Accuracy Of Finite Element Method Research Articles

Compact Electro-Mechanical-Fluidic Model for Actuated Fluid Flow System

This paper presents a compact electro-mechanical-fluidic system-modeling method for multidomain system simulation based on multidomain physics that considers the total energy conservation condition, in terms of respective potential and flow quantities. Models for electrical, mechanical, and fluidic domains are developed to design the example of a blood pumping system, where the blood flow is driven by electrically controlled organic actuators. The electrical domain includes an organic mosfet -based control circuit, the mechanical domain includes organic actuators, and the fluidic domain includes a flexible fluid-flow channel. Control circuit, actuators, and fluid models are coupled through equivalent circuits, where interconnection relationships between two neighboring domains are expressed using the energy conservation concept. The model accuracy is verified with finite element method (FEM) based numerical simulation. Significantly faster simulation speed than with FEM and good accuracy were achieved.

塑性加工のための高精度有限要素解析プログラムの開発とその応用

塑性加工のための高精度有限要素解析プログラムの開発とその応用

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

Electroencephalography (EEG) forward modeling via H(div) finite element sources with focal interpolation

The goal of this study is to develop focal, accurate and robust finite element method (FEM) based approaches which can predict the electric potential on the surface of the computational domain given its structure and internal primary source current distribution. While conducting an EEG evaluation, the placement of source currents to the geometrically complex grey matter compartment is a challenging but necessary task to avoid forward errors attributable to tissue conductivity jumps. Here, this task is approached via a mathematically rigorous formulation, in which the current field is modeled via divergence conforming H(div) basis functions. Both linear and quadratic functions are used while the potential field is discretized via the standard linear Lagrangian (nodal) basis. The resulting model includes dipolar sources which are interpolated into a random set of positions and orientations utilizing two alternative approaches: the position based optimization (PBO) and the mean position/orientation (MPO) method. These results demonstrate that the present dipolar approach can reach or even surpass, at least in some respects, the accuracy of two classical reference methods, the partial integration (PI) and St. Venant (SV) approach which utilize monopolar loads instead of dipolar currents.

Modeling ellipsometric measurement of three-dimensional structures with rigorous coupled wave analysis and finite element method simulations

Using rigorous coupled wave analysis (RCWA) and finite element method (FEM) simulations together, many interesting ellipsometric measurements can be investigated. This work specifically focuses on simulating copper grating structures that are plasmonically active. Looking at near-field images and Mueller matrix spectra, understanding of physical phenomena is possible. A general strategy for combatting convergence difficulties in RCWA simulations is proposed and applied. The example used is a copper cross-grating structure with known slow convergence. Baseline simulations on simple samples are provided for comparison and determination of FEM accuracy.

Accuracy of Finite Element Methods for Boundary-Value Problems of Steady-State Fractional Diffusion Equations

Optimal-order error estimates in the energy norm and the $$L^2$$L2 norm were previously proved in the literature for finite element methods of Dirichlet boundary-value problems of steady-state fractional diffusion equations under the assumption that the true solutions have desired regularity and that the solution to the dual problem has full regularity for each right-hand side. We show that the solution to the homogeneous Dirichlet boundary-value problem of a one-dimensional steady-state fractional diffusion equation of constant coefficient and source term is not necessarily in the Sobolev space $$H^1$$H1. This fact has the following implications: (i) Up to now, there are no verifiable conditions on the coefficients and source terms of fractional diffusion equations in the literature to ensure the high regularity of the true solutions, which are in turn needed to guarantee the high-order convergence rates of their numerical approximations. (ii) Any Nitsche-lifting based proof of optimal-order $$L^2$$L2 error estimates of finite element methods in the literature is invalid. We present numerical results to show that high-order finite element methods for a steady-state fractional diffusion equation with smooth data and source term fail to achieve high-order convergence rates. We present a preliminary development of an indirect finite element method, which reduces the solution of fractional diffusion equations to that of second-order diffusion equations postprocessed by a fractional differentiation. We prove that the corresponding high-order methods achieve high-order convergence rates even though the true solutions are not smooth, provided that the coefficient and source term of the problem have desired regularities. Numerical experiments are presented to substantiate the theoretical estimates.

Ultrasonic thermometry simulation in a random fluctuating medium: Evidence of the acoustic signature of a one-percent temperature difference

We study the development potential of ultrasonic thermometry in a liquid fluctuating sodium environment similar to that present in a Sodium-cooled Fast Reactor, and thus investigate if and how ultrasonic thermometry could be used to monitor the sodium flow at the outlet of the reactor core. In particular we study if small temperature variations in the sodium flow of e.g. about 1% of the sodium temperature, i.e., about 5°C, can have a reliably-measurable acoustic signature. Since to our knowledge no experimental setups are available for such a study, and considering the practical difficulties of experimentation in sodium, we resort to a numerical technique for full wave propagation called the spectral-element method, which is a highly accurate finite-element method owing to the high-degree basis functions it uses. We obtain clear time-of-flight variations in the case of a small temperature difference of one percent in the case of a static temperature gradient as well as in the presence of a random fluctuation of the temperature field in the turbulent flow. The numerical simulations underline the potential of ultrasonic thermometry in such a context.

