A topology and shape optimization method is presented for structural eigenfrequency optimization problems using the concept of Optimal Material Distribution (OMD). First, a mean-eigenvalue corresponding to the multiple eigenfrequencies of a structure is defined. Three optimization problems are then considered for obtaining the desired eigenfrequencies using this mean-eigenvalue: maximization of the specified structural eigenfrequencies, maximization of the distances of the specified structural eigenfrequencies from a given frequency or frequencies, and optimization of the structure for obtaining prescribed eigenfrequencies. Several examples are presented to demonstrate the capability of this new technique which can be used to deal with a wide range of practical design problems for improving the dynamic nature of a structure.
A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.
At the nanoscale, surface effect could cause atomistic structures a pre-stressed or
pre-deformed state, which would consequently have a great dependence on their bulk mechanical
properties. Besides, according to molecular mechanics [1,2], the effect of the non-bonding
interactions among the atoms that are separated by equal or more than two bonds, say, van der
Waals (vdW) forces, should be taken into account. Thus, the underlying objective of the study
attempts to explore the extent of the surface effect and the in-layer vdW interactions on the
mechanical properties of single/multi-walled carbon nanotubes(S/MWCNTs) with two different
types of chiralities, including zigzag and armchair.
To deal with the problem, an atomistic-continuum modeling (ACM) approach is introduced. The
ACM is established by molecular dynamics (MD) simulation and equivalent continuum modeling
(ECM). MD simulation is adopted to derive the initial equilibrium state of CNTs due to the surface
effect, and the ECM is applied to calculate the mechanical properties of CNTs. The ECM is
formulated based on the finite element (FE) approximations, which are composed of
three-dimensional beam elements and one-dimensional non-linear spring elements. They basically
represent the bonding and non-bonding interactions, respectively. The equivalent material constants
of these two types of elements are derived from classical molecular mechanics and beam theory.
The present results are also compared with those obtained from other simulations and experiments.
As the strained engineering technology of metal-oxide-semiconductor field effect transistors (MOSFET) is scaled beyond the 22 nm node critical dimension, shallow trench isolation (STI) becomes one of the most important resolutions for isolate devices to enhance the carrier mobility of advanced transistors. Several key design factors of n-type MOSFET (NMOSFET) under the resultant loadings of STI structures and contact etching stop layers are sensitively analyzed for silicon channel stress via finite element method-based simulations integrated with the use of design of experienmnts. NMOSFETs with 15 nm deep sunken STI have achieved a ~5% mobility enhancement as compared with a regular STI shape. By adopting simulation-based factorial designs, we have determined that the design factor of recess depth in STI is a critical factor influencing device performance. Moreover, a response surface curve on carrier mobility of NMOSFET under a consideration of combining the sunken STI and source/drain lengths is further presented in this research.
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