SIMPLIFIED SCALING TRANSFORMATION FOR THE NUMERICAL SIMULATION OF MEMS DEVICES WITH THIN FILM STRUCTURES

Thin film is a widely used structure in the present microelectromechanical systems （MEMS） and plays a vital role in many functional devices. However, the great size difference between the film＇s thickness and its planar dimensions makes it difficult to study the thin film performance numerically. In this work, a scaling transformation was presented to make the different dimensional sizes equivalent, and thereby, to improve the grid quality considerably. Two numerical experiments were studied to validate the present scaling transformation method. The numerical results indicated that the largest grid size difference can be decreased to one to two orders of magnitude by using the present scaling transformation, and the memory required by the numerical simulation, i.e., the total grid number, could be reduced by about two to three orders of magnitude, while the numerical accuracies with and without this scaling transformation were nearly the same.

Long-term settlement prediction of high-speed railway bridge pile foundation

The process and characteristics of loading on high-speed railway bridge pile foundation were firstly obtained by means of field research and analysis,and the corresponding loading function was presented.One-dimensional consolidation equation of elastic multilayered soils was then established with single drainage or double drainages under multilevel loading.Moreover,the formulas for calculating effective stress and settlement were derived from the Laplace numerical inversion transform.The three-dimensional composite analysis method of bridge pile group was improved,where the actual load conditions of pile foundation could be simulated,and the consolidation characteristics of soil layers beneath pile were also taken into account.Eventually,a corresponding program named LTPGS was developed to improve the calculation efficiency.The comparison between long-term settlement obtained from the proposed method and the in-situ measurements of pile foundation was illustrated,and a close agreement is obtained.The error between computed and measured results is less than 1 mm,and it gradually reduces with time.It is shown that the proposed method can effectively simulate the long-term settlement of pile foundation and program LTPGS can provide a reliable estimation.

Shear strength criteria for rock,rock joints,rockfill and rock masses:Problems and some solutions

Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.

Finite Element Method for Transient Electric Field by Using Indirect Laplace Transform with High Accuracy

This paper focuses on the finite element method in the complex frequency domain(CFD-FEM)for the transient electric field.First,the initial value and boundary value problem of the transient electric field under the electroquasistatic field in the complex frequency domain is given.In addition,the finite element equation and the constrained electric field equation on the boundary are derived.Secondly,the indirect algorithm of the numerical inverse Laplace transform is introduced.Based on it,the calculation procedures of the CFD-FEM are illustrated in detail.Thirdly,the step response,zero-state response under the positive periodic square waveform(PPSW)voltage,and the zero-input response by the CFD-FEM with direct algorithm and indirect algorithm are compared.Finally,the reason for the numerical oscillations of the zero-state response under the PPSW voltage is analyzed,and the method to reduce oscillations is proposed.The results show that the numerical accuracy of the indirect algorithm of the CFD-FEM is more than an order of magnitude higher than that of the direct algorithm when calculating the step response of the transient electric field.The proposed method can significantly reduce the numerical oscillations of the zero-state response under the PPSW voltage.The proposed method is helpful for the calculation of the transient electric field,especially in the case of frequency-dependent parameters.

Calculation of valence band structures of InAs/GaAs quantum ring and quantum dot:using numerical Fourier transform method

This article puts forward a new method in calculating the band structures of low-dimensional semiconductor structures. In this study, the valence band structures of InAs/GaAs quantum ring and lens-shaped quantum dot are calculated with four-band model, in the framework of effective-mass envelope function theory. To determine the Hamiltonian matrix elements, this article develops the numerical Fourier transform method instead of the widely used analytical integral method. The valence band mixing is considered. The hole energy levels change dramatically with the geometrical parameters of the quantum ring and quantum dot. It is demonstrated that numerical Fourier transform method can be adopted in low-dimensional structures with any shape. The results of Fourier transform method are consistent with the ones of analytical integral in literature; and they are helpful for studying and fabricating optoelectronic devices.

Efficient Numerical Valuation of Continuous Installment Options

In this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment options.We compare the results with the one obtained using other classical methods for the inverse Laplace transformation,like the Euler summation method or the Gaver-Stehfest method.