Microstructural topology optimization of structural-acoustic coupled systems for minimizing sound pressure level

The aim of this paper is to present a microstructural topology optimization methodology for the structural-acoustic coupled system. In the structural-acoustic system, the structure is considered to be a thin composite plate composed of periodic uniform microstructures. The discrete design variables are used in the microstructural topology optimization, and the constitutive matrix is interpolated by the power-law scheme at the micro scale. The equivalent macro material properties of the microstructure are computed through the homogenization method. The design objective is to minimize the sound pressure level (SPL) in an interior acoustic medium. The sensitivities of the SPL with respect to design variables are derived. The bi-directional evolutionary structural optimization (BESO) method is extended to solve the structural-acoustic coupled optimization problem to find the optimal material distribution of the microstructure. Numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented microstructural topology optimization method.     

Design of piezocomposite materials and piezoelectric transducers using topology optimization—Part I

Summary Currently developments of piezocomposite materials and piczoelectric actuators have been based on the use of simple analytical models, test of prototypes, and analysis using the finite element method (FEM), usually limiting the problem to a parametric optimization. By changing the topology of these devices or their components, we may obtain an improvement in their performance characteristics. Based on this idea, this paper discusses the application of topology optimization combined with the homogenization method and FEM for designing piezocomposite materials. The homogenization method allows us to calculate the effective properties of a composite material knowing its unit cell topology. New effective properties that improves the electromechanical efficiency of the piezocomposite material are obtained by designing the piezocomposite unit cell. This method consists of finding the distribution of the material and void phases in a periodic unit cell that optimizes the performance characteristics of the piezocomposite. The optimized solution is obtained using Sequential Linear Programming (SLP). A general homogenization method applied to piczoelectricity was implemented using the finite element method (FEM). This homogenization method has no limitations regarding volume fraction or shape of the composite constituents. The main assumptions are that the unit cell is periodic and that the scale of the composite part is much larger than the microstructure dimensions. Prototypes of the optimized piezocomposites were manufactured and experimental results confirmed the large improvement. Department of Mechanical Engineering and Applied Mechanics Department of Mechanical Engineering and Applied Mechanics     

Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures

This paper presents a novel concurrent topology optimization approach for finding the optimum topologies of macrostructures and their corresponding parameterized lattice microstructures in an integrated manner. Considering the manufacturability of the structure designs and computational efficiency, additional parameters are introduced to define the microstructure unit cell patterns and their non-uniform distribution, which avoids expensive iterative numerical homogenization calculations during topology optimization and results in an easier modelling of structure designs as well. It is worth mentioning that the equivalent properties of material microstructures serve as a link between the macro and the micro scale with the help of homogenization theory and the Porous Anisotropic Material with Penalization (PAMP) model. Besides, sensitivities of global structure compliance with respect to the pseudo-density variables and the microstructure parameter variables are derived, respectively. Moreover, several numerical examples are presented and reasonable solutions have been obtained to demonstrate the efficiency of the proposed method. Finally, mechanical testing is conducted to investigate the better performance of the optimized structure which is fabricated by 3D printing.     

Microstructural topology optimization with respect to sound power radiation

The paper deals with the problem of topological design of microstructure with respect to minimization of the sound power radiation from a vibrating macrostructure. The macrostructure is excited at a single or a band of excitation frequencies by a time-harmonic mechanical loading with prescribed amplitude and spatial distribution. The structural damping is considered to be proportional damping. The sound power is calculated using a high frequency approximation formulation and thus the sensitivity analysis may be performed in a very efficient manner. The microstructure composed of two different solid isotropic materials is assumed to be identical from point to point at the macro-level which implies that the interface between the structure and the acoustic medium is unchanged during the design process. The equivalent material properties of the macrostructure are calculated using homogenization method and the bi-material SIMP model is employed to achieve zero-one design at the micro-scale. Numerical examples are given to validate the model developed. Some interesting features of acoustic microstructure topology optimization are revealed and discussed.     

