scholarly journals Elastodynamic Solutions of a Finite Soil Layer under Interior Distributed Actions

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Shiping Zhang ◽  
Zhan Xu
Keyword(s):  
Elastic Layer ◽  
Integral Transformation ◽  
Boundary Integral Equations ◽  
Interaction Analysis ◽  
Soil Layer ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Generalized Solutions ◽  
Rigid Base ◽  
Surface Load

Through a method of displacement potentials, Fourier series, and Hankel integral transformation, the generalized solutions of an elastic layer resting on a rigid base under arbitrary, distributed, buried, and time-harmonic loads are developed in this study. With the proposed solution, the specific results for two kinds of uniform distributions as a kind of fundamental solutions in the interaction analysis of media and inclusions by the method of boundary integral equations are included as illustrations. Finally, numerical examples involving surface and buried patch loads are presented to validate the solutions and examine the effects of the thickness of the elastic layer. The results show that the proposed solution can cover the classical half-space solution by taking enough large thickness of the elastic layer (e.g., the ratio of the layer thickness beneath the load to the load radius ≥ 50 ) and the surface load solution by setting the load depth to zero; the underlying rigid base has significant and complex influence on the dynamic response of the thin layer due to wave reflections, which needs to be considered in the design and practice of related engineering.

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.

Analysis of Cracks in Functionally Graded Piezoelectric Materials by a Frequency-Domain BEM

2017 ◽  
Vol 754 ◽  
pp. 149-152
Author(s):  
Michael Wünsche ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Ch. Zhang ◽  
M. Repka
Keyword(s):  
Frequency Domain ◽  
Boundary Integral Equations ◽  
Piezoelectric Materials ◽  
Domain Boundary ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Singular Boundary ◽  
Square Root ◽  
Functionally Graded Piezoelectric Materials

Time-harmonic crack analysis in two-dimensional piezoelectric functionally graded materials (FGMs) is presented in this paper. A frequency-domain boundary element method (BEM) is developed for this purpose. Since fundamental solutions for piezoelectric FGMs are not available, a boundary-domain integral formulation is derived. This requires only the frequency-domain fundamental solutions for homogeneous piezoelectric materials. The radial integration method is adopted to compute the resulting domain integrals. The collocation method is used for the spatial discretization of the frequency-domain boundary integral equations. Adjacent the crack-tips square-root elements are implemented to capture the local square-root-behavior of the generalized crack-opening-displacements properly. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. Numerical examples will be presented and discussed to show the influences of the material gradation and the dynamic loading on the intensity factors.

Revisit of Two Classical Elasticity Problems by using the Null-Field Boundary Integral Equations

2010 ◽  
Vol 26 (3) ◽  
pp. 393-401 ◽  
Author(s):  
J. T. Chen ◽  
Y. T. Lee ◽  
K. H. Chou
Keyword(s):  
Fourier Series ◽  
Boundary Integral Equations ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Degenerate Kernel ◽  
Classical Elasticity ◽  
Field Boundary ◽  
Null Field ◽  
Lamé Problem ◽  
Elasticity Problems

AbstractIn this paper, the two classical elasticity problems, Lamé problem and stress concentration factor, are revisited by using the null-field boundary integral equation (BIE). The null-field boundary integral formulation is utilized in conjunction with degenerate kernels and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. In the two classical problems of elasticity, the null-field BIE is employed to derive the exact solutions. The Kelvin solution is first separated to degenerate kernel in this paper. After employing the null-field BIE, not only the stress but also the displacement field are obtained at the same time. In a similar way, Lamé problem is solved without any difficulty.

scholarly journals METHOD OF GENERALIZED FUNCTIONS IN PLANE BOUNDARY VALUE PROBLEMS OF UNCOUPLED THERMOELASTODYNAMICS

2021 ◽  
Author(s):  
Assiyat Dadayeva ◽  
Lyudmila Alexeyeva
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Generalized Functions ◽  
Boundary Integral ◽  
Generalized Solutions ◽  
Plane Boundary ◽  
Unknown Boundary ◽  
Singular Boundary

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

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.

scholarly journals Numerical quadrature for the approximation of singular oscillating integrals appearing in boundary integral equations

2006 ◽  
Vol 4 ◽  
pp. 11-15 ◽  
Author(s):  
L. O. Fichte ◽  
S. Lange ◽  
M. Clemens
Keyword(s):  
Integral Transformation ◽  
Boundary Integral Equations ◽  
Logarithmic Singularity ◽  
Error Function ◽  
Computation Time ◽  
Boundary Integral ◽  
Numerical Quadrature ◽  
Integration Techniques ◽  
Abstract Boundary ◽  
Standard Integration

Abstract. Boundary Integral Equation formulations can be used to describe electromagnetic shielding problems. Yet, this approach frequently leads to integrals which contain a singularity and an oscillating part. Those integrals are difficult to handle when integrated naivly using standard integration techniques, and in some cases even a very high number of integration nodes will not lead to precise results. We present a method for the numerical quadrature of an integral with a logarithmic singularity and a cosine oscillator: a modified Filon-Lobatto quadrature for the oscillating parts and an integral transformation based on the error function for the singularity. Since this integral can be solved analytically, we are in a position to verify the results of our investigations, with a focus on precision and computation time.

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