Abstract
The development of a numerical formulation is presented to describe viscoelastic behavior considering shear effects. The nonlinear positional formulation of the Finite Element Method is used considering plane frame elements with Reissner kinematics. The description of the viscoelastic behavior is considered through the adoption of a stress-strain relation based on Boltzmann rheological model. The used kinematics allows to describe the decoupling between the rotations and the displacements in element cross-sections. This approach allows to evaluate the contribution of shear effects in viscoelastic behavior in an original way. Based on the developments and the results obtained, it is possible to observe that strains and displacements due to viscoelastic behavior are significantly superior to the results obtained considering Bernoulli-Euler kinematics hypothesis. It is possible to notice a better agreement between the obtained numerical results and the results in the literature. Results obtained from the developed formulation allow the assessment of the shear effects on the viscoelastic behavior of plane frames.
Highlights
The continuous search for engineering solutions with efficient performance reiterates the importance of researches related to the knowledge of complex mechanical behaviors and their more accurate computational simulations
This paper aims to present the development of a numerical formulation based on the positional formulation of the Finite Element Method and capable of describing the viscoelastic mechanical behavior in structures discretized by plane frame elements, considering the shear effects
A parametric analysis and an example of a beam with several height/span ratios are presented in order to demonstrate the consistency of the positional formulation using Reissner kinematics and its capacity to describe the viscoelastic behavior considering the shear effects
Summary
The continuous search for engineering solutions with efficient performance reiterates the importance of researches related to the knowledge of complex mechanical behaviors and their more accurate computational simulations. In the structural engineering field, good strength/weight ratios are aimed, combined with safety, predictable and low cost structures In this context, several researches are related to nonconventional materials behavior modeling and more realistic and precise analyses of structures and structural components, aiming to address the diverse demands of areas such as infrastructure, civil construction, mechanical industry, aerospace industry, among others. Among the nonlinear behaviors to which a quasi-static structure is subjected, it is possible to highlight the physical nonlinearities described by the constitutive or rheological relations. These relations are expressed by stress-strain equations that may include the dependence on specific variables, such as time, temperature, humidity, among others. Real materials can exhibit these three behaviors separately, depending on material properties and service conditions, or simultaneously, through intermediate behaviors between two or three of these, such as viscoelastic, elastoplastic, and viscoelastoplastic (Marques and Creus, 2012; Christensen, 2003; Findley et al, 1989)
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