Physical and geometrical non-linear analysis of plane frames considering elastoplastic semi-rigid connections by the positional FEM

2016

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In this study a total lagrangian 2D finite element formulation is used to model plane frames developing large displacements and rotations considering sliding connections. This kind of connections is usually called prismatic and cylindrical joints. In order to be self-containing, the steps of the development of a frame finite element of any approximation order that considers the influence of shear strain by means of a generalized Reissner kinematics is presented. The adopted degrees of freedom are positions and rotations. Using positions as degrees of freedom simplifies the total lagrangian description and enables a comprehensive presentation of the proposed connections. Revolute connections are considered by direct degrees of freedom matching. Prismatic connections are modelled by the Lagrange multiplier technique that constrains positions and rotation of a sliding node to the varying position and rotation of a path element. Cylindrical joints are introduced in similar way by Lagrange multipliers releasing the sliding node rotation. The principle of stationary potential energy is used to write the non-linear equilibrium equation including the Lagrange multiplier influence. To solve the non-linear equation a Taylor expansion is carried out and the Newton-Raphson procedure is employed. The frame element is considered elastic, following the Saint-VenantKirchhoff constitutive model. Selected examples are used to validate the formulation and to show its possibilities of application.

Section: Sliding Connectionsmentioning

confidence: 99%

“…In this work we are interested to improve a previously developed total lagrangian frame finite element formulation (Coda;Paccola, 2014;Reis; to accomplish sliding connections for 2D elastostatic applications. In order to enable a comprehensive description of the proposed connections the frame formulation is described.…”

Section: Introductionmentioning

confidence: 99%

Development of Sliding Connections for Structural Analysis by a Total Lagrangian FEM Formulation

Siqueira

2016

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“…In this example, the behavior of the previous studied structure is analyzed when it is submitted to the effect of a real earthquake, see for instance Reis and Coda (2014), Coda and Paccola (2014) and <http://peer.berkeley.edu/peer_ground_motion_database/spectras/21713/unscaled_searches/84357 /edit.>. The imposed base movements in horizontal and vertical directions are depicted in figure 11.…”

Section: Structure Under Earthquake-2d Modelmentioning

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

2016

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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

“…However, it is possible to extend the proposed formulation to consider ductile or combined ruins introducing plastic joints, Coda and Paccola (2014) and Reis and Coda (2014).…”

Section: Introductionmentioning

confidence: 99%

Flexible Multibody Dynamics Finite Element Formulation Applied to Structural Progressive Collapse Analysis

Sanches

2017

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This paper presents a two-dimensional frame finite element methodology to deal with flexible multi-body dynamic systems and applies it to building progressive collapse analysis. The proposed methodology employs a frame element with Timoshenko kinematics and the dynamic governing equation is solved based on the stationary potential energy theorem written regarding nodal positions and generalized vectors components instead of displacements and rotations. The bodies are discretized by lose finite elements, which are assembled by Lagrange multipliers in order to make possible dynamical detachment. Due to the absence of rotation, the time integration is carried by classical Newmark algorithm, which reveals to be stable to the position based formulation. The accuracy of the proposed formulation is verified by simple examples and its capabilities regarding progressive collapse analysis is demonstrated in a more complete building analysis.