Kie-Chan Kwon

Material cloud method - A new topology optimization method

A newly developed material cloud method (MCM) for topology optimization is presented. In MCM, an optimal structure can be found by optimizing sizes and positions of material clouds, which are lumps of material with specified properties. A numerical analysis for a specific distribution of material clouds is carried out using fixed background finite element mesh. Optimal material distribution can be extracted from material clouds’ distribution. In MCM, an expansion-reduction procedure of design domain for finding out true optimal solution can be naturally realized. Also the convergence of material distribution is faster and well-defined material distribution with fewer intermediate densities can be obtained. In addition, the control of minimum-member sizes in the material distribution can be realized to a certain extent. In this paper, basic concept of MCM is introduced, and optimization results through MCM are compared with those of the traditional density distribution method (DDM) for 2D problems and also for a 3D problem.

The Least-Squares Meshfree Method for Linear Elasticity

The first-order least-squares meshfree method for linear elasticity is presented. The conventional and the compatibility-imposed least-squares formulations are studied on the convergence behavior of the solution and the robustness to integration error. Since the least-squares formulation is a type of mixed formulation and induces positive-definite system matrix, by using shape functions of same order for both primal and dual variables, higher rate of convergence is obtained for dual variables than Galerkin formulation. Numerical examples also show that the presented formulations do not exhibit any volumetric locking for the incompressible materials.

Numerical approach for the frequency-shifting analysis of electrostatic micromechanical actuator

An eigenvalue analysis of a tunable micro-mechanical actuator is presented. The actuator is modeled as a continuum structure. The eigenvalue modified by the tuning voltage is computed through the linearization of the relation between the electrostatic force and the displacement at the equilibrium. A staggered algorithm is employed to perform the coupled analysis of the electrostatic and elastic fields. The stiffness matrix of the actuator is modified at this equilibrium state. The displacement field is perturbed using an eigenmode profile of the actuator. The configuration change of the actuator due to perturbation modifies the electrostatic field and thus the electrostatic force. The equivalent stiffness matrix corresponding to the perturbation and the change in the electrostatic force is then added to stiffness matrix in order to explain natural frequency shifting. The numerical examples are presented and compared with the experiments in the literatures.