Dynamic Response of Elastic Half-Space with Cavity Subjected to P and SV Waves by Finite/Infinite Element Approach

2015 ◽  
Vol 15 (07) ◽  
pp. 1540009 ◽  
Author(s):  
Y. B. Yang ◽  
Hsiao-Hui Hung ◽  
Kuan-Chung Lin ◽  
Kai-Wen Cheng
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Three Solutions ◽  
Element Mesh ◽  
Infinite Element ◽  
Infinite Elements ◽  
Element Approach ◽  
The Difference ◽  
P And Sv Waves ◽  
Incident Waves

The problem of a half-space with cavity under vertically incident waves was solved by many researchers using different approaches. However, substantially different solutions were obtained, partially due to the difference in the method of formulation, and partially due to the lack of complete identical data for use in analysis. In this paper, the finite/infinite element approach has been adopted to study the two-dimensional response of an elastic half-space containing a buried, unlined, infinitely long cylindrical of circular shape subjected to harmonic P and SV waves. First, the analysis procedure based on the finite and infinite elements is summarized. Second, considerations in preparing the finite element mesh to ensure the accuracy and convergence of the solution are presented. Next, the validity of the procedure of solution is verified for some intuitive, fundamental cases. Finally, the problems solved by previous researchers with identical or assumed data will be re-solved, along with discussions on the discrepancies existing among the three solutions. One feature with the finite/infinite element approach is that it is simple and straightforward, involving less assumptions and mathematical operations, whose reliability has been verified in solving various soil vibration problems. The fact that the present solutions are in close agreement to those by Luco and De Barros (1994) for all the cases studied indicates that the latter is the most reliable one among the existing theories.

Numerical Analyses for Layered Foundation by Coupling Finite and Axis-Radiate Infinite Elements

2011 ◽  
Vol 90-93 ◽  
pp. 359-364
Author(s):  
Hong Yang Xie ◽  
Huan Yang ◽  
Jin Quan Yin
Keyword(s):  
Numerical Calculation ◽  
Good Accuracy ◽  
Elastic Recovery ◽  
Rigid Base ◽  
Artificial Boundary ◽  
Element Mesh ◽  
Mapping Functions ◽  
Infinite Element ◽  
Infinite Elements ◽  
Recovery Capacity

The model of the axis-radiate infinite element is developed for simulation of the infinite layered foundation underlain by a rigid base. Within the infinite element, the coordinate and displacement of any point are expressed by those of the nodes located on the artificial boundary, and concise mapping functions can easily express the attenuation character of the displacement field. By coupling finite and infinite elements, the elastic recovery capacity and radiation damping of the infinite layered foundation are simulated. In the numerical calculation, the infinite element mesh is performed only on the artificial boundary. Compared to FEM, the present approach needs less nodes and elements, and shows good accuracy and efficiency.

scholarly journals A COMPARISON OF TRANSIENT INFINITE ELEMENTS AND TRANSIENT KIRCHHOFF INTEGRAL METHODS FOR FAR FIELD ACOUSTIC ANALYSIS

2013 ◽  
Vol 21 (02) ◽  
pp. 1350006 ◽  
Author(s):  
TIMOTHY F. WALSH ◽  
ANDREA JONES ◽  
MANOJ BHARDWAJ ◽  
CLARK DOHRMANN ◽  
GARTH REESE ◽  
...  
Keyword(s):  
Acoustic Pressure ◽  
Acoustic Analysis ◽  
System Stability ◽  
Far Field ◽  
Element Analysis ◽  
Infinite Element ◽  
Infinite Elements ◽  
Integral Methods ◽  
Element Approach ◽  
Kirchhoff Integral

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, one derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. We show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.

Transient and Time-Harmonic Infinite Elements for Near-Surface Computations of Three-Dimensional Structures Submerged in a Half-Space

1995 ◽  
Author(s):  
Loukas F. Kallivokas ◽  
Jacobo Bielak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Half Space ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Near Surface ◽  
Infinite Element ◽  
Infinite Elements ◽  
Time Harmonic ◽  
Element Method

Abstract This paper is concerned with the numerical solution by the finite element method of transient and time-harmonic three-dimensional acoustic scattering problems in infinite and semi-infinite domains. Its main objective is to illustrate how a local second-order surface-only infinite element — either transient or time-harmonic — developed recently for the three-dimensional wave equation in a full-space can be applied readily to scattering problems with penetrable objects near a planar free surface. Taking a problem in structural acoustics as a prototype, the combined infinite element-finite element method is used here to determine the total and scattered pressure patterns generated when a traveling plane wave impinges upon a structure of general geometry submerged in an acoustic fluid in half-space. One key feature of this methodology is that the ordinary differential equations that result from the spatial discretization maintain the symmetry and sparsity associated with problems defined only over interior domains; the resulting equations can then be solved by standard step-by-step time integration techniques. Thus, the combination of low bandwidth matrices with the ease of use of the infinite elements places the method in an ideal position to meet the large computational demands typically associated with large-scale underwater acoustics problems.

Note on the use of reciprocity theorem for obtaining radiation patterns

1965 ◽  
Vol 55 (2) ◽  
pp. 277-281 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Far Field ◽  
Radiation Patterns ◽  
Vertical Displacements ◽  
Field Radiation ◽  
P And Sv Waves

Abstract Expressions for the horizontal and vertical displacements at the surface of an elastic half space when plane harmonic P or SV waves are incident at any given angle are already known. On the basis of the reciprocity theorem, these expressions are used to obtain “far-field” radiation patterns of P and SV waves due to horizontal and vertical forces applied at the free surface.

scholarly journals Studying the interaction of a reservoir with an ideal compressible fluid with an elastic half-space

2021 ◽  
Vol 2099 (1) ◽  
pp. 012032
Author(s):  
I S Telyatnikov ◽  
A V Pavlova ◽  
S E Rubtsov
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Compressible Fluid ◽  
Hydrodynamic Pressure ◽  
Factorization Method ◽  
Elastic Half Space ◽  
Harmonic Oscillations ◽  
Vibration Load ◽  
Vibration Loads ◽  
The Difference

Abstract We solve in a flat formulation the problem of harmonic oscillations for a basin with an ideal compressible fluid on an elastic half-space exposed to a localized surface vibration load. The problem reduces to an integral equation (IE) of the first kind for the amplitude of the contact hydrodynamic pressure with a kernel that depends on the difference and the sum of arguments. The IE was solved by the factorization method. A semi-analytical method is presented for determining the main parameters of the contact interaction in hydroelastic systems «liquid-soil» taking into account the effect of natural and man-made vibration loads on them. This makes it possible to identify the conditions for the occurrence of dynamic modes that are dangerous for the construction integrity and to estimate their frequencies range depending on defining characteristics of the system.

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