Semi-Permeable Cracks in Magnetoelectroelastic Solids under Impact Loading

2011 ◽  
Vol 488-489 ◽  
pp. 751-754 ◽  
Author(s):  
Michael Wünsche ◽  
Andrés Sáez ◽  
Chuan Zeng Zhang ◽  
Felipe García-Sánchez
Keyword(s):  
Boundary Conditions ◽  
Boundary Integral Equations ◽  
Domain Boundary ◽  
Crack Opening ◽  
Iterative Algorithms ◽  
Boundary Integral ◽  
Dynamic Crack ◽  
Permeable Crack ◽  
Crack Face ◽  
Magnetoelectroelastic Solids

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids by considering different electrical and magnetical crack-face boundary conditions is presented. For this purpose, a time-domain boundary element method (TDBEM) using dynamic fundamental solutions is developed. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is applied to compute the discrete boundary data and the generalized crack-opening-displacements. Iterative algorithms are implemented to deal with the non-linear electrical and magnetical semi-permeable crack-face boundary conditions.

Cracks in Magnetoelectroelastic Solids under Impact Loading

2009 ◽  
Vol 417-418 ◽  
pp. 377-380
Author(s):  
Michael Wünsche ◽  
Andrés Sáez ◽  
Felipe García-Sánchez ◽  
Chuan Zeng Zhang
Keyword(s):  
Boundary Integral Equations ◽  
Domain Boundary ◽  
Crack Opening ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Dynamic Crack ◽  
Time Stepping ◽  
Convolution Integrals ◽  
Magnetoelectroelastic Solids ◽  
Dynamic Loading Conditions

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed and the elastodynamic fundamental solutions for linear magnetoelectroelastic and anisotropic materials are derived. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the generalized crack-opening-displacements. To show the effects of the coupled fields and the different dynamic loading conditions on the dynamic intensity factors, numerical examples will be presented and discussed.

Interface Crack in Anisotropic Solids under Impact Loading

2007 ◽  
Vol 348-349 ◽  
pp. 73-76 ◽  
Author(s):  
Michael Wünsche ◽  
Chuan Zeng Zhang ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Sohichi Hirose
Keyword(s):  
Time Domain ◽  
Boundary Integral Equations ◽  
Domain Boundary ◽  
Crack Opening ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Dynamic Crack ◽  
Dynamic Stress Intensity Factors ◽  
Linear Elastic ◽  
Anisotropic Layers

In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear elastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The homogeneous and anisotropic layers are modeled by the multi-domain BEM formulation. Time-domain elastodynamic fundamental solutions for linear elastic and anisotropic solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the crack-opening-displacements (CODs). To show the effects of the material anisotropy and the dynamic loading on the dynamic stress intensity factors, numerical examples are presented and discussed.

Dynamic Crack Analysis in Layered Piezoelectric Composites under Time-Harmonic Loading

2013 ◽  
Vol 577-578 ◽  
pp. 449-452
Author(s):  
Michael Wünsche ◽  
Felipe García-Sánchez ◽  
Chuan Zeng Zhang ◽  
Andrés Sáez
Keyword(s):  
Frequency Domain ◽  
Boundary Integral Equations ◽  
Piezoelectric Materials ◽  
Iterative Solution ◽  
Boundary Integral ◽  
Dynamic Crack ◽  
Crack Face ◽  
Piezoelectric Composites ◽  
Crack Analysis ◽  
Time Harmonic

In this Paper, Time-Harmonic Dynamic Crack Analysis in Two-Dimensional (2D), Layered and Linear Piezoelectric Composites is Presented. A Frequency-Domain Symmetric Galerkin Boundary Element Method (SGBEM) is Developed for this Purpose. the Piecewise Homogeneous Sub-Layers of the Piezoelectric Composites are Modeled by the Multi-Domain BEM Formulation. the Frequency-Domain Dynamic Fundamental Solutions for Linear Piezoelectric Materials are Applied in the Present BEM. the Boundary Integral Equations are Solved Numerically by a Galerkin-Method Using Quadratic Elements. an Iterative Solution Algorithm is Implemented to Consider the Non-Linear Semi-Permeable Electrical Crack-Face Boundary Conditions. Numerical Examples will be Presented and Discussed to Show the Influences of the Location and Size of the Crack, the Material Combination of the Sub-Layers, the Piezoelectric Effect and the Time-Harmonic Dynamic Loading on the Dynamic Intensity Factors.

