Mixed finite elements for electromagnetic analysis

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where `double noding' is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems. (C) 2014 Elsevier Ltd. All rights reserved.

Role of interface curvature on stress distribution under indentation for ZrN/Zr multilayer coating

Contact damage in curved interface nano-layeredmetal/nitride (150 (ZrN)/10 (Zr) nm) multilayer is investigated in order to understand the role of interface morphology on contact damage under indentation. A finite element method (FEM) model was formulated with different wavelengths of 1000 nm, 500 nm, 250 nm and common height of 50 nm, which gives insight on the effect of different curvature on stress field generated under indentation. Elastic-plastic properties were assigned to the metal layer and substrate while the nitride layer was assigned perfectly elastic properties. Curved interface multilayers show delamination along the metal/nitride interface and vertical cracks emanating from the ends of the delamination. FEM revealed the presence of tensile stress normal to the interface even under the contact, along with tensile radial stresses, both present at the valley part of the curve, which leads to vertical cracks associated with interfacial delamination. Stress enhancement was seen to be relatively insensitive to curvature. (C) 2014 Elsevier B.V. All rights reserved.

Matrix Crack Detection in Composite Plate with Spatially Random Material Properties using Fractal Dimension

Fractal dimension based damage detection method is investigated for a composite plate with random material properties. Composite material shows spatially varying random material properties because of complex manufacturing processes. Matrix cracks are considered as damage in the composite plate. Such cracks are often seen as the initial damage mechanism in composites under fatigue loading and also occur due to low velocity impact. Static deflection of the cantilevered composite plate with uniform loading is calculated using the finite element method. Damage detection is carried out based on sliding window fractal dimension operator using the static deflection. Two dimensional homogeneous Gaussian random field is generated using Karhunen-Loeve (KL) expansion to represent the spatial variation of composite material property. The robustness of fractal dimension based damage detection method is demonstrated considering the composite material properties as a two dimensional random field.

Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Rotating Circular Cylinder

The entropy generation due to mixed convective heat transfer of nanofluids past a rotating circular cylinder placed in a uniform cross stream is investigated via streamline upwind Petrov-Galerkin based finite element method. Nanosized copper (Cu) particles suspended in water are used with Prandtl number (Pr)=6.9. The computations are carried out at a representative Reynolds number (Re) of 100. The dimensionless cylinder rotation rate, a, is varied between 0 and 2. The range of nanoparticle volume fractions (phi) considered is 0 <= phi <= 5%. Effect of aiding buoyancy is brought about by considering two fixed values of the Richardson number (Ri) as 0.5 and 1.0. A new model for predicting the effective viscosity and thermal conductivity of dilute suspensions of nanoscale colloidal particles is presented. The model addresses the details of the agglomeration-deagglomeration in tune with the pertinent variations in the effective particulate dimensions, volume fractions, as well as the aggregate structure of the particulate system. The total entropy generation is found to decrease sharply with cylinder rotation rates and nanoparticle volume fractions. Increase in nanoparticle agglomeration shows decrease in heat transfer irreversibility. The Bejan number falls sharply with increase in alpha and phi.

Matrix crack detection in spatially random composite structures using fractal dimension

Fractal dimension based damage detection method is studied for a composite structure with random material properties. A composite plate with localized matrix crack is considered. Matrix cracks are often seen as the initial damage mechanism in composites. Fractal dimension based method is applied to the static deformation curve of the structure to detect localized damage. Static deflection of a cantilevered composite plate under uniform loading is calculated using the finite element method. Composite material shows spatially varying random material properties because of complex manufacturing processes. Spatial variation of material property is represented as a two dimensional homogeneous Gaussian random field. Karhunen-Loeve (KL) expansion is used to generate a random field. The robustness of fractal dimension based damage detection methods is studied considering the composite plate with spatial variation in material properties.

