Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems

This article presents an evolutionary topology optimization method for compliance minimization of structures under design-dependent pressure loads. In traditional density based topology optimization methods, intermediate values of densities for the solid elements arise along the iterations. Extra boundary parametrization schemes are demanded when these methods are applied to pressure loading problems. An alternative methodology is suggested in this article for handling this type of load. With an extended bi-directional evolutionary structural optimization method associated with a partially coupled fluid–structure formulation, pressure loads are modelled with hydrostatic fluid finite elements. Due to the discrete nature of the method, the problem is solved without any need of pressure load surfaces parametrization. Furthermore, the introduction of a separate fluid domain allows the algorithm to model non-constant pressure fields with Laplace's equation. Three benchmark examples are explored in order to show the achievements of the proposed method.

[1]  Renato Pavanello,et al.  Synthesis of porous–acoustic absorbing systems by an evolutionary optimization method , 2010 .

[2]  Y. Xie,et al.  Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials , 2009 .

[3]  Noboru Kikuchi,et al.  Advances in computational design and optimization with application to MEMS , 2001 .

[4]  Y. Xie,et al.  Evolutionary methods for topology optimisation of continuous structures with design dependent loads , 2005 .

[5]  H. Gea,et al.  Topology optimization with design-dependent pressure loading , 2009 .

[6]  J. Antunes,et al.  Modelling of Mechanical Systems: Fluid- Structure Interaction: 3 , 2017 .

[7]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[8]  M. Bruggi,et al.  An alternative truly-mixed formulation to solve pressure load problems in topology optimization , 2009 .

[9]  Jakob S. Jensen,et al.  Acoustic design by topology optimization , 2008 .

[10]  Joaquim R. R. A. Martins,et al.  Structural topology optimization with design-dependent pressure loads , 2012 .

[11]  Yi Min Xie,et al.  Evolutionary Topology Optimization of Continuum Structures: Methods and Applications , 2010 .

[12]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[13]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[14]  N. Olhoff,et al.  Topology optimization of continuum structures subjected to pressure loading , 2000 .

[15]  N. Olhoff,et al.  Topological optimization of continuum structures with design-dependent surface loading – Part II: algorithm and examples for 3D problems , 2004 .

[16]  Ole Sigmund,et al.  Topology Optimization of Fluid-Structure-Interaction Problems in Poroelasticity , 2013 .

[17]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[18]  O. Sigmund,et al.  Topology optimization using a mixed formulation: An alternative way to solve pressure load problems , 2007 .

[19]  Andrew R. Teel,et al.  ESAIM: Control, Optimisation and Calculus of Variations , 2022 .

[20]  N. Olhoff,et al.  Topological optimization of continuum structures with design-dependent surface loading – Part I: new computational approach for 2D problems , 2004 .

[21]  George I. N. Rozvany,et al.  Structural and Multidisciplinary Optimization , 1995 .

[22]  Shutian Liu,et al.  Topology optimization of 3D structures with design-dependent loads , 2010 .

[23]  Ole Sigmund,et al.  Design of multiphysics actuators using topology optimization - Part I: One-material structures , 2001 .

[24]  Xiong Zhang,et al.  A new boundary search scheme for topology optimization of continuum structures with design-dependent loads , 2008 .

[25]  Qing Li,et al.  Evolutionary topology and shape design for general physical field problems , 2000 .

[26]  Y. Xie,et al.  Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method , 2007 .

[27]  O. C. Zienkiewicz,et al.  Fluid‐structure dynamic interaction and wave forces. An introduction to numerical treatment , 1978 .

[28]  Grant P. Steven,et al.  Evolutionary structural optimization for dynamic problems , 1996 .

[29]  Grant P. Steven,et al.  Displacement minimization of thermoelastic structures by evolutionary thickness design , 1999 .

[30]  Roger Ohayon,et al.  Fluid-Structure Interaction: Applied Numerical Methods , 1995 .