Formulação posicional para descrição do comportamento mecânico de fluência em vigas e estruturas de pórtico

Abstract

RESUMOEste trabalho trata do desenvolvimento de uma formulação numérica não linear para descrever o comportamento mecânico viscoelástico de estruturas de pórticos e vigas submetidas a estado de tensão constante (fenômeno conhecido como fluência) e discretizadas em elementos finitos de pórtico plano. O desenvolvimento é baseado na formulação posicional não linear do Método dos Elementos Finitos considerando a teoria clássica de Bernoulli-Euler. Essa formulação possibilita a realização de uma análise estrutural não linear física e geométrica. A não linearidade geométrica considerada refere-se à análise do equilíbrio da estrutura na posição deformada utilizando o método de Newton-Raphson. Já a não linearidade física considerada refere-se à adoção de uma relação reológica baseada no modelo de Maxwell generalizado. Três exemplos numéricos são analisados utilizando-se a formulação desenvolvida. Os dois primeiros descrevem e comparam o comportamento de fluência em uma viga com diferentes condições de contorno. O terceiro exemplo descreve o comportamento de fluência em um pórtico formado por dois pilares e uma viga. Além disso, uma calibração simples da formulação é realizada em relação à solicitação axial de uma barra de Plástico Reforçado com Fibra de Vidro. Palavras-chave: Viscoelasticidade, Fluência, Formulação Posicional, Método dos Elementos Finitos, Modelo Reológico. ABSTRACTThe present work aims to develop a nonlinear numerical formulation used to describe the viscoelastic mechanical behavior of framed structures and beams under a constant stress state (known as creep phenomenon) and discretized by plane framed elements. The development is based on the nonlinear positional formulation of the Finite Element Method and it takes into consideration the beam kinematics of Bernoulli-Euler. This approach allows to perform a structural analysis with physical and geometrical nonlinearities. The geometrical nonlinearity involved refers to structural equilibrium in the deformed position obtained by the Newton-Raphson method. The physical nonlinearity is associated with the adoption of a viscoelastic behavior through a suitable rheological relation. This rheological relation is derived from the uniaxial rheological model, based on the generalized Maxwell model. Three numerical examples are analyzed by the developed formulation. The first two examples describe and compare the creep behavior of a beam with different boundary conditions. The third example describes the creep behavior of a framed structure, formed by two columns and one beam. Furthermore, a simple calibration of the formulation is performed considering axial loading experimental results of bar made by Glass Fiber Reinforced Polymers material.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

“…It is important to note that the approach used here to evaluate strain rate is different from the approach used in the works of dos Santos Becho et al [11] and Rabelo et al [15]. In such works, the strain rate is evaluated by direct use of chain rule in terms of nodal positions as follows:…”

“…Different numerical formulations have been developed to analyze the viscoelastic behavior of solid materials, as demonstrated in the works of Chen [1], Aköz and Kadioǧlu [2], Beijer and Spoormaker [3], Zheng et al [4], Mesquita and Coda [5], Galucio et al [6], Bottoni et al [7], Payette and Reddy [8], Panagiotopoulos et al [9], Latorre and Montáns [10], dos Santos Becho et al [11], Carniel et al [12], Oliveira and Leonel [13], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. is interest is due to the need for modeling behavior of unconventional materials and the more complex and realistic analyzes of structures and structural components.…”

“…us, structural engineering aims to address the demands for technological advances in the most diverse areas, such as infrastructure, civil construction, mechanical industry, aerospace industry, and others. Part of these studies are related to the analyses of structures with viscoelastic behavior adopting stress-strain relation deduced from rheological models, as demonstrated in the works of Aköz and Kadioǧlu [2], Mesquita and Coda [5], Panagiotopoulos et al [9], dos Santos Becho et al [11], Carniel et al [12], Oliveira and Leonel [13], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. ese rheological models are schematic representations that combine elastic and viscous elements to obtain a physical interpretation of stress-strain relationships.…”

“…It is worth mentioning that part of these studies uses the positional formulation of the finite element method to describe the viscoelastic behavior, as demonstrated in the works of dos Santos Becho et al [11], Pascon and Coda [14], Rabelo et al [15], and Fernandes et al [16]. e use of such a formulation is justified by the capacity and simplicity of its application in the analysis of nonlinear problems as highlighted in Coda and Greco [17] and Greco and Coda [18].…”