Finite Element Method Method Research Articles

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Abstract Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

High-performance localized surface plasmon resonance fiber sensor based on nano-metal-gear array

Utilizing the outstanding-sensitivity characteristic of localized surface plasmon resonance (LSPR), this study developed a new high-performance sensor design model. Based on a cross-sectional view of the component, the proposed new LSPR fiber sensor comprises a single-mode fiber (SMF), nano-metal rings, and nano-metal gears. The numerical simulation method that combines the finite element method (FEM) and eigenmode expansion method (EEM) was used to design and analyze the sensor. In addition, to increase the accuracy of the numerical simulation results, the proposed numerical simulation method included a perfectly matched layer (PML) and a perfectly reflecting boundary condition (PRB). In other words, the FEM and EEM numerical methods involve not only discrete guided modes and discrete LSPR modes in the simulation and design process, but also discrete radiation modes, that is, continuous radiation modes converted using PML and PRB. This study found that the current metallic patterns in the fiber sensor can trigger the LSPR by the electric field Er of the core mode HE11, which is the main reason the novel fiber sensor yields a high performance. After algorithms were performed, images showed evident excitation of the LSPR. The LSPR fiber sensor designed in this study possesses the advantageous attributes of a short length (77.01764μm), high resolution (approximately −80dB), and high sensitivity (approximately 45,062nm/RIU).

Passive control of marine hydrokinetic turbine blades

Marine hydrokinetic (MHK) turbine blades are generally constructed from fiber reinforced polymer composites and are subject to large, highly dynamic fluid forces. The bend-twist deformation coupling behavior of these materials can be hydroelastically tailored to improve system performance over the expected life of the turbine by way of rapid, passive pitch control that can increase lifetime power generation, reduce hydrodynamic instabilities, and improve load shedding and structural performance. There are practical concerns, however, that make the design of these devices complex. Constraints on system components such as the rated power of the generator system, maximum rotational speed, or material degradation can affect the extent to which passive control can enhance performance. Using a previously validated boundary element method-finite element method solver, this paper examines the capabilities of passive pitch adaptation under both instantaneous and long-term variable amplitude loading to better describe potential benefits while considering practical design and operational restrictions.

Rigorous analysis of highly tunable cylindrical transverse magnetic mode re-entrant cavities

Cylindrical re-entrant cavities are unique three-dimensional structures that resonate with their electric and magnetic fields in separate parts of the cavity. To further understand these devices, we undertake rigorous analysis of the properties of the resonance using "in-house" developed Finite Element Method (FEM) software capable of dealing with small gap structures of extreme aspect ratio. Comparisons between the FEM method and experiments are consistent and we illustrate where predictions using established lumped element models work well and where they are limited. With the aid of the modeling we design a highly tunable cavity that can be tuned from 2 GHz to 22 GHz just by inserting a post into a fixed dimensioned cylindrical cavity. We show this is possible, as the mode structure transforms from a re-entrant mode during the tuning process to a standard cylindrical transverse magnetic mode.

A hybrid boundary element-finite element approach to modeling plane wave 3D electromagnetic induction responses in the Earth

A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geo-electromagnetic induction problems. To achieve this goal, first the Galerkin edge-based finite-element method (FEM) using unstructured meshes is adopted to solve the electric field differential equation in the heterogeneous Earth, where arbitrary distributions of conductivity, magnetic permeability and dielectric permittivity are allowed for. Second, the point collocation boundary-element method (BEM) is used to solve a surface integral formula in terms of the reduced electrical vector potential on the arbitrarily shaped air–Earth interface. Third, to avoid explicit storage of the system matrix arising from large-scale problems and to reduce the horrendous time complexity of the product of the system matrix with an initial vector of unknowns, the adaptive multilevel fast multipole method is applied. This leads to a matrix-free form suitable for the application of iterative solvers. Furthermore, a highly sparse problem-dependent preconditioner is developed to significantly reduce the number of iterations used by the iterative solvers.The efficacy of the presented hybrid scheme is verified on two synthetic examples against different numerical techniques such as goal-oriented adaptive finite-element methods. Numerical experiments show that at low frequencies, where the quasi-static approximation is applicable, standard FEM methods prove to be superior to our hybrid BEM–FEM solutions in terms of computational time, because the FEM method requires only a coarse discretization of the air domain and offers an advantageous sparsity of the system matrix. At radio-magnetotelluric frequencies of a few hundred kHz, the hybrid BEM–FEM scheme outperforms the FEM method, because it avoids explicit storage of the system matrices as well as dense volume discretization of the air domain required by FEM methods at high frequencies. In summary, to the best of our knowledge, this study is the first attempt at completely removing the air space for large scale complicated electromagnetic induction modeling in the Earth.

