average runtimes. It was established that the procedure involving the MSAA, yields lower computational times in problems with more refined meshes. Finally, the material distribution and the energy values obtained were similar to those reported in the work of Andreassen giving validity to the work presented here.

Abstract

O Modelo de Bielas e Tirantes pode ser uma excelente alternativa para o dimensionamento de elementos estruturais em concreto armado submetidos a estado plano de tensão e para regiões que apresentem descontinuidade de ordem geométrica ou estática, substituindo procedimentos empíricos por uma metodologia racional de projeto. Para tornar a concepção do modelo menos dependente da experiência do projetista, o presente artigo tem como objetivo aliar a técnica de otimização topológica ESO (Evolutionary Structural Optimization) ao Método dos Elementos Finitos para geração automática dos modelos de bielas e tirantes. O critério de evolução do método de otimização topológica adotado considera a eliminação de elementos menos solicitados em termos de tensão, a partir de uma análise elástico-linear. Nesse contexto, é possível obter soluções otimizadas de problemas complexos envolvendo o concreto estrutural. São apresentados três exemplos numéricos para comprovação e validação das formulações e técnicas implementadas,  cujos modelos de bielas e tirantes obtidos apresentam boa concordância em relação às respostas encontradas em trabalhos científicos precursores sobre o tema.

Abstract

Is presented hereby the creation of an optimization software for the design of reinforcing steel for any type of structural elements which may be considered as columns, pillars, pilots or foundation dies, subjected to flexo-compression mechanic stresses for rectangular and circular cross section elements with the support of computational numeric methods and a new mathematical original model named "The idealized steel profile" for the optimization of constructions costs, in which the reinforcing steel is idealized as a steel structural profile embeded in concrete columns, so that then an approxiamte required reinforcing steel area may be determined in order to compute all the possible reinforcing bar options over the element cross section making comparisons in structural efficiency and cost for each option generated to then determine the optimal topology regarding cost and efficiency. The optimization problem is adapted so that it makes the resultant designs practical and convenient for its application in the construction industry in Mexico, based on certain design criteria from the <span style="color: #800000;">NTC-2017</span> (Technical Construction Normative of Mexico City) and questioning other such criteria.

It will be shown how such optimization algorithm was adapted, as well as other general numeric methods for engineering. Moreover the implementation of this program as a software for its practical application in the industry for any concrete structure with "n" number of concrete elements is presented. At the end, results of various experiments with the optimization program are shown, making comparisons between different resultant structural models regarding structural eficciency and geometry.

Abstract

Is presented hereby the creation of an optimization software for the design of reinforcing steel for any type of structural elements which may be considered as columns, pillars, pilots or foundation dies, subjected to flexo-compression mechanic stresses for rectangular and circular cross section elements with the support of computational numeric methods and a new mathematical original model named "The idealized steel profile" for the optimization of constructions costs, in which the reinforcing steel is idealized as a steel structural profile embeded in concrete columns, so that then an approxiamte required reinforcing steel area may be determined in order to compute all the possible reinforcing bar options over the element cross section making comparisons in structural efficiency and cost for each option generated to then determine the optimal topology regarding cost and efficiency. The optimization problem is adapted so that it makes the resultant designs practical and convenient for its application in the construction industry in Mexico, based on certain design criteria from the <span style="color: #800000;">NTC-2017</span> (Technical Construction Normative of Mexico City) and questioning other such criteria.

It will be shown how such optimization algorithm was adapted, as well as other general numeric methods for engineering. Moreover the implementation of this program as a software for its practical application in the industry for any concrete structure with "n" number of concrete elements is presented. At the end, results of various experiments with the optimization program are shown, making comparisons between different resultant structural models regarding structural eficciency and geometry.

Abstract