Fast MATLAB assembly of FEM matrices in 2D and 3D using cell-array approach

2016 ◽  
Vol 07 (02) ◽  
pp. 1650010 ◽  
Author(s):  
Jonas Koko
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Mass Matrix ◽  
Standard Form ◽  
Three Dimensional ◽  
Cell Array ◽  
Right Hand ◽  
Cell Arrays ◽  
Matlab Implementation ◽  
The Right

We propose a MATLAB implementation of the [Formula: see text] finite element method for the numerical solutions of the Poisson problem and the linear elasticity problem in two-dimensional (2D) and three-dimensional (3D). The code consists of vectorized (and short) assembling functions for the matrices (mass and stiffness) and the right-hand sides. Since for the [Formula: see text] finite element, the element mass matrix and right-hand side are simple, the implementation uses only the MATLAB function sparse on the elements volume. For the stiffness matrix, to obtain a MATLAB implementation close to the standard form, cell-arrays are used to store the gradients of the element basis functions. The assembling procedure can then use matrix/vector products on small size cell-arrays. Numerical experiments show that our implementation is fast, scalable with respect to time, and outperforms existing vectorized MATLAB FEM codes.

Modeling and experimental verification on directivity of an electret cell array loudspeaker

2012 ◽  
Vol 24 (3) ◽  
pp. 326-333 ◽  
Author(s):  
Yu-Chi Chen ◽  
Wen-Ching Ko ◽  
Han-Lung Chen ◽  
Hsu-Ching Liao ◽  
Wen-Jong Wu ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Digital Control System ◽  
Analysis Model ◽  
Cell Array ◽  
Element Analysis ◽  
Finite Element Analysis Model ◽  
The Finite Element Analysis ◽  
Directivity Characteristics

We propose a model to give us a method to investigate the characteristic three-dimensional directivity in an arbitrarily configured flexible electret-based loudspeaker. In recent years, novel electret loudspeakers have attracted much interest due to their being lightweight, paper thin, and possessing excellent mid- to high-frequency responses. Increasing or decreasing the directivity of an electret loudspeaker makes it excellent for adoption to many applications, especially for directing sound to a particular area or specific audio location. Herein, we detail a novel electret loudspeaker that possesses various directivities and is based on various structures of spacers instead of having to use multichannel amplifiers and a complicated digital control system. In order to study the directivity of an electret loudspeaker based on an array structure which can be adopted for various applications, the horizontal and vertical polar directivity characteristics as a function of frequency were simulated by a finite-element analysis model. To validate the finite-element analysis model, the beam pattern of the electret loudspeaker was measured in an anechoic room. Both the simulated and experimental results are detailed in this article to validate the various assertions related to the directivity of electret cell-based smart speakers.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

Consistent Hydrodynamic Mass for Parallel Prismatic Beams in a Fluid-Filled Container

1984 ◽  
Vol 106 (3) ◽  
pp. 270-275
Author(s):  
J. F. Loeber
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Incompressible Fluid ◽  
Finite Element Methods ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Beam Length ◽  
Step Process ◽  
Beam Bending

In this paper, representation of the effects of incompressible fluid on the dynamic response of parallel beams in fluid-filled containers is developed using the concept of hydrodynamic mass. Using a two-step process, first the hydrodynamic mass matrix per unit (beam) length is derived using finite element methods with a thermal analogy. Second, this mass matrix is distributed in a consistent mass fashion along the beam lengths in a manner that accommodates three-dimensional beam bending plus torsion. The technique is illustrated by application to analysis of an experiment involving vibration of an array of four tubes in a fluid-filled cylinder.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Layered Media Under Thermomechanical Surface Loading

2002 ◽  
Vol 125 (1) ◽  
pp. 52-59 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Layered Medium ◽  
Numerical Solutions ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Thin Layers ◽  
Surface Loading ◽  
Elastic Plastic ◽  
Thermomechanical Surface

The simultaneous effects of mechanical and thermal surface loadings on the deformation of layered media were analyzed with the finite element method. A three-dimensional model of an elastic sphere sliding over an elastic-plastic layered medium was developed and validated by comparing finite element results with analytical and numerical solutions for the stresses and temperature distribution at the surface of an elastic homogeneous half-space. The evolution of deformation in the layered medium due to thermomechanical surface loading is interpreted in light of the dependence of temperature, von Mises equivalent stress, first principal stress, and equivalent plastic strain on the layer thickness, Peclet number, and sliding distance. The propensity for plastic flow and microcracking in the layered medium is discussed in terms of the thickness and thermal properties of the layer, sliding speed, medium compliance, and normal load. It is shown that frictional shear traction and thermal loading promote stress intensification and plasticity, especially in the case of relatively thin layers exhibiting low thermal conductivity.

scholarly journals A finite element analysis of sacroiliac joint displacements and ligament strains in response to three manipulations

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Zhun Xu ◽  
Yikai Li ◽  
Shaoqun Zhang ◽  
Liqing Liao ◽  
Kai Wu ◽  
...  
Keyword(s):  
Finite Element ◽  
Sacroiliac Joint ◽  
Clinical Effect ◽  
Three Dimensional ◽  
Element Model ◽  
Element Analysis ◽  
Ligament Strain ◽  
Dimensional Finite Element ◽  
The Right ◽  
Three Dimensional Finite Element

Abstract Background Clinical studies have found that manipulations have a good clinical effect on sacroiliac joint (SIJ) pain without specific causes. However, the specific mechanisms underlying the effect of manipulations are still unclear. The purpose of this study was to investigate the effects of three common manipulations on the stresses and displacements of the normal SIJ and the strains of the surrounding ligaments. Methods A three-dimensional finite element model of the pelvis-femur was developed. The manipulations of hip and knee flexion (MHKF), oblique pulling (MOP), and lower limb hyperextension (MLLH) were simulated. The stresses and displacements of the SIJ and the strains of the surrounding ligaments were analyzed during the three manipulations. Results MOP produced the highest stress on the left SIJ, at 6.6 MPa, while MHKF produced the lowest stress on the right SIJ, at 1.5 MPa. The displacements of the SIJ were all less than 1 mm during the three manipulations. The three manipulations caused different degrees of ligament strain around the SIJ, and MOP produced the greatest straining of the ligaments. Conclusion The three manipulations all produced small displacements of the SIJ and different degrees of ligament strains, which might be the mechanism through which they relieve SIJ pain. MOP produced the largest displacement and the greatest ligament strains.