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

A B-Spline Based BEM for Unsteady Free-Surface Flows

1999 ◽  
Vol 43 (01) ◽  
pp. 13-24
Author(s):  
M. Landrini ◽  
G. Grytøyr ◽  
O. M. Faltinsen
Keyword(s):  
Free Surface ◽  
Evolution Equations ◽  
Boundary Integral Equations ◽  
Fluid Dynamic ◽  
Domain Boundary ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Surface Flows ◽  
B Spline ◽  
Nonlinear Free Surface

Fully nonlinear free-surface flows are numerically studied in the framework of the potential theory. The problem is formulated in terms of boundary integral equations which are solved by means of an arbitrary high-order boundary element method based on B-Spline representation of both the geometry and the fluid dynamic variables along the domain boundary. The solution is stepped forward in time either by following Lagrangian points attached to the free surface or by a less conventional scheme in which evolution equations for the B-Spline coefficients are integrated in time. Numerical examples for inner and outer free-surface flows are shown. The accuracy of the numerical solution is assessed either by checking mass and energy conservation or by comparing with reference solutions. Good results are generally obtained. Extended use of the developed algorithm to more applied problems in the context of naval hydrodynamics is now under development.

Dynamic Fracture Analysis of Plates Loaded in Tension and Bending Using the Dual Boundary Element Method

2019 ◽  
Vol 827 ◽  
pp. 440-445
Author(s):  
Jun Li ◽  
Zahra Sharif Khodaei ◽  
Ferri M.H. Aliabadi
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Dynamic Fracture ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Fracture Analysis ◽  
Boundary Integral ◽  
Mindlin Plate ◽  
Dual Boundary Element Method ◽  
Element Method

The purpose of this paper is to solve dynamic fracture problems of plates under both tension and bending using the boundary element method (BEM). The dynamic problems were solved in the Laplace-transform domain, which avoided the calculation of the domain integrals resulting from the inertial terms. The dual boundary element method, in which both displacement and traction boundary integral equations are utilized, was applied to the modelling of cracks. The dynamic fracture analysis of a plate under combined tension and bending loads was conducted using the BEM formulations for the generalized plane stress theory and Mindlin plate bending theory. Dynamic stress intensity factors were estimated based on the crack opening displacements.

ALTERNATIVE TIME DOMAIN BOUNDARY INTEGRAL EQUATIONS FOR THE SCALAR WAVE EQUATION USING DIVERGENCE-FREE REGULARIZATION TERMS

2009 ◽  
Vol 17 (02) ◽  
pp. 211-218
Author(s):  
GEORGIOS NATSIOPOULOS
Keyword(s):  
Wave Equation ◽  
Integral Equations ◽  
Time Domain ◽  
Boundary Integral Equations ◽  
Domain Boundary ◽  
Short Note ◽  
Boundary Integral ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Divergence Free

In this short note alternative time domain boundary integral equations (TDBIE) for the scalar wave equation are formulated on a surface enclosing a volume. The technique used follows the traditional approach of subtracting and adding back relevant Taylor expansion terms of the field variable, but does not restrict this to the surface patches that contain the singularity only. From the divergence-free property of the added-back integrands, together with an application of Stokes' theorem, it follows that the added-back terms can be evaluated using line integrals defined on a cut between the surface and a sphere whose radius increases with time. Moreover, after a certain time, the line integrals may be evaluated directly. The results provide additional insight into the theoretical formulations, and might be used to improve numerical implementations in terms of stability and accuracy.

Vibration of a Simply Supported L-Shaped Plate

1997 ◽  
Vol 119 (3) ◽  
pp. 464-467 ◽  
Author(s):  
R. Solecki
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Natural Vibration ◽  
Boundary Integral Equations ◽  
Rectangular Domain ◽  
Boundary Integral ◽  
Theoretical Development ◽  
Natural Vibrations ◽  
Simply Supported ◽  
Discontinuous Functions

Recently Solecki (1996) has shown that a differential equation for vibration of a rectangular plate with a cutout can be reduced to boundary integral equations. This was accomplished by filling the cutout with a “patch” made of the same material as the rest of the plate and separated from it by an infinitesimal gap. Thanks to this procedure it was possible to apply finite Fourier transformation of discontinuous functions in a rectangular domain. Subsequent application of the available boundary conditions led to a system of boundary integral equations. A plate simply supported along the perimeter, and fixed along the cutout (an L-shaped plate), was analyzed as an example. The general solution obtained by Solecki (1996) serves here to determine the frequencies of natural vibration of a L-shaped plate simply supported all around its perimeter. This problem is, however, more complicated than the previous example: to satisfy the boundary conditions an infinite series depending on discontinuous functions must be differentiated. The theoretical development is illustrated by numerical values of the frequencies of the natural vibrations of a square plate with a square cutout. The results are compared with the results obtained using finite elements method.

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