Compressive flow behavior of Al-Si based alloy: Role of heat treatment

The flow characteristics of a near eutectic Al-Si based cast alloy have been examined in compression at strain rates varying from 3 x 10(-4) to 10(2) s(-1) and at three different temperatures, i.e., room temperature (RT), 100 degrees C and 200 degrees C. The dependence of the flow behavior on heat treatment is studied by testing the alloy in non-heat treated (NHT) and heat treated (HT) conditions. The heat treatment has strong influence on strain rate sensitivity (SRS), strength and work hardening behavior of the alloy. It is observed that the strength of the alloy increases with increase in strain rate and it increases more rapidly above the strain rate of 10(-1) s(-1) in HT condition at all the temperatures, and at 100 degrees C and 200 degrees C in NHT condition. The thermally dependent process taking place in the HT matrix is responsible for the observed greater SRS in HT condition. The alloy in HT condition exhibits a larger work hardening rate than in NHT condition during initial stages of straining. However, the hardening rate decreases more sharply at higher strains in HT condition due to precipitate shearing and higher rate of Si particle fracture. Thermal hardening is observed at 200 degrees C in NHT condition due to precipitate formation, which results in increased SRS at higher temperatures. Thermal softening is observed in HT condition at 200 C due to precipitate coarsening, which leads to a decrease in SRS at higher temperatures. Stress simulations by a finite element method support the experimentally observed particle and matrix fracture behavior. A negative SRS and serrated flow are observed in the lower strain rate regime (3 x 10(-4)-10(-2) s(-1)) at RT and 100 degrees C, in both NHT and HT conditions. The observations show that both dynamic strain aging (DSA) and precipitate shearing play a role in serrated flow. (C) 2015 Elsevier B.V. All rights reserved.

Mixed Mode Analysis of Obliquely Oriented Edge Cracked Semicircular Disk Under Compression

A new mixed-mode compression fracture specimen, obliquely oriented edge cracked semicircular disk (OECSD) is analyzed by extending pure opening mode configuration of edge cracked semicircular disk (ECSD) under Hertzian compression. Photoelastic experiments are conducted on two different specimens of OECSD of same size and different crack lengths and inclinations. Finite element method (FEM) is used to solve a number of cases of the problem varying crack length and crack inclination. FE results show a good match with experiments. Inclination of edge crack in OECSD can be so made as to obtain any mode-mixity ratio between zero and one and beyond for any crack length. The new specimen can be used for fracture testing under compression more conveniently than the existing ones in several ways.

A Study of Pressure-Dependent Squeeze Film Stiffness as a Resonance Modulator Using Static and Dynamic Measurements

We report on the resonant frequency modulation of inertial microelectromechanical systems (MEMS) structures due to squeeze film stiffness over a range of working pressures. Squeeze film effects have been studied extensively, but mostly in the context of damping and Q-factor determination of dynamic MEMS structures, typically suspended over a fixed substrate with a very thin air gap. Here, we show with experimental measurements and analytical calculations how the pressure-dependent air springs (squeeze film stiffness) change the resonant frequency of an inertial MEMS structure by as much as five times. For capturing the isolated effect of the squeeze film stiffness, we first determine the static stiffness of our structure with atomic force microscope probing and then study the effect of the air spring by measuring the dynamic response of the structure, thus finding the resonant frequencies while varying the air pressure from 1 to 905 mbar. We also verify our results by analytical and Finite Element Method calculations. Our findings show that the pressure-dependent squeeze film stiffness can affect a rather huge range of frequency modulation (>400%) and, therefore, can be used as a design parameter for exploiting this effect in MEMS devices. 2014-0310]

