Analytical solution to scattering of SH waves by a circular lined tunnel embedded in a semi–circular alluvial valley in an elastic half–space

2020 ◽  
Vol 106 ◽  
pp. 103615
Author(s):  
Ning Zhang ◽  
Xin Chen ◽  
Yufeng Gao ◽  
Denghui Dai
Keyword(s):  
Analytical Solution ◽  
Half Space ◽  
Elastic Half Space ◽  
Alluvial Valley ◽  
Sh Waves

Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

2021 ◽  
pp. 1-24
Author(s):  
Liguo Jin ◽  
Liting Du ◽  
Haiyan Wang
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Half Space ◽  
Strong Interaction ◽  
Rigid Foundation ◽  
Structural Stiffness ◽  
Sh Waves ◽  
Closed Form Analytical Solution ◽  
Flexible Foundation ◽  
Plane Sh Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

Dynamic Response of a Hemispherical Foundation Embedded in an Elastic Half-Space

1998 ◽  
Vol 120 (4) ◽  
pp. 343-348 ◽  
Author(s):  
C.-S. Yeh ◽  
T.-J. Teng ◽  
W.-I. Liao
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Ground Surface ◽  
Integral Equation Method ◽  
Elastic Half Space ◽  
Least Square ◽  
Sh Waves ◽  
Soil Foundation ◽  
External Forces ◽  
Impedance Functions

The dynamic response of a massless rigid hemispherical foundation embedded in a uniform homogeneous elastic half-space is considered in this study. The foundation is subjected to external forces, moments, plane harmonic P and SH waves, respectively. The series solutions are constructed by three sequences of Lamb’s singular solutions which satisfy the traction-free conditions on ground surface and radiation conditions at infinity, automatically, and their coefficients are determined by the boundary conditions along the soil-foundation interface in the least square sense. The fictitious eigen-frequencies, which arise in integral equation method, will not appear in the numerical calculation by the proposed method. The impedance functions which characterize the response of the foundation to external harmonic forces and moments at low and intermediate frequencies are calculated and the translational and rocking responses of the foundation when subjected to plane P and SH waves are also presented and discussed in detail.

Analytical solution of elastic deformations inside and outside circular contact area between tilted rigid punch and elastic half space

2019 ◽  
Vol 230 (12) ◽  
pp. 4311-4320 ◽  
Author(s):  
Yoji Iguchi ◽  
Pasomphone Hemthavy ◽  
Shigeki Saito ◽  
Kunio Takahashi
Keyword(s):  
Analytical Solution ◽  
Half Space ◽  
Contact Area ◽  
Elastic Half Space ◽  
Rigid Punch ◽  
Elastic Deformations ◽  
Circular Contact

An Efficient Semi-Analytical Method to Compute Displacements and Stresses in an Elastic Half-Space with a Hemispherical Pit

2015 ◽  
Vol 7 (3) ◽  
pp. 295-322 ◽  
Author(s):  
Valeria Boccardo ◽  
Eduardo Godoy ◽  
Mario Durán
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Half Space ◽  
Plane Surface ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Quadratic Functional ◽  
Infinite Plane ◽  
Equilibrium Equations ◽  
Finite Element Software

AbstractThis paper presents an efficient method to calculate the displacement and stress fields in an isotropic elastic half-space having a hemispherical pit and being subject to gravity. The method is semi-analytical and takes advantage of the axisymmetry of the problem. The Boussinesq potentials are used to obtain an analytical solution in series form, which satisfies the equilibrium equations of elastostatics, traction-free boundary conditions on the infinite plane surface and decaying conditions at infinity. The boundary conditions on the free surface of the pit are then imposed numerically, by minimising a quadratic functional of surface elastic energy. The minimisation yields a symmetric and positive definite linear system of equations for the coefficients of the series, whose particular block structure allows its solution in an efficient and robust way. The convergence of the series is verified and the obtained semi-analytical solution is then evaluated, providing numerical results. The method is validated by comparing the semi-analytical solution with the numerical results obtained using a commercial finite element software.

Scattering of SH waves by a shallow rectangular cavity in an elastic half space

2016 ◽  
Vol 90 ◽  
pp. 147-157 ◽  
Author(s):  
Qijian Liu ◽  
Chao Zhang ◽  
Maria I. Todorovska
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Rectangular Cavity ◽  
Sh Waves

scholarly journals MATHEMATICAL MODELING OF EXPERIMENT ON BERKOVICH NANOINDENTATION OF ZRN COATING ON STEEL SUBSTRATE

2020 ◽  
Vol 27 ◽  
pp. 18-21
Author(s):  
Evgeniy Sadyrin ◽  
Andrey Vasiliev ◽  
Sergei Volkov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Steel Substrate ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Good Agreement

In the present paper the experiment on Berkovich nanoindentation of ZrN coating on steel substrate is modelled using the proposed effective mathematical model. The model is intended for describing the experiments on indentation of samples with coatings (layered or functionally graded). The model is based on approximated analytical solution of the contact problem on indentation of an elastic half-space with a coating by a punch. It is shown that the results of the model and the experiment are in good agreement.

Sign in / Sign up

Export Citation Format

Share Document