Master's Dissertation
DOI
https://doi.org/10.11606/D.18.2016.tde-02032016-104021
Document
Author
Full name
Tiago Morkis Siqueira
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Coda, Humberto Breves (President)
Rubert, José Benaque
Title in Portuguese
Análise dinâmica não linear geométrica de estruturas e mecanismos reticulados planos com ligações deslizantes
Keywords in Portuguese
Dinâmica não linear
Ligações deslizantes
Método dos elementos finitos posicional
Abstract in Portuguese
Title in English
Geometrical nonlinear dynamical analysis of plane frame structures and mechanisms with sliding joints
Keywords in English
Nonlinear dynamics
Positional finite element method
Sliding joints
Abstract in English
A total lagrangian finite element method formulation is developed for the dynamic analysis of plane frame structures and mechanisms containing sliding joints that undergoes large displacements and rotations. Those connections are introduced in the mechanical system as prismatic and cylindrical joints by the method of Lagrange multipliers, allowing its use on the simulation of several types of structures and mechanisms. Hinges between bars are also considered by kinematic compatibility of the degrees of freedom on the common node. The adopted finite element formulation uses as nodal parameters uncoupled positions and angles. Therefore, Reissner exact kinematics for bars can be utilized for structural finite deformation. The Saint-Venant-Kirchhoff constitutive model, which relates the objective Green-Lagrange strain measure with the second Piola-Kirchhoff stress tensor, is adopted. The principle of stationary total energy is used to obtain the dynamic nonlinear equilibrium of the system and the solution of the resulting nonlinear system of equations is done by the Newton-Raphson method. The Newmark method is adopted for time integration. Several examples are presented for the validation of the developed formulation, and those are compared with analytical solutions in order to clarify the possibilities of application of the proposed formulation.

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Publishing Date
2016-03-07

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