Role of Si modification on the compressive flow behavior of Al-Si based alloy

The flow characteristics of a near-eutectic heat-treated Al-Si based cast alloy have been examined in compression at strain rates varying from 3 x 10(-4) to 10(2) s(-1) and at three different temperatures, i.e., room temperature (RT), 100 degrees C and 200 degrees C. The dependence of flow behavior on modification is examined by testing the alloy in both the unmodified and modified conditions. Modification has strong influence on strain rate sensitivity (SRS), strength and work hardening behavior of the alloy. The strength of the alloy is found to increase with increase in strain rate for both the conditions. The increase is more rapid above the strain rate of 10(-1) s(-1) for the unmodified alloy at all the temperatures. This rapid increase is observed at 1 s(-1) at RT and 100 degrees C, and at 10(-2) s(-1) at 200 degrees C for the modified alloy. The thermally dependent process of the Al matrix is rate controlling in the unmodified alloy. On the other hand, the thermally dependent process of both Al matrix and Si particles are rate controlling, which is responsible for the higher strain rate sensitivity (SRS) in the modified alloy. The unmodified alloy exhibits a larger work hardening rate than the modified alloy during the initial stages of straining due to fiber loading of unmodified Si particles. However, the hardening rate decreases sharply at higher strains for the unmodified alloy due to a higher rate of Si particle fracture. Thermal softening is observed for both alloys at 200 degrees C due to precipitate coarsening, which leads to a decrease in SRS at higher temperatures. Stress simulations by microstructure based finite element method support the experimentally observed particle and matrix fracture behavior. Negative SRS and serrated flow are observed at lower strain rate regime (3 x 10(-4) to 10(-2) s(-1)) at RT and 100 degrees C, in both alloys. The critical onset strain is found to be lower and the magnitude of serration is found to be higher for the modified alloy, which suggests that, in addition to dynamic strain aging, Si particle size and morphology also play a role in serrated flow. (C) 2015 Elsevier Inc All rights reserved.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

Numerical analysis of segmented-electrode Orbitraps

Simple geometries which are possible alternatives for the Orbitrap are studied in this paper. We have taken up for numerical investigation two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap have been replaced by 35 rings and 35 discs of fixed radii, respectively. In this structure two segmented end cap electrodes have been added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap were replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. In the present study 45 steps have been used. In the ORB2, like the Orbitrap, the inner electrode is held at a negative potential and the outer electrode is at ground potential. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies have been undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) simulation of image currents. These studies have been carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM was developed specifically for this study. It has been seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It has been shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analyzers. A novel technique of optimization of the electric field has been proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode traps having the same design as ORB1 show that it can provide accurate mass analysis. (C) 2015 Elsevier B.V. All rights reserved.

Numerical analysis of segmented-electrode Orbitraps

Simple geometries which are possible alternatives for the Orbitrap are studied in this paper. We have taken up for numerical investigation two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap have been replaced by 35 rings and 35 discs of fixed radii, respectively. In this structure two segmented end cap electrodes have been added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap were replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. In the present study 45 steps have been used. In the ORB2, like the Orbitrap, the inner electrode is held at a negative potential and the outer electrode is at ground potential. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies have been undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) simulation of image currents. These studies have been carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM was developed specifically for this study. It has been seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It has been shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analyzers. A novel technique of optimization of the electric field has been proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode traps having the same design as ORB1 show that it can provide accurate mass analysis. (C) 2015 Elsevier B.V. All rights reserved.

FEM Simulations and Optimization about Residual Stresses in Coating Structures with Functionally Graded Materials Layer

An elasto-plastic finite element method is developed to predict the residual stresses of thermal spraying coatings with functionally graded material layer. In numerical simulations, temperature sensitivity of various material constants is included and mix

Parameters Inversion of Fluid-Saturated Porous Media Based on Neural Networks

The multi-layers feedforward neural network is used for inversion of material constants of fluid-saturated porous media. The direct analysis of fluid-saturated porous media is carried out with the boundary element method. The dynamic displacement responses obtained from direct analysis for prescribed material parameters constitute the sample sets training neural network. By virtue of the effective L-M training algorithm and the Tikhonov regularization method as well as the GCV method for an appropriate selection of regularization parameter, the inverse mapping from dynamic displacement responses to material constants is performed. Numerical examples demonstrate the validity of the neural network method.

具有单元分裂功能的间断有限元方法

介绍一种能够模拟材料开裂过程的有限元方法,该方法引入单元分裂和界面分离技术,结合具体的破坏准则,模拟材料变形中的破坏,同时还可以方便地处理材料中任意分布的界面结构.以三点弯曲实验为例,通过数值模拟结果和实验数据的比较,验证了该方法的适用性.