Abstract This article presents a formulation for the optimization problem that minimizes the CO2 emission of pile caps with variations of geometry and pile position. The problem is defined by the design variables: concrete pile cap dimensions, rebar ratio, concrete compressive strength, the number of piles, the diameter, and length. The environmental impact was chosen as the objective function, taking CO2 emission as the main parameter. The design procedure was based on the ABNT NBR 6118:2014 (2014), and by the formulation proposed by Blévot & Frémy (1967). Also, the soil structure interaction between the cap and the piles was considered in the optimization problem. The problem was implemented using MATLAB (2016) and solved via a Genetic Algorithm native to the program. Results obtained from numerical examples were compared with structural designs solutions located in the Grande Vitória metropolitan area, Espírito Santo, Brazil and validated with a commercial software. The analyses indicate that design optimizations of pile caps considering the compressive strength of concrete, the diameter and length of piles and the optimal geometry of the pile caps may lead to significant reductions of material consumption, and consequently, a reduction of environmental impacts.

Abstract The objective of this study is to present the formulation and applications of the optimization problem of steel-concrete composite alveolar beams. In addition to presenting the formulation, a comparative analysis of the predominant collapse modes is performed numerically via the finite element method. The optimization program was developed with the GUI platform available in Matlab 2016. Since this is a discrete problem, a Genetic Algorithm (GA) was used to solve the optimization model, implemented with the Matlab optimization toolbox. Numerical examples using finite elements model are presented to validate the solution and analyze its effectiveness, along with an assesment of the predominant collapse modes for a group of 12 beams. The results show that more efficient designs are obtained when optimization tools are applied.

RESUMO: Neste artigo analisa-se a influência dos efeitos construtivos incrementais (EI) e da interação solo estrutura (ISE) em edifícios altos de concreto armado com fundações superficiais assentes sobre solos arenosos. Foram realizadas avaliações dos EI e ISE nos parâmetros de instabilidade global, deslocamentos horizontais máximos, cargas de fundação e recalques de uma planta simétrica e uma não simétrica de um edifício com 23pavimentos. Para análise do EI considerou-se a variação do módulo de elasticidade ao longo do tempo, bem como as fases de aplicação de cargas na edificação. Para análise do ISE foi considerado o meio contínuo e o modelo de cálculo considera uma série de molas discretas sob a base da fundação da edificação. Os resultados mostram uma redistribuição significativa nos esforços da fundação e sugerem que a não consideração desses efeitos em conjunto na estrutura pode levar a projetos que não atendam as especificações de norma quanto aos parâmetros de estabilidade e deslocamentos globais da estrutura.

Abstract: The influence of incremental constructive effects (IE) and soil-structure interaction (SSI) on high-rise buildings of reinforced concrete with shallow foundations on sandy soils were analyzed. IE and SSI evaluations were carried out by the parameters of global instability, maximum horizontal displacements, foundation loads, and settlements of a symmetrical and non-symmetrical plant of a 23-storey building For the analysis of the IE, the variation of the modulus of elasticity was considered over time along with the phases of application of loads in the building. For ISS analysis, the continuous medium was considered, and the calculation model considers a multi-spring-mass system under the foundation of the building. The results show a significant redistribution in the foundation efforts and suggest that a failure in considering these effects along with the structure can lead to projects that do not meet the standard specifications regarding stability parameters and overall structure displacements.

Abstract The goal of this article is to present the formulation of the optimization problem of truss structures with geometric nonlinearity under dynamic loads and provide examples of this problem. The formulated optimization problem aims to determine the cross-sectional area of the bars that minimizes the weight of the structure, imposing constraints on nodal displacements and axial stresses. To solve this problem, computational routines were developed in MATLAB® using Sequential Quadratic Programming (SQP), the algorithm of which is available on MATLAB’s Optimization ToolboxTM. The nonlinear finite space truss element is described by an updated Lagrangian formulation. The geometric nonlinear dynamic analysis performed combines the Newmark method with Newton-Raphson iterations. It was validated by a comparison with solutions available in literature and with solutions generated by the ANSYS® software. Optimization examples of trusses under different dynamic loading were studied considering their geometric nonlinearity. The results indicate a significant reduction in structure weight for both undamped and damped cases.

Abstract This study presents an optimization method for the thickness of shell elements subjected to dynamic loads. Structural analyses were carried out using the finite element method. The analyzed domains were modeled using NURBS, and meshes were generated using a transformation of the parametric domain into the geometric domain via a geometric function. The shell element considered is a combination of a CST membrane element and a DKT plate element, forming an element with 15 degrees of freedom. The Newmark method with constant acceleration was applied to solve the equation of motion. The optimization approach was considered in two different ways: with uniform and variable thickness throughout the shell element. Due to the nonlinear constraints of the problem, the Sequential Quadratic Programming (SQP) method was employed. SQP routines are available in MATLAB, in which this study was performed. Useful examples were detailed in this study to demonstrate the applicability of the optimization method to real structures, such as the Igrejinha da Pampulha, a church located in Belo Horizonte, Brazil, whose modeling was performed.

Problemas de otimização estrutural, envolvendo carregamento estático, já vêm sendo estudados há algum tempo e, de certa forma, esse tipo de problema já está bem definido na literatura especializada, porém problemas envolvendo carregamento dinâmico ainda são poucos estudados e problemas envolvendo carregamento dinâmico não determinístico menos ainda. O presente trabalho apresenta a formulação do problema de otimização de placas submetidas a carregamentos randômicos. Para a modelagem da estrutura, utilizou-se o elemento de placa à flexão AST6, que fornece essas matrizes explicitamente. Uma redução dinâmica das matrizes de massa e rigidez foi utilizada para reduzir o custo computacional do problema. A solução do problema foi obtida utilizando o Método dos Pontos Interiores e, para a análise de sensibilidade das matrizes de massa e rigidez da estrutura, foi utilizado o método semianalítico. Três exemplos são apresentados para demonstrar a confiabilidade do processo. O primeiro exemplo é de uma placa isotrópica e os dois outros são problemas envolvendo placas do tipo sanduíche. Em todos os exemplos, obteve-se um projeto melhorado, em relação à geometria inicialmente proposta.

Structural optimization problems involving static loading have been studied for some time and in a way these kinds of problems are widely encountered in literature, but problems involving dynamic loading still have few studies not to mention problems involving nondeterministic dynamic loading. This paper presents a formulation of the optimization problem of plates subjected to random loadings. For the modeling of the structure, it used the bending plate element AST6 that explicitly provides these matrices, and dynamic mass reduction and rigidity matrices were used to reduce the computational cost of the problem. . The solution was achieved using the Interior Point Method and the sensitivity analysis of mass, and for the structure's stiffness matrixes the semi-analytical method was used. Three examples are presented to demonstrate the reliability of the process. The first example is an isotropic plate and the other two are problems involving sandwich plates. In all examples, an improved design in respect to the initially proposed geometry was obtained.