英文关键词句.docVIP

***Keywords*** Homogenization Topology optimization Spectral analysis ***Methods*** A bound formulation(Bends?e et al. 1983; Taylor and Bends?e 1984; Olhoff 1989) An implicit Newmark scheme Eight-node 3D continuum finite elements with Wilson-incompatible displacement models Finite difference time domain （FDTD）method. Maximization of fundamental eigenfrequencies of vibrating elastic structures (Diaz and Kikuchi 1992; Ma et al. 1994, 1995; Diaz et al. 1994; Kosaka and Swan 1999; Krog and Olhoff 1999; Pedersen 2000). Monte-Carlo simulations Order N-approach （ONA J. B. Pendry, J. Phys. Condens. Matter 8, 1085 1996） Paté approximants (Jensen and Sigmund 2005) Representative volume element (RVE) SIMP (solid isotropic microstructure with penalty) [Bends?e 1989; Rozvany and Zhou 1991; Rozvany al. 1992; Bends?e and Sigmund 1999] Simultaneous analysis and design (SAND Bends?e 2006) The Adjoint method The boundary element method（BEM） The finite element method （FEM） The finite integration technique （FIT） The fixed point method (an OC (Optimality Criterion) based method, Cheng and Olhoff 1982) The Lagrange multiplier method The leapfrog-time integration scheme The Method of Moving Asymptotes (MMA Svanberg 1987) The mesh-independent filter (Sigmund 1997) The perfect boundary approximation （PBA CST-MWS） ***Ideas*** ***Words*** An asymptotic expansion An incompressible ?uid Derive symmetric and non-symmetric unit cell models Introducing relationships between stiffness components and the volumetric density of material ρ, which is a continuous variable, defined between limits 0 (corresponding to void) and 1 (corresponding to solid elastic material) over the admissible design domain. Numerical singularity Symmetric and positive definite stiffness and mass matrices The optimization iterations are stopped when the relative difference between two consecutive objective functions is less than 10-3. The ratio betw