A Combined Wavelet-Based Mesh-Free Method for Solving the Forward Problem in Electrical Impedance Tomography

In this paper, a combined wavelet-based mesh-free method is suggested to solve the forward problem in electrical impedance tomography (EIT). EIT is a noninvasive imaging modality based on the reconstruction of the conductivity profile inside a solution domain. The forward problem simulates measurement data for comparing with experimental data in the inverse problem. The forward problem can be solved by the finite element method (FEM) or the mesh-free method. Since the solution of the FEM depends on the mesh shape and boundary condition constraints are difficult to be applied to the mesh-free method, the combined wavelet-based mesh-free approach can resolve the disadvantages of both methods in the EIT forward problem. In order to apply interface conditions between different regions, slope jump functions are entered to the set of basis functions. Two different 2-D EIT problems are modeled. The simulation results obtained by the combined wavelet-based mesh-free method are compared with the FEM in terms of accuracy and computational cost. Moreover, the effects of object movement and deformation are investigated on the accuracy of the simulated electrode voltages using the standard FEM and combined wavelet-based mesh-free method.

Calculating Stress Intensity Factor (Mode I) for Composite Plate with Central Crack

A Stress Intensity Factor (SIF) Mode I is calculated for longitudinal composite plate with dimensions (104 mm × 40 mm) and fiber volume fraction (37.5%).The finite element method (FEM) (ANSYS) and MFree method are used for calculating the SIF of quarter model (i.e. (52 mm × 20 mm)) with constant displacement in ydirection that is applied at the ends of the plate. The crack length, material properties of fiber and material properties of matrix affect the SIF and these parameters are studied to understand the crack growth and the fracture mechanism in composite material. The value of SIF depends on the position of crack tip in additional to the material properties of fiber and matrix. A comparison between the FEM and MFree method is made to study the advantages and disadvantages of each method and to choose the suitable method for calculating SIF for composite plate. Generally, there is a good agreement between the FEM and MFree method but there is a slightly difference between them specially when the crack length increases. This slight difference happens due to the calculation technique of SIF used in each method. This difference makes the FEM accurate than the MFree method unless increasing the number of nodes around the crack tip in MFree method.

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.

FEM simulation of the die compaction of pharmaceutical products: Influence of visco-elastic phenomena and comparison with experiments

This work studies the influence of visco-elastic behavior in the finite element method (FEM) modeling of die compaction of pharmaceutical products and how such a visco-elastic behavior may improve the agreement between experimental and simulated compression curves. The modeling of the process was conducted on a pharmaceutical excipient, microcrystalline cellulose (MCC), by using Drucker-Prager cap model coupled with creep behavior in Abaqus(®) software. The experimental data were obtained on a compaction simulator (STYLCAM 200R). The elastic deformation of the press was determined by performing experimental tests on a calibration disk and was introduced in the simulation. Numerical optimization was performed to characterize creep parameters. The use of creep behavior in the simulations clearly improved the agreement between the numerical and experimental compression curves (stresses, thickness), mainly during the unloading part of the compaction cycle. For the first time, it was possible to reproduce numerically the fact that the minimum tablet thickness is not obtained at the maximum compression stress. This study proves that creep behavior must be taken into account when modeling the compaction of pharmaceutical products using FEM methods.

Numerical Analysis of Cold Crucible Induction Melting Employing FEM and MPS Method

This paper proposes a coupled method of 3-D finite element method (FEM) and moving particle semi-implicit (MPS) method for the analysis of cold crucible induction melting. In this method, the magnetic field is calculated by FEM and the fluid motion equation of the molten metal and the thermal distribution in the molten metal are calculated by the MPS method. In this paper, the phase transformation of the metal is not considered. The effectiveness of this method is verified through the analysis of the molten metal behavior in the crucible.

Numerical Analysis of Negative Ion by Electrostatic Atomization Employing FEM and MPS Method

This paper proposes a coupled method of 3-D finite element method (FEM) and Moving Particle Semi-implicit (MPS) method for the analysis of a negative ion that is produced by electrostatic atomization. In this method, the electric field is calculated by FEM and the fluid motion equation of a drop of water is calculated by the MPS method. The validity of this analysis method is verified by comparison with an experiment.