Kinetostatic modeling and analysis of an exechon parallel kinematic machine(PKM) module

As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method(FEM). The equilibrium equations of the platform are derived with Newton’s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system’s deflections. The platform’s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.

Maximum fundamental frequency of thick laminated composite plates by a hybrid optimization method

As a first attempt, a combined method is introduced to obtain maximum fundamental frequency of thick laminated composite plates via finding optimum fibers orientation. The governing equations are obtained based on the higher order shear deformation theory (HSDT). The robust and accurate finite element method (FEM) is used to discretize the governing equations. The transferred form of the equations in frequency domain is obtained and the fundamental frequency of the plate is achieved. High sensitivity of the problem with the fibers orientations is shown. To find the optimum fibers orientation of the thick plate a mixed implementable evolutionary algorithm is used. In the proposed genetic algorithms (GAs) base method, particle swarm optimization (PSO) method is added to improve specified percent of GAs population. Applicability and usefulness of the method is demonstrated by solving different examples.

Elastodynamic modeling and joint reaction prediction for 3-PRS PKM

To gain a thorough understanding of the load state of parallel kinematic machines (PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

A novel, highly efficient and accurate adaptive higher-order finite ele- ment method (hp-FEM) is used to simulate a multi-frequency resistivity logging- while-drilling (LWD) tool response in a borehole environment. Presented in this study are the vector expression of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of Maxwell's equations, and automatic hp- adaptivity strategy. The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numeri- cal experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive h-FEM. The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models, which further confirm the accuracy of the results using the Hermes library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool response in a borehole environment.

Projected finite elements for reaction–diffusion systems on stationary closed surfaces

In this paper we present a robust, efficient and accurate finite element method for solving reaction–diffusion systems on stationary spheroidal surfaces (these are surfaces which are deformations of the sphere such as ellipsoids, dumbbells, and heart-shaped surfaces) with potential applications in the areas of developmental biology, cancer research, wound healing, tissue regeneration, and cell motility among many others where such models are routinely used. Our method is inspired by the radially projected finite element method introduced in [39]. (Hence the name “projected” finite element method.) The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is “logically” rectangular. To demonstrate the robustness, applicability and generality of this numerical method, we present solutions of reaction–diffusion systems on various spheroidal surfaces. We show that the method presented in this paper preserves positivity of the solutions of reaction–diffusion equations which is not generally true for Galerkin type methods. We conclude that surface geometry plays a pivotal role in pattern formation. For a fixed set of model parameter values, different surfaces give rise to different pattern generation sequences of either spots or stripes or a combination (observed as circular spot-stripe patterns). These results clearly demonstrate the need for detailed theoretical analytical studies to elucidate how surface geometry and curvature influence pattern formation on complex surfaces.

사물인터넷 구현을 위한 고강도 콘크리트 박막벽체의 극한 편심하중 강도에 관한 연구

Recently, a high strength concrete(HSC) in excess of 80 MPa is popular to use in the domestic construction field. But there is no design standard of high strength concrete. It is reason why a study about structural behaviors of thin walls is required. In this paper, the accurate Finite Element Method as a virtual test is suggested considering material properties, which are concrete and steel, and the experimental fractural model suggested by Kupfer. It is conducted the comparison evaluation of the ultimate failure loads, lateral-displacements and crack propagation patterns between the results of experimental approach, which were carried on Saheb's test for normal strength concrete and Lee's test for high strength concrete. Therefore it is suggested to use the accurate virtual simulation test method and Ubiquitous Sensor Network(USN) by Finite Element Method for Internet of Things(IoT).

Numerical and intelligent analysis of silicon nitride laser grooving

A three-dimensional finite element model of evaporative laser grooving process has been developed for ceramic materials. The laser is assumed to be a continuous wave and approximated as Gaussian beam. The model can predict three-dimensional temperature distribution inside the specimen as well as resultant groove depth. By comparing the predicted groove depths with experimental data from literature, it was found that the effect of multiple reflections in deep grooves is significant. The computational model can be calibrated for deep grooves by increasing absorptivity for deeper cuts. The calibrated model was used to develop a fuzzy expert system (FES) which can reliably predict groove depth at relatively low computational costs. Fuzzy logic (FL) methodology, on the other hand, is a capable modeling tool which performs extremely robust in a nonlinear complex field with least trial data. In the fuzzy expert system, the goodness of fit was found to be 0.991, and the mean relative error was 4.714 % compared to goodness of fit of 0.897 and mean relative error of 10.675 % in finite element method (FEM). FES could successfully increase the accuracy of FEM without taking the complex phenomena of multiple reflections into computation.

