Positional description applied to the solution of geometrically non-linear plates and shells.

Coda, Humberto Breves; Paccola, Rodrigo Ribeiro; Sampaio, Maria do Socorro Martins

doi:10.1016/j.finel.2012.12.001

Cited by 19 publications

(13 citation statements)

References 30 publications

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“…The enhancement is proposed based on these initial kinematics. This procedure guarantees good results from the basic kinematics [8,22] for transverse displacements and stresses parallel to the reference surface without increasing the number of degrees of freedom. Moreover, using the proposed enhancement, transverse strains will be discontinuous, which provides the desired continuity of stresses.…”

Section: Introductionmentioning

confidence: 91%

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A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

Coda

Sampaio

Paccola

2015

Finite Elements in Analysis and Design

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Section: Introductionmentioning

confidence: 91%

“…The rate of thickness variation of each lamina T lam ℓ can be recovered from its average representation T ℓ by T lam ℓ ¼ ðh lam 0 =2ÞT ℓ ; see [22]. Applying Eq.…”

Section: The Pure and Basic Reissner-mindlin Kinematics: A Positionalmentioning

confidence: 99%

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

Coda

Sampaio

Paccola

2015

Finite Elements in Analysis and Design

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“…where the mass proportional damping is also introduced, following Coda et al (2013), Coda and Paccola (2014) and Coda and Paccola (2008), in order to not loss the generality. The Newmark approximations are used in the following form,…”

Section: Nonlinear Equilibrium Equation and Solution Proceduresmentioning

confidence: 99%

“…Updated Lagrangian and co-rotational formulations can be seen, for example, in Bathe et al (1975), Simo and Vu-Quoc (1986), Armero (2006), Jelenic and Crisfield (2001) and Yoo et al (2007). Total Lagrangian formulations based on positions and unconstrained vectors can be seen in Coda et al (2013), Reis and Coda (2014) and Coda and Paccola (2008). The sole advantage of updated Lagrangian and co-rotational formulations is that they are extensions of linear formulations and, as a consequence, various well known literature solutions can be used to improve results.…”

Section: Introductionmentioning

confidence: 99%

Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

Madeira

Coda

2016

Lat. Am. j. solids struct.

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This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique

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“…The formulation is described in Total Lagrangian reference using as unknowns the nodal positions instead of the displacement. This formulation shows a simple language in respect to nonlinear geometric approach where the main advantage is the absence of co-rotational axes (the formulation can be carried on directly with global axes only) Carrazedo and Coda, 2010;Coda and Paccola, 2011;Coda et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Cavalcante

Maciel

Greco

et al. 2017

Lat. Am. j. solids struct.

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The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

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Positional description applied to the solution of geometrically non-linear plates and shells.

Cited by 19 publications

References 30 publications

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

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