Electromagnetic induction by a finite electric dipole source over a 2-D earth

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Martyn J. Unsworth ◽  
Bryan J. Travis ◽  
Alan D. Chave
Keyword(s):  
Finite Element ◽  
Electromagnetic Fields ◽  
Electric Dipole ◽  
Numerical Solutions ◽  
Current Source ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Horizontal Electric Dipole

A numerical solution for the frequency domain electromagnetic response of a two‐dimensional (2-D) conductivity structure to excitation by a three‐dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite‐element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far‐field. In combination with an iterative solution for the along‐strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air‐earth interface are presented to illustrate the usefulness of the code.

scholarly journals Preconditioned Cell Array Optimized for a Three-Dimensional Culture of Hepatocytes

2009 ◽  
Vol 18 (5-6) ◽  
pp. 677-682 ◽  
Author(s):  
Yoshitaka Miyamoto ◽  
Takeshi Ikeya ◽  
Shin Enosawa
Keyword(s):  
Cell Biology ◽  
Culture Medium ◽  
Biological Activities ◽  
Three Dimensional ◽  
Rat Hepatocytes ◽  
Cell Array ◽  
Cell Arrays ◽  
A Cell ◽  
Three Dimensional Culture ◽  
Hepatocyte Spheroids

Three-dimensional culture procedures have attracted attention in various fields of cell biology. A newly developed cell array assisted in the formation of hepatocyte spheroids by two innovations: 1) micropatterning by a hydrophilic polymer, and 2) the use of bovine carotid artery-derived HH cells as feeder cells. The former contributes to the standardization of the spheroid size and the latter to the maintenance of the spheroids. We created a way to provide a ready-to-use cell array by cryopreservation of an HH feeder cell cultured array. After inoculation of HH cells on the cell array, the culture medium was replaced by freezing medium containing dimethyl sulfoxide. Thereafter, the array was frozen and stored in a −80°C deep freezer. At the start of the hepatocyte culture, the cryopreserved HH cell array was thawed by adding warmed (37°C) culture medium. The morphology and biological activities of the cryopreserved HH cells were intact, as confirmed by phase contrast microscopy and functional staining with calcein and formazan. The rat hepatocytes formed perfect spheroids on the cryopreserved HH cell array without any differences from those on the freshly prepared HH cell array. The CYP3A drug metabolism activities of the hepatocytes were well maintained on the cryopreserved and fresh cell arrays. The present protocol greatly shortened the time and labor required to prepare a cell array for culturing hepatocytes.

Numerical Simulation of Polymer Flows in Coat-Hanger Die Using Wagner Constitutive Model

2011 ◽  
Vol 189-193 ◽  
pp. 1941-1945
Author(s):  
Yong Li ◽  
Jian Rong Zheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Computing Time ◽  
Three Dimensional ◽  
Die Design ◽  
Dimensional Simulation ◽  
Element Method

An understanding of flow behavior of polymer melts through a slit die is extremely important for optimizing die design. In this paper numerical simulations have been undertaken for the flow of linear low-density polyethylene through Coat-hanger sheet dies. A new finite element method is proposed to simulate the flow in slit channel using Wagner constitutive model. This is one kind of finite element semi-analytical method by which the velocity distributions in thickness direction is approach by Fourier series. Numerical results of volumetric flow and pressure in coat-hanger dies are given to compare to the three-dimensional simulation using the finite element method. It appears that numerical solutions are as accurate as the complete 3D calculations and the computing time can be saved.

Extrapolating and interpolating surfaces in depth

1985 ◽  
Vol 224 (1234) ◽  
pp. 43-56 ◽  
Keyword(s):  
Three Dimensional ◽  
Surface Orientation ◽  
Three Dimensions ◽  
Apparent Depth ◽  
Right Hand ◽  
Pictorial Cues ◽  
Random Dot Stereograms ◽  
Sloping Surface ◽  
The Right ◽  
Hand Image

Random -dot stereograms were generated with a blank area placed in part of the right-hand image so making a patchwork of monocular and binocular areas. The perceived depth and shape of the monocular region, where depth was not explicitly marked, depended in p art on the depth and surface orientation of adjacent binocular areas. Thus a monocular rectangle flanked by two binocular rectangles which were placed in different fronto-parallel planes was seen as a sloping surface spanning the depth between the binocular regions, and, under some conditions, the gradient of a sloping binocular plane extended into a neighbouring monocular area. Division of the monocular region into two by textural discontinuities or discontinuities of motion sometimes altered the shape of the extrapolated surface. Often, though, the shape was unchanged by such discontinuities implying that both two- and three-dimensional features are used to segment a scene into separate surfaces. Pictorial cues also contribute to the shape and apparent depth of the monocular surface. For instance, when subjects viewed a display consisting of portions of a cube of which two ends were shown stereoscopically and one side monocularly, the monocular side was seen in three dimensions filling the gap between the ends. When stereo cues were pitted against pictorial cues, sometimes pictorial cues and sometimes stereo cues dominated, and sometimes the surface contained sharp discontinuities enabling both to be accommodated.

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