Extension of Time-Domain Finite Element Method to Nonlinear Frequency-Sweeping Problems

Applications of magnetic-resonant wireless power transfer technology have been extensively researched because of its high efficiency, security and convenience. To recharge batteries, the induced ac voltage in the receiver coil of wireless systems must be rectified to dc, hence the power transfer systems are inevitably nonlinear. In this paper, a novel approach based on time-domain finite element method (FEM) is presented to analyze the nonlinear system in order to obtain frequency-sweeping solutions quickly. At the first step of the proposed method, the wireless power transfer system, excluding the rectifier circuit, will be equivalent to a voltage source and a general impedance at different frequencies. The equivalent circuit is then connected to the rectifier circuit. Numerical example being reported in this paper indicates that the results obtained using the proposed methodology are consistent with those obtained using traditional time-domain FEM method. If solutions at different operating frequencies are required, the proposed method can save a lot of computation time, because one just needs to solve the field problem using the time-domain FEM twice. From the numerical example on the performance analysis of the wireless power transfer system being studied, the computing time of the proposed time-domain method is only 2% of that required if traditional time-domain FEM method is used.

Slope stabilization in difficult conditions: the case study of a debris slide in NW Italian Alps

A case study of a debris slide (estimated volume of about 35,000 m3) is described in this paper. This slide occurred in April 2009 in the North Western Italian Alps (Aosta valley) and damaged the SR25 road along the Valgrisenche valley. Ground investigations started with severe safety and logistic issues being posed. Given the need to open as soon as possible the road, the design of the landslide stabilization works was carried out using a “design as you go” approach. The stabilization measures were conceived to be flexible in order to allow for changes and integration during construction, in line with the progressive refinement of the geological–geotechnical slope model being developed. Back analysis by means of the limit equilibrium method (LEM) and the finite element method (FEM) was used. Groundwater level rise following heavy rainfall and spring snow melting was found to be the main cause of the debris slide. The stabilization works were designed by using both the LEM and FEM methods. The stability conditions of the engineered slope were assessed based on the available performance monitoring data.

Numeric Solution of the Fokker-Planck-Kolmogorov Equation

The solution of an n-dimensional stochastic differential equation driven by Gaussian white noises is a Markov vector. In this way, the transition joint probability density function (JPDF) of this vector is given by a deterministic parabolic partial differential equation, the so-called Fokker-Planck-Kolmogorov (FPK) equation. There exist few exact solutions of this equation so that the analyst must resort to approximate or numerical procedures. The finite element method (FE) is among the latter, and is reviewed in this paper. Suitable computer codes are written for the two fundamental versions of the FE method, the Bubnov-Galerkin and the Petrov-Galerkin method. In order to reduce the computational effort, which is to reduce the number of nodal points, the following refinements to the method are proposed: 1) exponential (Gaussian) weighting functions different from the shape functions are tested; 2) quadratic and cubic splines are used to interpolate the nodal values that are known in a limited number of points. In the applications, the transient state is studied for first order systems only, while for second order systems, the steady-state JPDF is determined, and it is compared with exact solutions or with simulative solutions: a very good agreement is found.

The Numerical Simulation of Multi-Directional Forging 6700 Steering Knuckle

The numerical simulation of multi-directional precise contour forging of 6700 steering knuckle was studied in this paper. A 3D thermodynamic coupling finite element method (FEM) was established for each process of the deformation, based on the rigid-viscoplastic finite element method FEM. The results showed that the shape and size of the blanking billet can be optimized and the materials utilization ratio and the dimensional accuracy can be increased dramatically by using multi-directional precise contour forging

Analysis of Wireless Power Transfer System Based on 3-D Finite-Element Method Including Displacement Current

With the advent of electronic technology, researchers are devoting increasing interests to wireless power transfer methods. Generally finite-element method (FEM) is a powerful tool for numerical simulation of such systems. Due to the relatively high operating frequency, the presence of inductance and distributed capacitance in the system as well as eddy current and displacement current become two essential issues in the study of electromagnetic field distribution in wireless power transfer systems. One of the major problems to be addressed is the gap between low and high frequencies as conventional low frequency methods cannot include displacement current, while common high frequency methods focus mainly on the ultrahigh frequencies, such as in antenna studies. In this paper, a 3-D FEM including displacement current is developed to model wireless power transfer system to include displacement current and eddy current and close the gap of high and low frequency modeling methods. No frequency sweeping, which is required in conventional studies, is necessary in the proposed algorithm. Hence the computing time of the proposed algorithm requires only 1.5% of the normal time domain FEM method and this is a significant accomplishment for the electromagnetic community.

