Electromagnetic modelling with topography on regular grids with equivalent materials

2019 ◽  
Vol 220 (3) ◽  
pp. 2021-2038
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Rafael Abreu
Keyword(s):  
Finite Element ◽  
Coordinate System ◽  
Equivalent Model ◽  
Earth Model ◽  
System Matrix ◽  
Property A ◽  
Secondary Field ◽  
Linear System Of Equations ◽  
Electromagnetic Modelling ◽  
Conductivity Anomalies

SUMMARY Maxwell’s equations are valid regardless of the choice of the coordinate system. By this property a change of coordinates can be equivalently expressed as a change of the material parameters. This idea opens a new approach to the problem of accurate electromagnetic modelling in the vicinity of steep topography or bathymetry. Via a change of coordinates, any earth model with complicated layer interfaces can be represented by an equivalent model where those interfaces are flat, but with its materials correspondingly altered. This new model could then be discretized on a regular mesh and fields could be computed by an appropriate finite difference or integral equation code. Unfortunately, this is not straightforward because both the new electric and magnetic materials are fully anisotropic. By instead applying a finite element secondary field approach to the equivalent model, we can completely account for the topography interface in the planar layered background model. The only modification required to existing finite element formulations is a slightly more complicated right-hand side of the linear system of equations, whereas the system matrix is unchanged in any coordinate system. In a numerical modelling experiment we confirm that our technique gives increased accuracy when compared with a recently published technique for dealing with topography in a secondary field formulation for the case of a magnetotelluric source field. In turn, in the vicinity of conductivity anomalies, accuracy can also be negatively affected.

scholarly journals Modeling Stray Capacitances of High-Voltage Capacitive Dividers for Conventional Measurement Setups

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1262
Author(s):  
Alessandro Mingotti ◽  
Federica Costa ◽  
Lorenzo Peretto ◽  
Roberto Tinarelli ◽  
Paolo Mazza
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equivalent Circuit ◽  
High Voltage ◽  
Equivalent Model ◽  
Simulation Environment ◽  
Element Analysis ◽  
Ratio Error ◽  
Complicated Geometries

Stray capacitances (SCs) are a serious issue in high-voltage (HV) applications. Their presence can alter the circuit or the operation of a device, resulting in wrong or even disastrous consequences. To this purpose, in this work, we describe the modeling of SCs in HV capacitive dividers. Such modeling does not rely on finite element analysis or complicated geometries; instead, it starts from an equivalent circuit of a conventional measurement setup described by the standard IEC 61869-11. Once the equivalent model including the SCs is found, closed expressions of the SCs are derived starting from the ratio error definition. Afterwards, they are validated in a simulation environment by implementing various circuit configurations. The results demonstrate the expressions applicability and effectiveness; hence, thanks to their simplicity, they can be implemented by system operators, researchers, and manufacturers avoiding the use of complicated methods and technologies.

2-D electromagnetic modeling by finite‐element method with a dipole source and topography

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 465-475 ◽  
Author(s):  
Yuji Mitsuhata
Keyword(s):  
Finite Element ◽  
Delta Function ◽  
Dipole Source ◽  
Electromagnetic Modeling ◽  
Secondary Field ◽  
Controlled Source ◽  
Transient Electromagnetic ◽  
Isoparametric Finite Element ◽  
Anomalous Bodies ◽  
Element Technique

I present a method for calculating frequency‐domain electromagnetic responses caused by a dipole source over a 2-D structure. In modeling controlled‐source electromagnetic data, it is usual to separate the electromagnetic field into a primary (background) and a secondary (scattered) field to avoid a source singularity, and only the secondary field caused by anomalous bodies is computed numerically. However, this conventional scheme is not effective for complex structures lacking a simple background structure. The present modeling method uses a pseudo‐delta function to distribute the dipole source current, and does not need the separation of the primary and the secondary field. In addition, the method employs an isoparametric finite‐element technique to represent realistic topography. Numerical experiments are used to validate the code. Finally, a simulation of a source overprint effect and the response of topography for the long‐offset transient electromagnetic and the controlled‐source magnetotelluric measurements is presented.

