Xiao Dong Huang

Topology optimization of functionally graded cellular materials

Design of functionally graded material (FGM), in which the mechanical property varies along one direction, is the focus of this study. It is assumed that the microstructure of the FGM is composed of a series of base cells in the variation direction and self-repeated in other directions. Bi-directional evolutionary structural optimization technique in the form of inverse homogenization is used for the design of the FGM for specified variation in bulk or shear modulus. Instead of designing a series of base cells simultaneously, the base cells are optimized progressively by considering three base cells at each stage. Thus, the proper connections between adjacent base cells can be achieved with high computational efficiency. Numerical examples demonstrate the effectiveness of the proposed method for designing microstructures of 2D and 3D FGMs with specified variation in bulk or shear modulus. The proposed algorithm can also be easily extended to design FGMs with other functional properties.

Topological optimization for the design of microstructures of isotropic cellular materials

The aim of this study was to design isotropic periodic microstructures of cellular materials using the bidirectional evolutionary structural optimization (BESO) technique. The goal was to determine the optimal distribution of material phase within the periodic base cell. Maximizing bulk modulus or shear modulus was selected as the objective of the material design subject to an isotropy constraint and a volume constraint. The effective properties of the material were found using the homogenization method based on finite element analyses of the base cell. The proposed BESO procedure utilizes the gradient-based sensitivity method to impose the isotropy constraint and gradually evolve the microstructures of cellular materials to an optimum. Numerical examples show the computational efficiency of the approach. A series of new and interesting microstructures of isotropic cellular materials that maximize the bulk or shear modulus have been found and presented. The methodology can be extended to incorporate other material properties of interest such as designing isotropic cellular materials with negative Poissons ratio.

Compressive Behavior of Luffa Sponge Material at High Strain Rate

The strain rate effect of luffa sponge material is an indispensable property for it to be used for acoustic, vibration, and impact energy absorption. Compressive tests at different strain rates on cylindrical column specimens of luffa sponge material were conducted over a wide density ranging from 24 to 64 kg/m3. A photographic technique was applied to measure the section area of the specimen with irregular shape. The mechanical properties of luffa sponge material at various strain rates were obtained based on this measurement. The dynamic data were compared to those of quasi-static experiments. It was found that compressive strength, plateau stress and specific energy absorption of luffa sponge material were sensitive to the rate of loading. Empirical formulae were developed for strength, densification strain and specific energy absorption at various strain rates in the macroscopic level by considering the luffa fiber as base material.

Bi-Directional Evolutionary Structural Optimization for Design of Compliant Mechanisms

This research presents a topology optimization approach based on Bi-directional Evolutionary Structural Optimization (BESO) for optimal design of compliant mechanisms. Due to the complexity of the design for various compliant mechanisms, a new multi-objective optimization model is established by considering the mechanism flexibility and structural stiffness simultaneously. The sensitivity analysis is performed by applying the adjoint sensitivity approach to both the kinematical function and the structural function. The sensitivity numbers are derived according to the variation of the objective function with respect to the design variables. Some numerical examples are given to demonstrate the effectiveness of the proposed method for the design of various compliant mechanisms.

Concurrent Design of Structures and Materials Based on the Bi-Directional Evolutionary Structural Optimization

Different from the independent optimization of macrostructures or materials, a two-scale topology optimization algorithm is developed in this paper based on the bi-directional evolutionary structural optimization (BESO) method for concurrently designing a macrostructure and its composite microstructure. The objective is to minimize the mean compliance of the structure which is composed of a two-phase composite. The effective properties of the composite are calculated through the homogenization method and integrated into the finite element analysis of the structure. Sensitivity analysis for the structure and microstructure is conducted by the adjoint method. Based on the derived sensitivity numbers, the BESO approach is applied for iteratively updating the topologies for both the structure at the macro level and the microstructure of composite at the micro level. Numerical examples are presented to validate the effectiveness of the proposed optimization algorithm.

Luffa Sponge as a Sustainable Engineering Material

The paper presents the first scientific study of the stiffness, strength and energy absorption characteristics of the luffa sponge with a view to using it as an alternative sustainable engineering material for various practical applications. A series of compression tests on luffa sponge columns have been carried out. The stress-strain curves show a near constant plateau stress over a long strain range, which is ideal for energy absorption applications. It is found that the luffa sponge material exhibits remarkable stiffness, strength and energy absorption capacity that are comparable to those of some commonly-used metallic cellular materials. These properties are due to its light-weight base material, and its structural hierarchy at several length scales. Empirical formulae have been developed for stiffness, strength, densification strain and specific energy absorption at the macroscopic level by considering the luffa fiber as the base material. A comparative study shows that the luffa sponge material outperforms a variety of traditional engineering materials.

Multi-Phase Microstructures for Materials with Extreme Bulk Modulus or Thermal Conductivity

This paper describes a methodology based on “Bidirectional Evolutionary Structural Optimization” (BESO) for topological design of microstructures of materials with more than two constituent phases. The composite material is made by repeating microstructures known as periodic base cells. The aim is to achieve appropriate topology of microstructure phases that enhances the material’s bulk or thermal conductivity performance in macro-scale. Constituent phases are divided into some groups and by performing finite element analyses on microstructure, sensitivity numbers are calculated with the application of Homogenization theory. Properties of elements are gradually changed in the finite element model based on their sensitivity numbers and controlling volume of each constituent phase in the model. Some sample microstructures are generated and presented to show the capability of the approach. The results indicate that the proposed approach is very cost efficient. Moreover, there are distinctive boundaries between the constituent phases in the generated microstructures; which is an inherent advantage of application of BESO approach.

Numerical Analysis and Parametric Study of Phononic Band Gap Structures

Phononic band gap crystals (PnCs) are periodic composite materials and well known for their novel property that can prohibit the propagation of mechanical waves in certain range of frequency. This paper develops the finite element method to calculate band structures of bi-material phononic crystals. Through finite element analysis, complete band gap for longitudinal and transverse waves are obtained by characterizing the dispersion relation in phononic crystals. Phononic crystals with different inclusion shapes in a square and hexagonal unit cell are investigated to study the influence of unit cell topology on band gap size. For a specific pattern, the existence of complete band gap in relation to the density and Lamé constant modulus of composites is studied and critical density ratio and Lamé constant ratio of inclusions versus base material for opening complete band gap are given. The results provide theoretical guidance for designing phononic crystals in practical applications.

Topology optimization of microstructures for multi-functional graded composites

Functionally graded materials (FGMs) are inhomogeneous composites which are characterized by gradual variation in their physical properties. This study proposes a computational approach based on the bi-directional evolutionary structural optimization (BESO) for topologically designing microstructures of such materials with multi-functional properties, e.g. bulk modulus and thermal conductivity. It is assumed that the base cells are composed of two constituents. The smooth transition between adjacent base cells is realized by considering three base cells at each stage of the optimization. Effectiveness and efficiency of the proposed approach has been demonstrated by several numerical examples.

Topology Optimization of Photonic Band Gap Crystals

This paper proposes a new topology optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method for the design of photonic band gap crystals. The photonic crystals are assumed to be periodically composed of two given dielectric materials. Based on the finite element analysis, the proposed BESO algorithm gradually re-distributes dielectric materials within the unit cell until the resulting photonic crystals possess a maximal band gap at the desirable frequency level. Numerical examples for both transverse magnetic (TM) and transverse electric (TE) polarizations are presented, and the optimized photonic crystals exhibit novel patterns markedly different from traditional designs of photonic crystals.