Mechanics of nanostructures and semiconductor quantum heterostructures
MOTIVATION:
The self-organized (or self-assembled) quantum wells/wires/dots can produce a large strain and electric fields that can directly influence the design of the semiconductor heterostructures at nanoscale. Therefore, accurate prediction of the elastic and piezoelectric fields in semiconductor quantum wells/wires/dots is crucial to these devices.
APPROACH:
Use continuum Green’s function solutions to calculate these fields and develop a computational program that can be used by the nano-device designer in order to predict the electronic and optical properties of the device for a given nanostructure model.
SOME RESULTS (Click here for details)
Microelectromechanical systems (MEMS) and magneto-electro-elastic coupling
MOTIVATION:
Owing to their unique feature of transferring energies from one form to the other (among the mechanical, electric, and magnetic energies), the piezoelectric and magnetic materials have been increasingly applied to MEMS or smart systems. We want to understand the effect of material layering (stacking sequence) and anisotropy on the smart system made of multilayered magneto-electro-elastic materials.
APPROACH:
Develop various exact solutions, including the Green’s functions in such systems. Using these solutions as the kernel functions, an efficient computational tool based on the integral equation method has been developed, which would offer a broad scenario of applications in this and other emerging fields, with an emphasis on the study of the coupling behaviors.
SOME RESULTS (Click here for details)
Wave propagation and nondestructive evaluation
MOTIVATION:
Waves that propagate in a structure carry a lot of useful information that can be employed to invert the internal structure of the concerned system by use of ultrasonic method, without damaging the structure (nondestructive evaluation).
APPROACH:
Derive various analytical and numerical solutions for multilayered anisotropic elastic, piezoelectric, or even electro-magneto-elastic structures. These solutions are essential in nondestructive evaluation, vibration control, and health monitoring of structures.
SOME RESULTS (Click here for details)
Layered structures and composite laminates
MOTIVATION:
Multilayered structures, in particular, composite laminates have been extensively applied to various aeronautical industries due to their unique light-weight/high-strength ratio. Since laminates are usually made of many plies, they pose great difficulty for all existing numerical methods.
APPROACH:
Recently, we have successfully developed a computationally efficient and accurate formulation specifically designed for multilayered composite laminates. It is based on a single-domain BEM combined with the layered Green’s functions involving certain advanced mathematical formalisms, i.e., the Stroh formalism.
SOME RESULTS (Click here for details)
Green’s functions and applications
MOTIVATION:
It is well known that Green’s functions are foundations of many numerical methods when analyzing an engineering or physical problem. In particular, Green’s functions are essential to various integral equation methods. Furthermore, they can be also directly applied to other modern physical areas, such as elastic and piezoelectric fields in nanoscale semiconductors and atomistic simulations of dislocations and defects in crystals.
APPROACH:
We have derived a variety of Green’s functions utilizing certain advanced mathematical approaches.
SOME RESULTS (Click here for details)
Computational mechanics
MOTIVATION:
While the BEM has the advantage of reducing the problem dimensions by one, the FEM has the merit of treating the heterogeneous and nonlinear media friendly. During the past ten years, we have developed various BEM formulations and coded the corresponding programs.
APPROACH:
We have proposed an efficient and computational advanced single-domain BEM formulation for fracture analysis of cracked anisotropic media (no double nodes are required along the surface of the crack), for both 2D and 3D systems, and even for the piezoelectric material.
SOME RESULTS (Click here for details)
Geomechanics
MOTIVATION:
As a multidisciplinary team, our research group is also interested in deformation, stress, and fracture analyses in layered earth models, in poroelastic (biomechanical or soil) media, and in anisotropic rock masses.
APPROACH:
An elegant and powerful numerical conformal mapping method has been developed to handle irregular topography, and the layered earth/poroelastic structures are modeled in terms of the system of vector functions and of the propagator matrix method. We have also derived the analytical solutions for functionally graded earth models and rock foundations.
SOME RESULTS (Click here for details)