Piezoresistive device optimization using topological derivative concepts

A piezoresistive sensor is composed of a piezoresistive membrane attached to a flexible plate. The piezoresistive material is anisotropic, and its electrical properties change when subjected to mechanical stresses. In this work, the topology design of a piezoresistive pressure sensor is addressed. More specifically, an optimization technique based on topological sensitivity analysis is proposed in order to obtain the optimized distribution of piezoresistive material over the plate. In most of the works regarding topological sensitivity analysis, isotropic materials are considered. However, the problem of conductivity in an anisotropic non-homogeneous domain has been recently addressed, and a closed form for the topological derivative associated to the energy shape functional has been presented. In this work, on the other hand, a closed form for the topological derivative associated with a multi-objective shape functional related to the steady-state anisotropic current density diffusion problem is presented. To illustrate the applicability of the closed formula and the proposed optimization procedure, numerical examples regarding the conceptual design of piezoresistive sensors, considering distinct optimization parameters and boundary conditions in the conductivity problem, are presented.     

Optimal design of periodic functionally graded composites with prescribed properties

The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of materials in the last few years. In this work, the objective is to extend the material design method to obtain functionally graded material architectures, i.e. materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional material gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric material gradation, and a material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded material cell design. Finally the influence of material gradation on extreme materials is investigated, which includes materials with near-zero shear modulus, and materials with negative Poisson’s ratio.     

A review of homogenization and topology optimization III-topology optimization using optimality criteria

This is the first part of a three-paper review of homogenization and topology optimization, viewed from an engineering standpoint and with the ultimate aim of clarifying the ideas so that interested researchers can easily implement the concepts described. In the first paper we focus on the theory of the homogenization method where we are concerned with the main concepts and derivation of the equations for computation of effective constitutive parameters of complex materials with a periodic micro structure. Such materials are described by the base cell, which is the smallest repetitive unit of material, and the evaluation of the effective constitutive parameters may be carried out by analysing the base cell alone. For simple microstructures this may be achieved analytically, whereas for more complicated systems numerical methods such as the finite element method must be employed. In the second paper, we consider numerical and analytical solutions of the homogenization equations. Topology optimization of structures is a rapidly growing research area, and as opposed to shape optimization allows the introduction of holes in structures, with consequent savings in weight and improved structural characteristics. The homogenization approach, with an emphasis on the optimality criteria method, will be the topic of the third paper in this review.     

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

Self-collimating phononic crystals (PCs) are periodic structures that enable self-collimation of waves. While various design parameters such as material property, period, lattice symmetry, and material distribution in a unit cell affect wave scattering inside a PC, this work aims to find an optimal material distribution in a unit cell that exhibits the desired self-collimation properties. While earlier studies were mainly focused on the arrangement of self-collimating PCs or shape changes of inclusions in a unit cell having a specific topological layout, we present a topology optimization formulation to find a desired material distribution. Specifically, a finite element based formulation is set up to find the matrix and inclusion material distribution that can make elastic shear-horizontal bulk waves propagate along a desired target direction. The proposed topology optimization formulation newly employs the geometric properties of equi-frequency contours (EFCs) in the wave vector space as essential elements in forming objective and constraint functions. The sensitivities of these functions with respect to design variables are explicitly derived to utilize a gradient-based optimizer. To show the effectiveness of the formulation, several case studies are considered.     

Optimal shape design in biomimetics based on homogenization and adaptivity

Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. The paper is devoted to the shape optimization of new biomorphic microcellular silicon carbide ceramics produced from natural wood by biotemplating. This is a novel technology in the field of biomimetics which features a material synthesis from biologically grown materials into ceramic composites by fast high-temperature processing. We are interested in finding the best material-and-shape combination in order to achieve the optimal prespecified performance of the composite material. The computation of the effective material properties is carried out using the homogenization method. Adaptive mesh-refinement technique based on the computation of recovered stresses is applied in the microstructure to find the homogenized elasticity coefficients. Numerical results show the reliability of the implemented a posteriori error estimators.     

基于Cosserat理论的微观结构对非均质材料有效性能的影响分析

为更有效地研究具有周期性微观结构的非均质材料平面应变问题,用基于Cosserat理论的渐进均匀化方法得到微观结构对非均质材料有效性能的影响情况．计算结果表明,单胞内夹杂体的形状对有效杨氏弹性模量、有效泊松比、有效Cosserat弹性常数和有效材料特征长度有影响,并且随着夹杂体与单胞体积比的增大而影响明显．