Hong-Lae Jang

Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures

An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atoms degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.

Cold welding of gold nanoparticles on mica substrate: Self-adjustment and enhanced diffusion

From the images of HR-TEM, FE-SEM, and AFM, the cold welding of gold nanoparticles (AuNPs) on a mica substrate is observed. The cold-welded gold nanoparticles of 25 nm diameters are found on the mica substrate in AFM measurement whereas the size of cold welding is limited to 10 nm for nanowires and 2~3 nm for nanofilms. Contrary to the nanowires requiring pressure, the AuNPs are able to rotate freely due to the attractive forces from the mica substrate and thus the cold welding goes along by adjusting lattice structures. The gold nanoparticles on the mica substrate are numerically modeled and whose physical characteristics are obtained by the molecular dynamic simulations of LAMMPS. The potential and kinetic energies of AuNPs on the mica substrate provide sufficient energy to overcome the diffusion barrier of gold atoms. After the cold welding, the regularity of lattice structure is maintained since the rotation of AuNPs is allowed due to the presence of mica substrate. It turns out that the growth of AuNPs can be controlled arbitrarily and the welded region is nearly perfect and provides the same crystal orientation and strength as the rest of the nanostructures.

Reliability-based design optimization of fluid–solid interaction problems

Using a sampling-based reliability-based design optimization method, we present a shape reliability-based design optimization method for coupled fluid–solid interaction problems. For the fluid–solid interaction problem in arbitrary Lagrangian–Eulerian formulation, a coupled variational equation is derived from a steady state Navier–Stokes equation for incompressible flows, an equilibrium equation for geometrically nonlinear solids, and a traction continuity condition at interfaces. The fluid–solid interaction problem is solved using the finite element method and the Newton–Raphson scheme. For the fluid mesh movement, we formulated and solved a pseudo-structural sub-problem. The shape of the solid is modeled using the Non-Uniform Rational B-Spline (NURBS) surface, and the coordinate components of the control points are selected as random design variables. The sensitivity of the probabilistic constraint is calculated using the first-order score functions obtained from the input distributions and from the Monte Carlo simulation on the surrogate model constructed by using the Dynamic Kriging method. The sequential quadratic programming algorithm is used for the optimization. In two numerical examples, the proposed optimization method is applied to the shape design problems of solid structure which is loaded by prescribed fluid flow, and this proves that the sampling-based reliability-based design optimization can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problems.

Adjoint Design Sensitivity Analysis of Fracture Mechanics Using Molecular-Continuum Multiscale Approach

We have developed a multiscale design sensitivity analysis method for transient dynamics using a bridging scale method by a projection operator for scale decomposition. Employing a mass-weighted projection operator, we can fully decouple the equations of motion into fine and coarse scales using the orthogonal property of complimentary projector to the mass matrix. Thus, independent solvers in response analyses can be utilized for the fine scale analysis of molecular dynamic (MD) and the coarse scale analysis of finite element analysis. To reduce the size of problems and to improve the computational efficiency, a generalized Langevin equation is used for a localized MD analysis. Through demonstrative numerical examples, it turns out that the derived sensitivity analysis method is accurate and efficient compared with finite difference sensitivity.Copyright