Topological Derivative-Based Topology Optimization of Plate Structures Under Bending Effects
- PDF / 2,264,702 Bytes
- 14 Pages / 595.224 x 790.955 pts Page_size
- 99 Downloads / 191 Views
RESEARCH PAPER
Topological Derivative-Based Topology Optimization of Plate Structures Under Bending Effects F. S. Carvalho1 · D. Ruscheinsky1 · S. M. Giusti2 · C. T. M. Anflor1
· A. A. Novotny3
Received: 30 May 2020 / Revised: 28 July 2020 / Accepted: 31 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, the topological derivatives of L2 and energy norms associated with the solution to Kirchhoff and ReissnerMindlin plate bending models are introduced. Based on existing theoretical results, closed forms of the sensitivities are presented. A zero-order term is introduced in the equilibrium equations, which allows for adapting the obtained sensitivities to the context of topology optimization of plates under elastic support and free vibration condition as well. The resulting analytical formulae are used together with a level-set domain representation method to devise a simple topology design algorithm. Several finite element-based representative numerical experiments are presented showing its applications to the compliance minimization and eigenvalue maximization of Kirchhoff as well as Reissner-Mindlin plate structures under bending effects. Keywords Optimal design of plates · Topological derivative · Compliance minimization · Eigenvalue maximization
1 Introduction Plates are structural elements where one of its dimensions, namely thickness, is much smaller than the others, contained Responsible Editor: Palaniappan Ramu C. T. M. Anflor
[email protected] F. S. Carvalho [email protected] D. Ruscheinsky [email protected] S. M. Giusti [email protected] A. A. Novotny [email protected] 1
Group of Experimental and Computational Mechanics, University of Brasilia, Gama, Brazil
2
Facultad Regional C´ordoba UTN-FRC / CONICET, Universidad Tecnol´ogica Nacional, Maestro M. L´opez esq. Cruz Roja Argentina, X5016ZAA C´ordoba, Argentina
3
Coordenac¸a˜ o de M´etodos Matem´aticos e Computacionais, Laborat´orio Nacional de Computac¸a˜ o Cient´ıfica LNCC/MCT, Av. Get´ulio Vargas 333, 25651-075 Petr´opolis RJ, Brazil
in a plane. These elements are widely used in the naval, nuclear, aeronautical, and civil industries, among others, due to their structural capability to cover large distances or surfaces. Based on the previous geometrical description, the mechanical behavior of the structural element can be reduced to an analysis over the middle plane of the plate. Therefore, some hypothesis over the thickness must be made. The first theory introduced for plates was the classical thin plate theory of Kirchhoff (1850), where some assumptions were imposed by omitting the shear deformations and rotary inertia. In the papers by Reissner (1945) and Mindlin (1951), the shear deformations are considered and the rotation and lateral deflections are decoupled giving rise to the Reissner-Mindlin theory, which allowed more accurate results in thick plate bending analysis. Since then, these theories have been widely and successfully used to analyze several structural problems modeled by plates i
Data Loading...
