Comparison of different boundary integral formulations when coupled with finite elements in three dimensions

1988 ◽  
Vol 135 (8) ◽  
pp. 501 ◽  
Author(s):  
Z. Ren ◽  
F. Bouillault ◽  
A. Razek ◽  
J.C. Verite
Keyword(s):  
Finite Elements ◽  
Boundary Integral ◽  
Three Dimensions

scholarly journals Solitary flexural–gravity waves in three dimensions

2018 ◽  
Vol 376 (2129) ◽  
pp. 20170345 ◽  
Author(s):  
Olga Trichtchenko ◽  
Emilian I. Părău ◽  
Jean-Marc Vanden-Broeck ◽  
Paul Milewski
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Cosserat Theory ◽  
Theme Issue ◽  
Flexural Gravity Waves ◽  
Forced Waves ◽  
Ice Phenomena

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369 , 2942–2956 ( doi:10.1098/rsta.2011.0104 )). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

Analysis of Dynamic Response for Piezoelectric Vibration Converter by Finite Element Simulation

2007 ◽  
Vol 336-338 ◽  
pp. 335-337
Author(s):  
Xiang Cheng Chu ◽  
Ren Bo Yan ◽  
Wen Gong ◽  
Long Tu Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Dynamic Response ◽  
Finite Element Modeling ◽  
Three Dimensions ◽  
Dynamic Motion ◽  
Element Simulation ◽  
Piezoelectric Coupling ◽  
Piezoelectric Vibration

The dynamic behavior of a vibration converter of an ultrasonic motor is described using finite element method. Tetrahedral finite elements with three dimensions are formulated with the effects of piezoelectric coupling. And the solution of the coupled electroelastic equations of dynamic motion is presented. The simulated response of the vibration converter is calculated, and shows excellent consistency with experimental results, which proved that finite element modeling is a good approach to optimize piezoelectric apparatus design. A gradual optimized method is employed to ascertain the most compatible structure.

scholarly journals Finite elements for symmetric tensors in three dimensions

2008 ◽  
Vol 77 (263) ◽  
pp. 1229-1251 ◽  
Author(s):  
Douglas N. Arnold ◽  
Gerard Awanou ◽  
Ragnar Winther
Keyword(s):  
Finite Elements ◽  
Three Dimensions ◽  
Symmetric Tensors

3D Adaptive Remeshing Procedure and its Application to Large Deformation Problems

2012 ◽  
Vol 498 ◽  
pp. 199-209
Author(s):  
Jie Zhang ◽  
Abel Cherouat ◽  
Houman Borouchaki
Keyword(s):  
Finite Elements ◽  
Orthogonal Cutting ◽  
Nonlinear Problems ◽  
Posteriori Error ◽  
Three Dimensions ◽  
Local Conditions ◽  
Adaptive Remeshing ◽  
Damage Initiation ◽  
Material Behaviors ◽  
Physical Fields

Metal orthogonal cutting and blanking are two important forming processes which include material removing. During finite element analyzing, the nonlinear problems of boundary, material and geometry must be considered to obtain the accurate calculating results. In this paper, we present an advanced adaptive remeshing procedure which has the capacities to simulate material removing processes in three dimensions. The sizes of finite elements are well adapted to local conditions which have the high distributions of physical fields using priori and posteriori error estimates. Based on constraint Delaunay Kernel, the unit mesh strategy is proposed to improve the mesh quality. By optimizing of both mesh edges and mesh elements, the mesh shape qualities are strictly controlled as the regular tetrahedrons. In this paper, Johnson-cook model is considered to simulate the elastic-visco-plastical material behaviors. The damage initiation is also judged by Johnson-cook criterion. The finite elements which reach the criterion will be killed and the material removing processes finished step by step. The proposed adaptive remeshing scheme is well present using the simulation of metal orthogonal cutting, milling and blanking processes.

A Spectral Boundary-Integral Method for Quasi-Dynamic Ruptures of Multiple Parallel Faults

2021 ◽  
Author(s):  
Sylvain Barbot
Keyword(s):  
Integral Method ◽  
Numerical Models ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Three Dimensions ◽  
Power Law Distribution ◽  
Slow Slip Events ◽  
Multiple Faults ◽  
Rupture Dynamics ◽  
Wide Range

ABSTRACT Numerical models of rupture dynamics provide great insights into the physics of fault failure. However, resolving stress interactions among multiple faults remains challenging numerically. Here, we derive the elastostatic Green’s functions for stress and displacement caused by arbitrary slip distributions along multiple parallel faults. The equations are derived in the Fourier domain, providing an efficient means to calculate stress interactions with the fast Fourier transform. We demonstrate the relevance of the method for a wide range of applications, by simulating the rupture dynamics of single and multiple parallel faults controlled by a rate- and state-dependent frictional contact, using the spectral boundary integral method and the radiation-damping approximation. Within the antiplane strain approximation, we show seismic cycle simulations with a power-law distribution of rupture sizes and, in a different parameter regime, sequences of seismogenic slow-slip events. Using the in-plane strain approximation, we simulate the rupture dynamics of a restraining stepover. Finally, we describe cycles of large earthquakes along several parallel strike-slip faults in three dimensions. The approach is useful to explore the dynamics of interacting or isolated faults with many degrees of freedom.

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