Boundary element with wavenumber integration simulation of wave propagation in a fluid‐filled borehole with arbitrary shape: Theory and preliminary results

2007 ◽  
Author(s):  
Zengxi Ge ◽  
Xiaofei Chen
Keyword(s):  
Wave Propagation ◽  
Boundary Element ◽  
Arbitrary Shape ◽  
Shape Theory ◽  
Preliminary Results

Modeling of Wave Propagation in the Unsaturated Soils Using Boundary Element Method

2017 ◽  
Vol 743 ◽  
pp. 158-161
Author(s):  
Andrey Petrov ◽  
Sergey Aizikovich ◽  
Leonid A. Igumnov
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equation ◽  
Boundary Integral Equations ◽  
Water Pressure ◽  
Boundary Integral ◽  
Element Method

Problems of wave propagation in poroelastic bodies and media are considered. The behavior of the poroelastic medium is described by Biot theory for partially saturated material. Mathematical model is written in term of five basic functions – elastic skeleton displacements, pore water pressure and pore air pressure. Boundary element method (BEM) is used with step method of numerical inversion of Laplace transform to obtain the solution. Research is based on direct boundary integral equation of three-dimensional isotropic linear theory of poroelasticity. Green’s matrices and, based on it, boundary integral equations are written for basic differential equations in partial derivatives. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. To approximate the boundary consider its decomposition to a set of quadrangular and triangular 8-node biquadratic elements, where triangular elements are treated as singular quadrangular. Every element is mapped to a reference one. Interpolation nodes for boundary unknowns are a subset of geometrical boundary-element grid nodes. Local approximation follows the Goldshteyn’s generalized displacement-stress matched model: generalized boundary displacements are approximated by bilinear elements whereas generalized tractions are approximated by constant. Integrals in discretized boundary integral equations are calculated using Gaussian quadrature in combination with singularity decreasing and eliminating algorithms.

scholarly journals A New BEM for Modeling and Simulation of Laser Generated Ultrasound Waves in 3T Fractional Nonlinear Generalized Micropolar Poro-Thermoelastic FGA Structures

2020 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Wave Propagation ◽  
Modeling And Simulation ◽  
Boundary Element ◽  
Functionally Graded ◽  
Acoustic Wave Propagation ◽  
Ultrasound Waves ◽  
Special Cases ◽  
Waves Propagation ◽  
Element Technique ◽  
Boundary Element Technique

In this chapter, we introduce a new theory called acoustic wave propagation of three-temperature fractional nonlinear generalized micropolar poro-thermoelasticity and we propose a new boundary element technique for modeling and simulation of laser-generated ultrasonic wave propagation problems of functionally graded anisotropic (FGA) structures which are linked with the proposed theory. Since it is very difficult to solve general acoustic problems of this theory analytically, we need to develop and use new computational modeling techniques. So, we propose a new boundary element technique for solving such problems. The numerical results are shown graphically to depict the effects of three temperatures on the thermal stress waves propagation. The validity, accuracy, and efficiency of our proposed theory and the technique are examined and demonstrated by comparing the obtained outcomes with those previously reported in the literature as special cases of our general study.

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