Gil Ho Yoon

Multi-resolution multi-scale topology optimization-a new paradigm

Abstract The purpose of this work is to present a new-concept multi-resolution multi-scale topology optimization. The key idea of the present strategy is that design optimization should be performed progressively from low to high resolution, not at a single resolution level. To achieve the multi-resolution strategy, design optimization is formulated in a wavelet-based variable space, not in a direct density variable space. The major advantages of the multi-resolution design optimization include: (1) topologically simple and close-to-the-global-optimum structures may be obtained without any explicit constraint, and (2) the convergence is not sensitive to mathematical programming methods. For the efficient numerical implementation of the multi-resolution approach, the side constraints imposed on the direct density variables are removed by mapping the density variables into intermediate variables. These intermediate variables are then wavelet-transformed to new design variables. It is addressed that the present multi-resolution topology optimization can resolve major numerical instability problems such as mesh-dependencies and local minima. The usefulness of the multi-scale nature of the wavelets in the present multi-resolution multi-scale optimization formulation is also discussed.

The role of s-shape mapping functions in the SIMP approach for topology optimization

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

Topology optimization of piezoelectric energy harvesting devices considering static and harmonic dynamic loads

A topology optimization (TO) procedure is developed to design optimal layouts for piezoelectric energy harvesting devices (EHDs) by considering the effect of static and harmonic dynamic mechanical loads. To determine the optimal material distributions of a piezoelectric material considering the harmonic dynamic coupling effects between the electric energy and a structure for efficient EHDs, harmonic dynamic responses and the complex sensitivity analyses for various objectives related to the energy efficiency are calculated and derived. For the relaxation method of the density design variable for TO, material properties such as the anisotropic linear elasticity coefficients, piezoelectric coefficients, and permittivity coefficients are independently interpolated through the solid isotropic material with penalization (SIMP) approach with three penalization values. Through several numerical tests for various configurations of piezoelectric materials, it is found that depending on the choice of penalization value, complex behaviors of energies are possible and these in turn lead to a serious local optima issue in TO. Through several three-dimensional design problems, the validity and usefulness of the developed optimization procedure for efficient EHDs are demonstrated.

Constraint force design method for topology optimization of planar rigid-body mechanisms

This study develops a new design method called the constraint force design method, which allows topology optimization for planar rigid-body mechanisms. In conventional mechanism synthesis methods, the kinematics of a mechanism are analytically derived and the positions and types of joints of a fixed configuration (hereafter the topology) are optimized to obtain an optimal rigid-body mechanism tracking the intended output trajectory. Therefore, in conventional methods, modification of the configuration or topology of joints and links is normally considered impossible. In order to circumvent the fixed topology limitation in optimally designing rigid-body mechanisms, we present the constraint force design method. This method distributes unit masses simulating revolute or prismatic joints depending on the number of assigned degrees of freedom, analyzes the kinetics of unit masses coupled with constraint forces, and designs the existence of these constraint forces to minimize the root-mean-square error of the output paths of synthesized linkages and a target linkage using a genetic algorithm. The applicability and limitations of the newly developed method are discussed in the context of its application to several rigid-body synthesis problems.

Toward a stress-based topology optimization procedure with indirect calculation of internal finite element information

Abstract In this work, a novel computational approach is developed for the gradient-based stress-based topology optimization method, where the volume is minimized according to locally defined stress constraints of static failure criteria in the framework of tailored finite element (FE) software without direct access to an internal finite element information database. Tailored finite element codes that require substantial understanding and modification (reprogramming) or do not directly provide internal finite element information have rarely been used for stress-based topology optimization with solid isotropic material with penalization (SIMP) methods. Therefore, much research has been confined to two-dimensional problems with rectilinear basic finite elements, as complex three-dimensional geometries with advanced finite element formulations are not supported. To overcome this problem, we developed a new computational procedure for sensitivity analysis without direct access to an internal information database, a task that has previously been regarded as almost impossible. Since the calculation of linear strain–displacement matrices is required in the sensitivity analysis, the present procedure includes a node selection algorithm to efficiently calculate the matrices of irregular-shaped finite elements by displacement perturbations. The benefits of the present approach are that well-established powerful finite element codes, i.e., commercial or sophisticated public FE codes, can be easily incorporated for linear stress-based topology optimization, and any type of finite element formulation can be readily employed. In contrast to classical sensitivity analysis, small computations are used for sensitivity analysis in this work. To demonstrate the validity and efficiency of the present procedure and approach, several topology optimization problems with 3D and shell elements are solved.

