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We propose a numerical method for a topology optimisation of composite elastic metamaterial slabs. We aim to realise some anomalous functionalities such as perfect absorption, wave-mode conversion, and negative refraction by designing the shape and topology of (visco-)elastic inclusions. Instead of manipulating effective material constants, we propose to utilise the far-field characteristics of scattered waves. This allows us to achieve novel functionalities for waves in not only low- but also high-frequency ranges. The design sensitivity corresponding to the far-field characteristics is rigorously derived using the adjoint variable method and incorporated into a level-set–based topology optimisation algorithm. The design sensitivity is computed by the boundary element method with periodic Green's function instead of the standard finite element method to rigorously deal with the radiation of scattered waves without absorbing boundaries. We show some numerical examples to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering. Specifically, the development of energy dissipation devices with vibration control remains a key consideration. The aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level set based topology optimization of transient flow using the lattice Boltzmann method is simultaneously applied to forward and reverse direction flows to deal with oscillating flows in real-world engineering designs. Although several studies have examined topology optimization to minimize dissipated kinetic energy, this study introduces an objective function for maximizing the dissipated kinetic energy in time-varying fluid flows via velocity gradients. [ABSTRACT FROM AUTHOR]

This paper presents a structural optimisation method in three-dimensional acoustic–elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic–elastic coupled problems. In this paper, the acoustic–elastic coupled problems are solved by a BEM–FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM–FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

This paper presents a topology optimization method for flow channel design using the lattice kinetic scheme (LKS). LKS is a numerical scheme merging the lattice Boltzmann method with the kinetic scheme for solving the incompressible Navier-Stokes equations. In the lattice Boltzmann method, the discrete distribution functions for every grid in the analysis domain need to be stored to compute the flow field, while in the LKS, only the flow velocities and the densities are stored, and thus requiring less storage. Moreover, in the LKS, the macroscopic boundary conditions in terms of the velocity and the pressure can be imposed directly rather than considering the bounce-back boundary condition against the distribution function. In this study, the optimization is performed based on the gradient of the objective functional with respect to the design variables and the design sensitivity is computed by the adjoint variable method. Both the forward and the adjoint problems are solved using the LKS. The validity of the design sensitivity is verified by comparing it with the finite difference approximation of objective functional. Numerical examples of solving two-dimensional flow channel design problems are presented to demonstrate the proposed method. [ABSTRACT FROM AUTHOR]