Shiang-Woei Chyuan

Boundary element analysis and design in seepage problems using dual integral formulation

Abstract A dual integral formulation with a hypersingular integral is derived to solve the boundary value problem with singularity arising from a degenerate boundary. A seepage flow under a dam with sheet piles is analyzed to check the validity of the mathematical model. The closed-form integral formulae containing the four kernel functions in the dual integral equations are presented and clearly reveal the properties of the single- and double-layer potentials and their derivatives. The field and boundary quantities of the potential heads and normal fluxes can thus be expressed in terms of both boundary potentials and boundary normal fluxes through the dual boundary integral equations. To facilitate the computation of the seepage flow along and near the boundary, an expression for the flux tangential to the boundary is also derived. The numerical implementations are compared with analytical solutions and the results of a general purpose commercial finite element program. Finally, four design cases of sheet piles are examined, and the best choice among them is suggested.

INTEGRAL REPRESENTATIONS AND REGULARIZATIONS FOR A DIVERGENT SERIES SOLUTION OF A BEAM SUBJECTED TO SUPPORT MOTIONS

SUMMARY Derived herein is the integral representation solution of a Rayleigh-damped Bernoulli-Euler beam subjected to multi-support motion, which is free from calculation of a quasi-static solution, and in which the modal participation factor for support motion is formulated as a boundary modal reaction, thus making efficient calculation feasible. Three analytical methods, including ( 1 ) the quasi-static decomposition method, (2) the integral representation with the Cesaro sum technique, and (3) the integral representation in conjunction with Stokes’ transformation, are presented. Two additional numerical methods of (4) the large mass FEM simulation technique and (5) large stiffness FEM simulation technique are easily incorporated into a commercial program to solve the problem. It is found that the results obtained by using these five methods are in good agreement, and that both the Cesiro sum and Stokes’ transformation regularization techniques can extract the finite part of the divergent series of the integral representation. In comparison with the Mindlin method and Cesaro sum technique, Stokes’ transformation is the best way because it is not only free of calculation of the quasi-static solution, but also because it can obtain the convergence rate as rapidly as the mode acceleration method can.

Computational study of the effect of finger width and aspect ratios for the electrostatic levitating force of MEMS combdrive

Since the width ratio between movable and fixed fingers, and the aspect ratio between the height and width of fingers, can play very important roles for combdrive levitation control, computational study of variations in those parameters for electrostatic levitating force acting on the movable finger is indispensable for MEMS performance. For diverse finger width and aspect ratios of MEMS combdrive design, the BEM has become a better method than the domain-type FEM because BEM can provide a complete solution in terms of boundary values only, with substantial saving in modeling effort. DBEM still has some advantages over conventional BEM for singularity, so the DBEM was used to simulate the fringing of field around the edges of the fixed finger and movable finger of MEMS combdrive for diverse finger width and aspect ratios. Results show that the less the finger width ratio is, the larger the levitating force acting is. Furthermore, the levitating force becomes more dominant as the aspect ratio increases, but it will be kept constant while the aspect ratio becomes larger.

Nonlinear thermoviscoelastic analysis of solid propellant grains subjected to temperature loading

Abstract Traditionally, the nonlinear thermoviscoelastic analysis of solid propellant grains subjected temperature loading was not considered, and quasi-elastic analysis was widely adopted for structural integrity because of simplifying the analytical task. But it does not mean that the nonlinear effect is not useful and could be neglected arbitrarily, and this effect usually plays a very important role for some critical design. In order to simulate the material and geometrical nonlinearities, a step-by-step finite element model accompanied by concepts of time–temperature shift principle, reduced integration and thermorheologically simple material assumption was used. Results show that the material nonlinear effect is important for structural integrity of solid propellant grains under higher temperature surrounding, the effect of nonlinearity is not obvious under lower temperature surrounding, and the differences between linear and nonlinear analysis results become more and more predominant as temperature increases. In addition, the maximum shear stress obtained from the nonlinear simulation considering bulk modulus variation with compressive stresses are higher than those from linear simulation, and the effect of material nonlinearity is more predominant as compared to the effect of geometrical nonlinearity. From the work of linear and nonlinear analyses, the nonlinear thermoviscoelastic analysis highlighted several areas of interest and a more accurate and reasonable result could be obtained for engineer.

A study of loading history effect for thermoviscoelastic solid propellant grains

Abstract The results of an investigation on solid propellant grains considering loading history effect are presented. Traditionally, the thermal loading history effect of solid propellant grains was not considered for simplifying the analytical task, and a higher safety factor was inevitable for structural integrity. But this does not mean that the thermal loading history effect is not useful and could be neglected arbitrarily, and this effect usually plays a very important role for some critical design. In order to simulate the time–temperature-dependent behavior of thermoviscoelastic and incompressible polymer materials, concepts of time–temperature shift principle, cumulative damage theory and reduced integration were used. In addition, five different types of thermal loading history assumption were performed using the finite element method for discussing the thermal loading history effect. Results show that the thermal loading history effect is important for structural integrity of solid propellant grains, and improper negligence may cause structural failure of missile systems.

An efficient method for solving electrostatic problems

Electrostatic problems are those that deal with the effects of electric charges at rest. For modern electron and microelectromechanical systems (MEMS), an accurate electrostatic analysis is both essential and indispensable. We know that if we use the conventional boundary element method for electrostatic problems that have singularity due to degenerate boundaries, the coincidence of the boundaries gives rise to a difficult, or ill-conditioned, problem. The coincidence is when different elements use the same nodes, but there is a free-edge between the elements. The dual boundary element method (DBEM) provides fast, accurate, and efficient solutions. We compare results between finite element method (FEM) and DBEM analyses to prove DBEMs superiority. Because model creation requires the most effort in electrical engineering practices, we strongly recommend DBEM for industrial applications.

