A continuum-based modeling of MEMS devices for estimating their resonant frequencies

A continuum-based modeling of coupled electrostatics-structure interactions is presented for the frequency computations of MEMS devices. The present general formulation of electrostatics accounting for free space is validated first by specializing it to one-dimensional uniform motion of conducting surfaces and comparing the resulting electrostatics to conventional lumped models. The general coupled electrostatics-structure interactions are then applied for the prediction of resonant frequencies of MEMS devices due to bias-voltage changes and temperature variations. Comparisons of predicted resonant frequencies obtained by the present coupled electrostatics-structure interaction models with experimental results available in the literature demonstrate that the proposed continuum-based interaction modeling yields high-confidence predictions of resonant frequencies of MEMS devices.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.     

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

This article studies tubular hydroforming of high strength low alloy (HSLA) and dual phase (DP600) straight tubes under the action of end feeding loads. Experiments demonstrate that higher end feed loads enhance the formability of the tubes and increase the internal fluid pressure for onset of necking and bursting. Because of the action of the internal pressure and the axial compressive load, the onset of localization (necking) is due to a complex three-dimensional state of stress. Using free expansion experiments, approximate upper and lower bound strain-based forming limit curves are determined for the tube materials. These limit curves, in turn, are used to derive upper and lower bound extended stress-based forming limit curves [Simha et al., Prediction of necking in tubular hydroforming using an extended stress-based FLC. Transactions of the ASME Journal of Engineering Materials and Technology 2007;129(1): 36-47]. In conjunction with finite element computations that use solid elements to model the tube, these stress-based limit curves are used to predict upper and lower bound necking pressures under the action of end feed loading. These predictions of necking pressures, when an appropriate coefficient of tube-die friction is used, are found to bracket the experimentally measured necking pressures. Computations using plane stress shell elements to model the tubes are shown to give erroneous results, since the plane stress approximation is not valid when tubes are hydroformed in a die.     

Estimation for the number of components in a mixture model using stepwise split-and-merge EM algorithm

The main difficulty with EM algorithm for mixture model concerns the number of components, say g. This is the question of model selection, and the EM algorithm itself could not estimate g. On the contrary, the algorithm requires g to be specified before the remaining parameters can be estimated. To solve this problem, a new algorithm, which is called stepwise split-and-merge EM (SSMEM) algorithm, is proposed. The SSMEM algorithm alternately splits and merges components, estimating g and other parameters of components simultaneously. Also, two novel criteria are introduced to efficiently select the components for split or merge. Experimental results on simulated and real data demonstrate the effectivity of the proposed algorithm.     

Fatigue Behavior and Retrofit Investigation of Distortion-Induced Web Gap Cracking

This paper studies a Kansas Department of Transportation welded plate girder bridge that developed fatigue cracks at small web gaps close to the girder top flange. Repair had been previously performed by softening the connection plate end with a slot retrofit, but cracks were recently found to have reinitiated at some of the repaired details and are again propagating. A comprehensive finite-element method study was performed to investigate the cracking behavior observed in the bridge and to recommend appropriate measures for future bridge retrofit. The analytical results show that stresses developed at the top flange web gaps could exceed yielding under the loading of an HS15 fatigue truck. The current slot repair used in the bridge was found to have introduced higher magnitude fatigue stresses in the web gap. To achieve a permanent repair of the bridge, it is recommended that a welded connection plate to flange attachment be used during future bridge retrofit. The web gap details should be able to withstand unlimited number of load cycles once this additional repair is performed.     

Structural Appraisal of the Florentine Gothic Construction System

The nave of Santa Maria Novella, a Dominican church in Florence Italy is representative of a Florentine Gothic system of construction. This system, consisting of domical rib vaults on square nave bays, high side aisles, and crypto-buttressing, differs substantially from the French high Gothic system of even-level-crown rib vaults on rectangular bays, with flying buttresses over relatively low aisles. An investigation into the structural aspects of the Florentine Gothic construction system reveals that the domical vaults increase the longitudinal thrust and reduce the transverse thrust, which may require additional precautions to be taken during construction, but entails a less elaborate buttressing system. The domical vaults are found to perform well structurally, with an absence of tensile stresses, and are more suitable for a square bay. In general, the structural system of the nave of Santa Maria Novella is found to be the product of carefully considered structural design, which may be accepted as an alternative to the French Gothic construction system.     

Numerical simulation of flying phenomena of the running tape on rotating drum

This paper analyzes the running mechanism of flexible and thin tape above rotating protrusion through a numerical simulation. The scope of analysis is confined to the phenomena of elastohydrodynamic lubrication between the rotating drum with a protrusion and the running tape. This model is based on the modified Reynolds equation and the equation of plate considering the effect of geometric nonlinearity and geometry of protrusion. Finite element method of Bubnov-Galerkin type is adopted as a numerical simulation technique to solve the above two coupled nonlinear equations. In numerical simulation, the influences of tape tension and protrusion velocity are evaluated in simple model. In complex models, the reciprocal action of two protrusions is simulated.     

The effect of particle distribution on damage formation in particulate reinforced metal matrix composites deformed in compression

Image analysis results are reported on the generation of damage in particulate reinforced metal matrix composites during compressive deformation. The technique allows the automated collection of data on the incidence of particle fracture and void formation in the matrix as a function of important microstructural parameters such as local particle volume fraction and particle size. There is a strong relationship between damage and the local volume fraction of the reinforcement proving that damage formation is accentuated in regions of particle clustering. With the SiC reinforced materials examined, there was observed to be a change in dominance of damage mechanism from particle fracture at low local volume fractions to void formation in the matrix within strongly clustered regions. The results are compared with finite element (FE) modelling of the compressive deformation of clustered particles using a simple cluster of equi-spaced particles. The FE results suggest that plastic flow is generally inhibited in clustered regions. In certain highly clustered configurations shielding is such that flow does not occur in the heart of the cluster even at high levels of average plastic strain. The modelling suggests that the change in dominance of damage mechanism is related to the dramatic increase in tensile hydrostatic stresses in the matrix with higher levels of particle clustering.