Modeling of a partially debonded piezoelectric actuator in smart composite laminates

A partially debonded piezoelectric actuator in smart composite laminates was modeled using an improved layerwise displacement field and Heaviside unit step functions. The finite element method with four node plate element and the extended Hamilton principle were used to derive the governing equation. The effects of actuator debonding on the smart composite laminate were investigated in both the frequency and time domains. The frequency and transient responses were obtained using the mode superposition method and the Newmark time integration algorithm, respectively. Two partial actuator debonding cases were studied to investigate the debonding effects on the actuation capability of the piezoelectric actuator. The effect of actuator debonding on the natural frequencies was subtler, but severe reductions of the actuation ability were observed in both the frequency and time responses, especially in the edge debonded actuator case. The results provided confirmation that the proposed modeling could be used in virtual experiments of actuator failure in smart composite laminates.

Design and fabrication of a micro PZT cantilever array actuator for applications in fluidic systems

In this article, a micro cantilever array actuated byPZT films is designed and fabricated for micro fluidic systems. The design features for maximizing tip deflections and minimizing fluid leakage are described. The governing equation of the composite PZT cantilever is derived and the actuating behavior predicted. The calculated value of the tip deflection was 15 µm at 5 V. The fabrication process from SIMOX (Separation by oxygen ion implantation) wafer is presented in detail with the PZT film deposition process. The PZT films are characterized by investigating the ferroelectric properties, dielectric constant, and dielectric loss. Tip deflections of 12 µm at 5 V are measured, which agreed well with the predicted value. The 18 µ1/s leakage rate of air was observed at a pressure difference of 1000 Pa. Micro cooler is introduced, and its possible application to micro compressor is discussed.

Topology Optimization for Acoustic-Structure Interaction Problems

We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz equation and the linear elasticity equation, respectively, and it is necessary that the governing equations should be properly evolved with respect to the design variables in the design domain. Moreover, all the boundary conditions obtained by computing surface coupling integrals should be properly imposed to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz equation and the linear elasticity equation, the mass density as well as the shear and bulk moduli are interpolated with the design variables. In this formulation, the coupled interface boundary conditions are automatically satisfied without having to compute surface coupling integrals. Two-dimensional acoustic-structure interaction problems are optimized to show the validity of the proposed method.

Topology optimization considering fatigue life in the frequency domain

This research develops a new topological optimization (TO) method to assess dynamic fatigue failure in the frequency domain for random excitation forces. Besides static failure, fatigue life (or fatigue failure) is an important design criterion for the safety of mechanical and building structures. Therefore, many assessment theories and computational approaches have been proposed, and they can be divided into two categories: time domain and frequency domain. Although both approaches have been successfully applied for engineering purposes, they are rarely considered in structural TO. To consider fatigue failure caused by stochastic mechanical loads in structural TO, this research adopts fatigue assessment approaches in the frequency domain, such as narrow band solution, the Wirsching and Light method, the Ortiz and Chen method, and Dirlik method. For TO, we perform an adjoint sensitivity analysis with those fatigue assessment methods. We consider some two-dimensional benchmark problems and show that the present design method successfully constrains fatigue.

Modeling and design of shape memory alloy actuators

This paper presents the application of systematic model-based design techniques to the design of shape memory alloy (SMA) actuators. Shape memory alloys are promising materials for (micro-)actuation, because of the relatively large deformations and forces that can be achieved. However, the complex constitutive behavior and the fact that several physical domains (electrical, thermal and mechanical) play a role makes it difficult to design effective SMA actuators with complex shapes and layouts. For this reason, design optimization techniques are expected to play an important role in the further development of SMA actuators. The present paper presents shape and topology optimization of SMA structures and shows the effectiveness of these design approaches by several representative examples.