Saturated poroelastic actuators generated by topology optimization

In this paper the fluid-structure interaction problem of a saturated porous media is considered. The pressure coupling properties of porous saturated materials change with the microstructure and this is utilized in the design of an actuator using a topology optimized porous material. By maximizing the coupling of internal fluid pressure and elastic shear stresses a slab of the optimized porous material deflects/deforms when a pressure is imposed and an actuator is created. Several phenomenologically based constraints are imposed in order to get a stable force transmitting actuator.

[1]  J. Shao,et al.  Study of poroelasticity material coefficients as response of microstructure , 2000 .

[2]  B. Bourdin Filters in topology optimization , 2001 .

[3]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[4]  S. Torquato,et al.  Composites with extremal thermal expansion coefficients , 1996 .

[5]  Ole Sigmund,et al.  On the design of 1–3 piezocomposites using topology optimization , 1998 .

[6]  M. Biot General Theory of Three‐Dimensional Consolidation , 1941 .

[7]  K. Svanberg The method of moving asymptotes—a new method for structural optimization , 1987 .

[8]  O. Sigmund Materials with prescribed constitutive parameters: An inverse homogenization problem , 1994 .

[9]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[10]  J. Auriault,et al.  Homogenization of Coupled Phenomena in Heterogenous Media , 2009 .

[11]  James K. Guest,et al.  Design of maximum permeability material structures , 2007 .

[12]  K. Maute,et al.  Conceptual design of aeroelastic structures by topology optimization , 2004 .

[13]  Martin Schanz,et al.  A comparative study of Biot's theory and the linear Theory of Porous Media for wave propagation problems , 2003 .

[14]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[15]  K. Maute,et al.  Topology optimization of flexible micro-fluidic devices , 2010 .

[16]  James K. Guest,et al.  Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability , 2006 .

[17]  M. Biot Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[18]  Wolfgang Ehlers,et al.  A historical review of the formulation of porous media theories , 1988 .

[19]  S. Torquato,et al.  Multifunctional composites: optimizing microstructures for simultaneous transport of heat and electricity. , 2002, Physical review letters.

[20]  Thomas J. R. Hughes,et al.  The Stokes problem with various well-posed boundary conditions - Symmetric formulations that converge for all velocity/pressure spaces , 1987 .

[21]  M. Biot THEORY OF ELASTICITY AND CONSOLIDATION FOR A POROUS ANISOTROPIC SOLID , 1955 .

[22]  Ole Sigmund,et al.  On the Optimality of Bone Microstructure , 1999 .

[23]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[24]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[25]  O. Sigmund A new class of extremal composites , 2000 .

[26]  G. Yoon Topology optimization for stationary fluid–structure interaction problems using a new monolithic formulation , 2010 .

[27]  Shengli Xu,et al.  Optimum material design of minimum structural compliance under seepage constraint , 2010 .

[28]  K. Svanberg,et al.  An alternative interpolation scheme for minimum compliance topology optimization , 2001 .

[29]  E. Sanchez-Palencia Non-Homogeneous Media and Vibration Theory , 1980 .