A coupled FDM–FEM method for free surface flow interaction with thin elastic plate

A partitioned approach by the coupling finite difference method (FDM) and the finite element method (FEM) is developed for simulating the interaction between free surface flow and a thin elastic plate. The FDM, in which the constraint interpolation profile method is applied, is used for solving the flow field in a regular fixed Cartesian grid, and the tangent of the hyperbola for interface capturing with the slope weighting scheme is used for capturing free surface. The FEM is used for solving structural deformation of the thin plate. A conservative momentum-exchange method, based on the immersed boundary method, is adopted to couple the FDM and the FEM. Background grid resolution of the thin plate in a regular fixed Cartesian grid is important to the computational accuracy by using this method. A virtual structure method is proposed to improve the background grid resolution of the thin plate. Both of the flow solver and the structural solver are carefully tested and extensive validations of the coupled FDM–FEM method are carried out on a benchmark experiment, a rolling tank sloshing with a thin elastic plate.

Comparison of Different Upscaling Methods for Predicting Thermal Conductivity of Complex Heterogeneous Materials System: Application on Nuclear Waste Forms

To develop strategies for determining thermal conductivity based on the prediction of a complex heterogeneous materials system and loaded nuclear waste forms, the computational efficiency and accuracy of different upscaling methods has been evaluated. The effective thermal conductivity, obtained from microstructure information and local thermal conductivity of different components, is critical in predicting the life and performance of waste forms during storage. Several methods, including the Taylor model, Sachs model, self-consistent model, and statistical upscaling method, were developed and implemented. Microstructure-based finite-element method (FEM) prediction results were used to as a benchmark to determine the accuracy of the different upscaling methods. Micrographs from waste forms with varying waste loadings were used in the prediction of thermal conductivity in FEM and homogenization methods. Prediction results demonstrated that in term of efficiency, boundary models (e.g., Taylor model and Sachs model) are stronger than the self-consistent model, statistical upscaling method, and finite-element method. However, when balancing computational efficiency and accuracy, statistical upscaling is a useful method in predicting effective thermal conductivity for nuclear waste forms.

无交叠垂直梳齿平动微镜的驱动特性

To design a non-overlap vertical electrostatic combdriver for the optical translational micromirror of an optical phase modulator,a mathematic model based on the conformal mapping was built to research the driving performance of the combdriver in detail.According to the theory of complex variable function,an analytical model was established for the electrostatic field of comb actuator by conformal mapping.Then,the electrostatic force in a certain displacement range was deduced by the analytical model for researching the movable comb finger.The results were compared with the corresponding resolution by the Finite Element Method(FEM).Finally,a non-overlap vertical combdriver was successfully fabricated by Micro Electronic Mechanic System(MEMS) process,and an optical Michelson interference system was constructed to measure the static driving charateristics of the comb driver.The result shows that the displacement of proposed non-overlap vertical electrostatic combdriver is 325 nm(phase difference 2π) with a dc driving voltage of 28 V and the offset vertical comb actuator can be actuated to 2.07 μm under a dc driving voltage of 90 V.The measured results accord excellently with the simulated results using the conformal mapping and FEM method,which proves proposed analytical model to be correct.It can provide theoretical and pratical bases for design of non-overlap vertical electrostatic combdrivers.

Scaling of the Transient Hydroelastic Response and Failure Mechanisms of Self-Adaptive Composite Marine Propellers

The load dependent deformation responses and complex failure mechanisms of self-adaptive composite propeller blades make the design, analysis, and scaling of these structures nontrivial. The objective of this work is to investigate and verify the dynamic similarity relationships for the hydroelastic response and potential failure mechanisms of self-adaptive composite marine propellers. A fully coupled, three-dimensional boundary element method-finite element method is used to compare the model and full-scale responses of a self-adaptive composite propeller. The effects of spatially varying inflow, transient sheet cavitation, and load-dependent blade deformation are considered. Three types of scaling are discussed: Reynolds scale, Froude scale, and Mach scale. The results show that Mach scaling, which requires the model inflow speed to be the same as the full scale, will lead to discrepancies in the spatial load distributions at low speeds due to differences in Froude number, but the differences between model and full-scale results become negligible at high speeds. Thus, Mach scaling is recommended for a composite marine propeller because it allows the same material and layering scheme to be used between the model and the full scale, leading to similar 3D stress distributions, and hence similar failure mechanisms, between the model and the full scale.