scholarly journals Laplace Transform for Finite Element Analysis of Electromagnetic Interferences in Underground Metallic Structures

2022 ◽  
Vol 12 (2) ◽  
pp. 872
Author(s):  
Andrea Cristofolini ◽  
Arturo Popoli ◽  
Leonardo Sandrolini ◽  
Giacomo Pierotti ◽  
Mattia Simonazzi
Keyword(s):  
Finite Element ◽  
Laplace Transform ◽  
Electromagnetic Interference ◽  
Inverse Laplace Transform ◽  
Element Analysis ◽  
Metallic Structures ◽  
Numerical Inverse Laplace Transform ◽  
Transient Electromagnetic ◽  
The Time Domain ◽  
High Voltage Power Lines

A numerical methodology is proposed for the calculation of transient electromagnetic interference induced by overhead high-voltage power lines in metallic structures buried in soil—pipelines for oil or gas transportation. A series of 2D finite element simulations was employed to sample the harmonic response of a given geometry section. The numerical inverse Laplace transform of the results allowed obtaining the time domain evolution of the induced voltages and currents in the buried conductors, for any given condition of the power line.

Finite Element Analysis of Vibration of Toroidal Field Coils Coupled With Laplace Transform

1982 ◽  
Vol 49 (3) ◽  
pp. 594-600 ◽  
Author(s):  
K. Miya ◽  
M. Uesaka ◽  
F. C. Moon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Laplace Transform ◽  
Equations Of Motion ◽  
Toroidal Field ◽  
Inverse Laplace Transform ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Original Domain ◽  
Element Method

A numerical analysis of a vibration of toroidal field coils in a magnetic fusion reactor is shown here on the basis of the finite element method coupled with Laplace transform. Lagrangian consisting of kinetic, elastic strain, and magnetic energies was utilized to deduce equations of motion of the coils. The equations were solved numerically by applying the Laplace transform to a formulation with respect to time and the finite element method to one with respect to space. The Fast Fourier Transform algorithm was utilized for a calculation of the inverse Laplace transform to obtain a nodal vector of the coil’s displacement in the original domain. Numerical results reasonably explain a dependency of the coil current on a frequency of the coil.

scholarly journals Semi-analytical solution for consolidation of vertical drain to unsaturated soils considering well resistance and smear effect under time-varying loadings

2020 ◽  
Vol 198 ◽  
pp. 02033
Author(s):  
Aifang Qin ◽  
Lianghua Jiang ◽  
Linzhong Li ◽  
Xinhao Li
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Unsaturated Soils ◽  
Inverse Laplace Transform ◽  
Loading Frequency ◽  
Time Varying ◽  
Numerical Inverse Laplace Transform ◽  
Vertical Drain ◽  
Special Cases ◽  
The Time Domain

In this paper, based on equal-strain assumption a semi-analytical solution, considering well re-sistance, smear effect and time-varying loading, is deduced for radial consolidation aided by vertical drain (VD) to unsaturated soils. Firstly, by employing the general integration, Laplace transform, decoupling methods and numerical inverse Laplace transform, the semi-analytical solution in the time domain is ob-tained. Then, its validity is verified by the special cases of the proposed solution under instantaneous loading. Finally, the case analysis show that the dissipation of excess pore pressures is accelerated with the decrease of smear coefficients (αa or αw) or well resistance factors (Ga or Gw). In addition, when the well resistance factor is less than 1, the barrier of VD material to flow can be ignored. Furthermore, a smaller value of the loading frequency of cyclic loading, the bigger the amplitude, and the less fluctuation period in the dissipa-tion rates. Moreover, the current solution can analyse the consolidation characteristics of unsaturated soils with VDs under arbitrary time-varying loadings, including cyclic loadings.

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

scholarly journals Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Chen Xia ◽  
Chengzhi Qi ◽  
Xiaozhao Li
Keyword(s):  
Finite Element ◽  
Seismic Response ◽  
Time Domain ◽  
Seismic Waves ◽  
Three Dimensional ◽  
Seismic Loads ◽  
Element Analysis ◽  
Artificial Boundaries ◽  
The Time Domain ◽  
Transmitting Boundaries

Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

A finite‐element solution for the transient electromagnetic response of an arbitrary two‐dimensional resistivity distribution

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1450-1461 ◽  
Author(s):  
Y. Goldman ◽  
C. Hubans ◽  
S. Nicoletis ◽  
S. Spitz
Keyword(s):  
Finite Element ◽  
Sparse Matrix ◽  
Equation System ◽  
Electromagnetic Response ◽  
Implicit Time ◽  
Two Dimensional ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Exact Boundary ◽  
The Time Domain

We present a numerical method for solving Maxwell’s equations in the case of an arbitrary two‐dimensional resistivity distribution excited by an infinite current line. The electric field is computed directly in the time domain. The computations are carried out in the lower half‐space only because exact boundary conditions are used on the free surface. The algorithm follows the finite‐element approach, which leads (after space discretization) to an equation system with a sparse matrix. Time stepping is done with an implicit time scheme. At each time step, the solution of the equation system is provided by the fast system ICCG(0). The resulting algorithm produces good results even when large resistivity contrasts are involved. We present a test of the algorithm’s performance in the case of a homogeneous earth. With a reasonable grid, the relative error with respect to the analytical solution does not exceed 1 percent, even 2 s after the source is turned off.

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