Hybrid Framework for Reliability-Based Design Optimization of Imperfect Stiffened Shells

Variations of manufacturing process parameters, environment aspects, and imperfections may significantly affect the quality and performance of stiffened shells. The reliability-based design optimization (RBDO) of stiffened shells, considering all these uncertainty factors simultaneously, is extremely time-consuming, even if the surrogate-based technology is used. Therefore, a hybrid bi-stage framework for RBDO of stiffened shells is presented to release the computational burden, where two main sources of uncertainties are considered: variations of material properties and geometric dimensions are described as random variables, while various forms of imperfections of stiffened shells are covered by the single perturbation load approach. The basic idea of the proposed method is to combine the efficiency of smeared stiffener method with the accuracy of finite element method, and then narrow the design window efficiently with little accuracy sacrifice. The adaptive chaos control method is used to ensure the robustness of the search process of the most probable target point. The numerical example illustrates the advantage of the proposed method over other RBDO approaches from the point of view of computational cost, accuracy and robustness of the result.

Higher Order NEM and FEM Accuracy Comparison

The natural-element method (NEM) has proved to be able to provide more accurate and computationally efficient solutions than the finite-element method (FEM) for first-order consistency approximations. However, higher order approximations in the NEM framework are not obtained straightforwardly. This paper addresses a method of constructing higher order approximations out of the standard first-order NEM shape functions. This process is achieved through the de Boor algorithm. Accuracy of the scheme is compared with FEM. Results show that in second-order approximations context the NEM is still able to provide better accuracies for a given number of degrees of freedom.

A Fast Finite Element Method for Space-Fractional Dispersion Equations on Bounded Domains in $\mathbb{R}^2$

We develop a fast and accurate finite element method for space-fractional dispersion equations in two space dimensions, which are expressed in terms of fractional directional derivatives in all the directions that are integrated with respect to a probability measure on the unit circle. The fast method significantly reduces the computational work of solving the discrete linear algebraic systems from $O(N^3)$ by a direct solver to $O(N \log N)$ per iteration and a memory requirement from $O(N^2)$ to $O(N)$. Furthermore, the fast method reduces the evaluation of the stiffness matrix, which often constitutes a large portion of the CPU time, from $O(N^2)$ to $O(N)$. The developed preconditioned fast Krylov subspace iterative solver significantly reduces the number of iterations in a Krylov subspace iterative method and may improve the convergence behavior of the solver. Numerical results show the utility of the method.

Explicit finite element analysis to predict impact damage response of osteoporosis hip bone

Hip fractures due to sideways falls are a worldwide health problem, especially amongst elderly people. The force experienced by the proximal femur during a fall, and therefore hip fracture, is significantly dependent on density, thickness and stiffness of the body during impact. The process of fracture and healing can only be understood in terms of the structure and composition of the bone and also its mechanical properties. Bone fracture analysis investigates the prediction of various failure mechanisms under different loading conditions. An accurate explicit finite element method will assist scientists and researchers to predict the impact damage response of bone structures. In this paper, the effect of low velocity impact on the osteoporotic hip in ageing people will be studied in LSDYNA. The first part aims to create a three-dimensional (3D) reconstruction and registration of semi-transparent computed tomography scan image data using Simpleware software. In the second part, the effect of cortical thickness and impact velocity on the energy absorption of the hip during a fall will be investigated on a 3D model using the latest techniques. The critical impulse loading of the hip will be the benchmark to improve the design of safety instruments and consequently the well-being of elderly people.

A finite-element method using dispersion reduced spline elements for room acoustics simulation

This paper presents a finite element method (FEM) using hexahedral 27-node spline acoustic elements (Spl27) with low numerical dispersion for room acoustics simulation in both the frequency and time domains, especially at higher frequencies. Dispersion error analysis in one dimension is performed to increase the accuracy of FEM using Spl27 by modifying the numerical integration points of element stiffness and mass matrices. The basic accuracy and efficiency of the FEM using the improved Spl27, which uses modified integration points, are presented through numerical experiments using benchmark problems in both the frequency and time domains, revealing that FEM using the improved Spl27 in both domains provides more accurate results than the conventional method does, and with fewer degrees of freedom. Moreover, the effectiveness of FEM using the improved Spl27 over that using hexahedral 27-node Lagrange elements is shown for time domain analysis of the sound field in a practical sized room.

High selectivity band pass filters on iso/anisotropic dielectric, ferrimagnetic, and metamaterial substrates

ABSTRACTThis work describes a frequency response investigation of a band pass microstrip filter geometry printed on different substrate materials. The filter geometry comprises a wavelength rectangular ring resonator that is side coupled to two quarter‐wavelength lines to provide the access ports. This filter geometry is particularly suitable for high‐frequency selective applications. The investigation of the properties of the filter geometry is carried out for iso/anisotropic dielectric, ferrimagnetic, and metamaterial substrates, for comparison purpose. Simulation and design are performed using Ansoft HFSS, a commercial software based on the accurate finite element method. Resonant frequency, return loss, insertion loss, and percent bandwidth results are compared and discussed, taking into account the effect produced by each material substrate on the filter performance. Prototypes of band pass filters on isotropic substrates are built and measured. Simulated and measured results are in agreement. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:201–206, 2014