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 spectral element for wave propagation in honeycomb sandwich construction considering core flexibility

Spectral elements are found to be extremely resourceful to study the wave propagation characteristics of structures at high frequencies. Most of the aerospace structures use honeycomb sandwich constructions. The existing spectral elements use single layer theories for a sandwich construction wherein the two face sheets vibrate together and this model is sufficient for low frequency excitations. At high frequencies, the two face sheets vibrate independently. The Extended Higher order SAndwich Plate theory (EHSaPT) is suitable for representing the independent motion of the face sheets. A 1D spectral element based on EHSaPT is developed in this work. The wave number and the wave speed characteristics are obtained using the developed spectral element. It is shown that the developed spectral element is capable of representing independent wave motions of the face sheets. The propagation speeds of a high frequency modulated pulse in the face sheets and the core of a honeycomb sandwich are demonstrated. Responses of a typical honeycomb sandwich beam to high frequency shock loads are obtained using the developed spectral element and the response match very well with the finite element results. It is shown that the developed spectral element is able to represent the flexibility of the core resulting into independent wave motions in the face sheets, for which a finite element method needs huge degrees of freedom. (C) 2015 Elsevier Ltd. All rights reserved.

Simulations using meshfree methods

In this paper, attempt is made to solve a few problems using the Polynomial Point Collocation Method (PPCM), the Radial Point Collocation Method (RPCM), Smoothed Particle Hydrodynamics (SPH), and the Finite Point Method (FPM). A few observations on the accuracy of these methods are recorded. All the simulations in this paper are three dimensional linear elastostatic simulations, without accounting for body forces.

Multi-transform based spectral element to include first order shear deformation in plates

For obtaining dynamic response of structure to high frequency shock excitation spectral elements have several advantages over conventional methods. At higher frequencies transverse shear and rotary inertia have a predominant role. These are represented by the First order Shear Deformation Theory (FSDT). But not much work is reported on spectral elements with FSDT. This work presents a new spectral element based on the FSDT/Mindlin Plate Theory which is essential for wave propagation analysis of sandwich plates. Multi-transformation method is used to solve the coupled partial differential equations, i.e., Laplace transforms for temporal approximation and wavelet transforms for spatial approximation. The formulation takes into account the axial-flexure and shear coupling. The ability of the element to represent different modes of wave motion is demonstrated. Impact on the derived wave motion characteristics in the absence of the developed spectral element is discussed. The transient response using the formulated element is validated by the results obtained using Finite Element Method (FEM) which needs significant computational effort. Experimental results are provided which confirms the need to having the developed spectral element for the high frequency response of structures. (C) 2015 Elsevier Ltd. All rights reserved.

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.

Region-of-interest diffuse optical tomography system

Diffuse optical tomography (DOT) using near-infrared light is a promising tool for non-invasive imaging of deep tissue. This technique is capable of quantitative reconstruction of absorption (mu(a)) and scattering coefficient (mu(s)) inhomogeneities in the tissue. The rationale for reconstructing the optical property map is that the absorption coefficient variation provides diagnostic information about metabolic and disease states of the tissue. The aim of DOT is to reconstruct the internal tissue cross section with good spatial resolution and contrast from noisy measurements non-invasively. We develop a region-of-interest scanning system based on DOT principles. Modulated light is injected into the phantom/tissue through one of the four light emitting diode sources. The light traversing through the tissue gets partially absorbed and scattered multiple times. The intensity and phase of the exiting light are measured using a set of photodetectors. The light transport through a tissue is diffusive in nature and is modeled using radiative transfer equation. However, a simplified model based on diffusion equation (DE) can be used if the system satisfies following conditions: (a) the optical parameter of the inhomogeneity is close to the optical property of the background, and (b) mu(s) of the medium is much greater than mu(a) (mu(s) >> mu(a)). The light transport through a highly scattering tissue satisfies both of these conditions. A discrete version of DE based on finite element method is used for solving the inverse problem. The depth of probing light inside the tissue depends on the wavelength of light, absorption, and scattering coefficients of the medium and the separation between the source and detector locations. Extensive simulation studies have been carried out and the results are validated using two sets of experimental measurements. The utility of the system can be further improved by using multiple wavelength light sources. In such a scheme, the spectroscopic variation of absorption coefficient in the tissue can be used to arrive at the oxygenation changes in the tissue. (C) 2016 AIP Publishing LLC.

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations. (C) 2016 AIP Publishing LLC.

同位网格摄动有限体积格式求解浮力驱动方腔流

利用对流扩散方程的摄动有限体积格式,在Rayleigh数从10~3到10~8的范围内对浮力驱动方腔流动问题作了数值模拟.对流扩散方程的摄动有限体积格式具有一阶迎风格式的简洁形式,使用相同的基点,重构近似精度高,特别是两相邻控制体中心到公共界面的距离相等或不相等,PFV格式公式相同等优点.在数值模拟中,无论均匀网格还是非均匀网格均获得与DSC方法、自适应有限元法、多重网格法等Benchmark解相符较好的数值结果,证明UPFV格式对高Rayleigh数对流传热问题的适用性和有效性.

Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

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

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.