A numerical approach based on finite element method for the wrinkling analysis of dielectric elastomer membranes

2021 ◽  
pp. 1-37
Author(s):  
Guoyong Mao ◽  
Wei Hong ◽  
Martin Kaltenbrunner ◽  
Shaoxing Qu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thickness Distribution ◽  
Numerical Approach ◽  
Dielectric Elastomer ◽  
Equivalent Model ◽  
Maxwell Stress ◽  
Buckling Mode ◽  
Post Buckling ◽  
Element Method

Abstract Dielectric elastomer (DE) actuators are deformable capacitors capable of a muscle-like actuation when charged. When subjected to voltage, DE membranes coated with compliant electrodes may form wrinkles due to the Maxwell stress. Here, we develop a numerical approach based on the finite element method (FEM) to predict the morphology of wrinkled DE membranes mounted on a rigid frame. The approach includes two steps, I) pre-buckling and II) post-buckling. In step I, the first buckling mode of the DE membrane is investigated by substituting the Maxwell stress with thermal stress in the built-in function of the FEM platform SIMULIA Abaqus. In step II, we use this first buckling mode as an artificial geometric imperfection to conduct the post-buckling analysis. For this purpose, we develop an equivalent model to simulate the mechanical behavior of DEs. Based on our approach, the thickness distribution and the thinnest site of the wrinkled DE membranes subjected to voltage are investigated. The simulations reveal that the crests/troughs of the wrinkles are the thinnest sites around the center of the membrane and corroborate these findings experimentally. Finally, we successfully predict the wrinkles of DE membranes mounted on an isosceles right triangle frame with various sizes of wrinkles generated simultaneously. These results shed light on the fundamental understanding of wrinkled dielectric elastomers but may also trigger new applications such as programmable wrinkles for optical devices or their prevention in DE actuators.

A Domain Decomposition Study for a Parallel Finite Element Code

1992 ◽  
Author(s):  
J. Rodriguez ◽  
J. Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Performance Criteria ◽  
Communication Overhead ◽  
Decomposition Algorithms ◽  
System Matrix ◽  
Single Wave ◽  
Parallel Finite Element ◽  
Computational Structural Mechanics ◽  
Parallel Fem

Abstract The primary objective of this study was the implementation and comparison of domain decomposition algorithms for a parallel Finite Element Method (FEM) used in the area of Computational Structural Mechanics (CSM). A parallelized FEM code exploits the concurrency inherent in the method to improve its computational efficiency. In order to use a larger size granularity in the parallel computation, the parallel FEM needs to partition its domain into subdomains in a proper manner. It is therefore necessary to search for domain decomposition algorithms to satisfy the special requirements of a parallel FEM. The domain decomposition algorithms investigated in this study physically decompose a meshed domain into a desired number of subdomains. Addressing the requirements of the parallel FEM, these algorithms are able to handle any type of two- and three-dimensional domains, balance the workloads across the multiple processors, minimize the communication overhead among the processors, maintain the integrity of each subdomain, minimize the overall bandwidth of the resulting system matrix, and require only a small amount of CPU time for the decomposition. Modifications to existing decomposition algorithms, such as the single wave propagating method and the bisecting method using vertical/horizontal cuts, are investigated. A new algorithm, based on the proposed multiple wave propagating method and the bisecting method using middle cuts, is formulated. These algorithms are compared with each other using performance criteria based on the overall FEM code and the algorithms themselves. An optimal combination algorithm is proposed. This algorithm combination is flexible and intelligent in some sense since several judgements are suggested to guide and organize different decompositions based on the general geometry of the meshes. The combination algorithm possesses both the desirable features of wave propagating and bisecting methods. As an application, the present algorithm is included in an existing parallel FEM code and some improvements in this code are made. The overall efficiency of the FEM code was increased.

