Plate theory in the resolution of thin-walled structures
Thiago Vieira Fernandes1; Paulo de Mattos Pimenta1
1 Polytechnic School at the University of São Paulo, São Paulo, Brazil
doi:10.20906/CPS/CILAMCE2017-0153
Resumo
The objective of this work is to arrive at reliable resolutions for thin plates with small or large deformations, using the methods of Kirchhoff-Love and Von Kármán. The approximation counts with Multiple Fixed Least Squares method. The problem formulation deal with static, kinematics and dynamics of the movement, weak form of the equations of motion, isotropic and orthotropic materials, internal energy and kinetic analysis and elastic behavior. The formulation is considering the geometric linearity and the use of incremental processes of composition of displacements, rotations, deformations, moments, kinetic energy and internal energy. Thus facilitating the resolution of singularities. The formulation presents non-linear aspects and is useful for the application of numerical methods. Similar with Pimenta and Campello (2010), the approximations of time and the algorithm of the weak form must respect the conservation of angular and linear moments. The resolution of the nonlinearities with the use of the HHT-α method because it presents energy decay, 2nd order of accuracy, to be unconditionally stable and to have an energy dissipation parameter. As in Pimenta (1993), this article defines cross sections with energetically conjugated tensors to facilitate the derivation of equilibrium equations. The analysis of equilibrium and the resistance of the system leads the end of the project. In addition, the work presents the resolution of the equations by programming in AceGen and later visualization in 3D with numerical examples of thin metal profiles discretized by plates, in an isolated environment as well as in a frame, and of a dome loaded transversely.
Palavras-chave: Thin-Walled Plate; Nonlinearity; Time Increment; Finite Element Application