FEM versus BEM

For the performance of electron devices, an accurate electrostatic analysis is essential, and the boundary element method (BEM) has become a better method than the domain-type finite element method (FEM) because BEM can provide a complete solution in terms of boundary values only with substantial savings in modeling effort for the variable design stage. But, for exterior problems with singularity arising from the degenerate boundary (e.g., the edge of parallel-plate capacitor), the dual BEM becomes one of the most efficacious and robust tools for simulating the fringing field near the edge of electron devices because no laborious artificial boundary technique was needed like conventional BEM. After the fringing field is known well, the charge and capacitance of electron devices can be accurately calculated, and we can also understand the minimum allowable data of dielectric strength for keeping off dielectric breakdown. Electrostatics, as used here, involves charges in motion as well as at rest. Generally, there are five fundamental quantities (voltage, charge, current, capacitance, and resistance) in electrostatics that are involved in almost all applications. For most electrical engineers, voltage, or electromotive force (EMF) is the most important one. Electrostatic problems generally play a very important role in improving the performance and reliability of electron devices in the design stage (Cheng, 1989). Although we all understand that the beginning of electrostatic theory is believed to have occurred several centuries before, the first meaningful application, the commercially electrostatic precipitator, was just installed by Cottrell in 1907. Besides two major present technologies from 1907 to now, electrostatic precipitation and electrostatic coating, Castle also suggested that there would be several new industrial applications to come from developments in the fields of micro electromechanical systems (MEMS), biotechnology, ultrafine particles, nanotechnology, and space for the future applications of electrostatics. Because electrostatics still affects the performance of MEMS and electron devices critically nowadays, how to accurately obtain the electric potential V and electric field intensity E becomes especially important for engineers. We all know that scientists and engineers usually use several techniques in solving continuum or field problems. Loosely speaking, these techniques can be classified as experimental, theoretical (or analytical), or numerical.

An alternatively efficient method (DBEM) for simulating the electrostatic field and levitating force of a MEMS combdrive

For MEMS combdrive design, the reduction of levitating force due to electrostatic fields is very important, and an accurate electrostatic analysis is essential and indispensable. For diverse MEMS combdrive designs, the boundary element method (BEM) has become a better method than the domain-type finite element method (FEM) because the BEM can provide a complete solution in terms of boundary values only, with substantial saving in modeling effort. Since dual BEM (DBEM) has some advantages over conventional BEM for a singularity, the DBEM was used to simulate the fringing of field around the edges of the fixed fingers and movable fingers of MEMS combdrives for diverse design cases. A number of electrostatic problems for typical MEMS combdrive designs were analyzed to check the efficiency and validity of this new technique. It is found that the numerical results computed by coarse mesh DBEM match the reference data from a large refined mesh FEM very well, and the accuracy and performance of DBEM are also better than those of conventional BEM for solving the electric intensity field of MEMS combdrives. By way of the DBEM presented in this paper, an accurate and reasonable electrostatic field can be obtained, and the follow-up control method of levitating force for the MEMS combdrive can be implemented more precisely.

Computer simulations for mask structure heating in X-ray lithography

Abstract Mask heating induced by X-ray exposures from synchrotron or plasma source is of great concern, because it may result in mask distortion due to the thermal stresses generated in the mask. To evaluate the heat transfer and stress issues of lithographic mask structure, numerical simulations were performed by using the MSC/NASTRAN finite element program with IDEAS pre-post processor system on a powerful CONVEX C201 minisupercomputer. For the heat calculations, a microscopic model consisting of a huge number of elements was employed to approach the realistic physical conditions in X-ray lithographic exposure. The temperature distributions, the thermal stress profiles, and the thermal displacement contour of a silicon-tungsten (Si-W) mask structure during X-ray exposure are presented in this paper. The simulated results indicate that the maximum temperatures occur in the regions where the W absorber patterns are most densely populated, and that the thermal stresses usually centralize at the Si-W interface and the edges of W absorber. Considering the absorber pattern displacements, the temperature change of the mask structure should be kept within 3.42 °C to suppress the micordistortion to within the acceptable limit of 25 nm for a Si mask substrate with 0.25-μm scale W features.

Normalized quasi-static mass—a new definition for multi-support motion problems

Abstract An efficient algorithm called the modal reaction method for calculating the modal participation factors in support motion problems has been proposed by Chen et al. [1]. In this paper, we extend this method to determine the number of modes needed to satisfy 90% of the sum of the base-shear modal mass as UBC(uniform building code) suggests. The sum of all the modes for each support in multi-support motions is found to be equal to the normalized quasi-static mass which is defined in this paper. The normalized quasi-static mass is equivalent to the total structure mass in the case of single supported structure. By extracting the reaction from the SPC force in data recovery using SOL 3 (linear modal analysis) or SOL 106 (nonlinear modal analysis) in MSC/NASTRAN, the modal participation factor and the base-shear modal mass ratio can be directly determined free from calculation of the influence vector, or the so-called quasi-static solution. To demonstrate this new concept of the normalized quasi-static mass, several examples including rod, beam, tower structures are given to check the validity of the proposed method using MSC/NASTRAN program. Finally, the minimum number of modes needed to reach 90% of the normalized quasi-static mass for each support is proposed as a reference for analysis and design engineers.