Axisymmetric Isothermal Forging

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Coordinate System ◽  
Three Dimensions ◽  
Cold Forging ◽  
Axially Symmetric ◽  
Rectangular Coordinate System ◽  
Complex Deformation ◽  
Fem Method ◽  
Natural Coordinate System ◽  
Main Dimension

According to Spies, the majority of forgings can be classified into three main groups. The first group consists of compact shapes that have approximately the same dimensions in all three directions. The second group consists of disk shapes that have two of the three dimensions (length and width) approximately equal and larger than the height. The third group consists of the long shapes that have one main dimension significantly larger than the two others. All axially symmetric forgings belong to the second group, which includes approximately 30% of all commonly used forgings. A basic axisymmetric forging process is compression of cylinders. It is a relatively simple operation and thus it is often used as a property test and as a preforming operation in hot and cold forging. The apparent simplicity, however, turns into a complex deformation when friction is present at the die–workpiece interface. With the finite-element method, this complex deformation mode can be examined in detail. In this chapter, compression of cylinders and related forming operations are discussed. Since friction at the tool–workpiece interface is an important factor in the analysis of metal-forming processes, this aspect is also given particular consideration. Further, applications of the FEM method for complex-shaped dies are shown in the examples of forging and cabbaging. Finite-element discretization with a quadrilateral element is similar to that given in Chap. 8. The cylindrical coordinate system (r, ϑ, z) is used instead of the rectangular coordinate system. The element is a ring element with a quadrilateral cross-section, as shown in Fig. 9.1. The ξ and η of the natural coordinate system vary from −1 to 1 within each element.

scholarly journals Influence of the Mechanical Properties of Elastoplastic Materials on the Nanoindentation Loading Response

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4842
Author(s):  
Huanping Yang ◽  
Wei Zhuang ◽  
Wenbin Yan ◽  
Yaomian Wang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
The Other ◽  
Equivalent Model ◽  
Strain Hardening Exponent ◽  
Mechanical Parameters ◽  
The Finite Element Method ◽  
Fem Simulations ◽  
Elastoplastic Materials

The nanoindentation loading response of elastoplastic materials was simulated by the finite element method (FEM). The influence of the Young’s modulus E, yield stress σy, strain hardening exponent n and Poisson’s ratio ν on the loading response was investigated. Based on an equivalent model, an equation with physical meaning was proposed to quantitatively describe the influence. The calculations agree well with the FEM simulations and experimental results in literature. Comparisons with the predictions using equations in the literature also show the reliability of the proposed equation. The investigations show that the loading curvature C increases with increasing E, σy, n and ν. The increase rates of C with E, σy, n and ν are different for their different influences on the flow stress after yielding. It is also found that the influence of one of the four mechanical parameters on C can be affected by the other mechanical parameters.

scholarly journals Multigrid solvers for immersed finite element methods and immersed isogeometric analysis

2019 ◽  
Vol 65 (3) ◽  
pp. 807-838 ◽  
Author(s):  
F. de Prenter ◽  
C. V. Verhoosel ◽  
E. H. van Brummelen ◽  
J. A. Evans ◽  
C. Messe ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Isogeometric Analysis ◽  
Convergence Rates ◽  
Computational Cost ◽  
Iterative Solvers ◽  
System Matrix ◽  
B Splines ◽  
Immersed Finite Element ◽  
Immersed Finite Element Methods

AbstractIll-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates. This preconditioning technique is applicable to higher-order discretizations, and enables solving large-scale immersed systems at a computational cost that scales linearly with the number of degrees of freedom. The performance of the preconditioner is demonstrated for conventional Lagrange basis functions and for isogeometric discretizations with both uniform B-splines and locally refined approximations based on truncated hierarchical B-splines.

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