Surface Green Function With Surface Stresses and Surface Elasticity Using Stroh’s Formalism

2008 ◽  
Vol 75 (6) ◽  
pp. 061014 ◽  
Author(s):  
Hideo Koguchi
Keyword(s):  
Green Function ◽  
Surface Elasticity ◽  
Surface Stresses ◽  
Stroh's Formalism ◽  
Surface Green Function ◽  
Stroh’S Formalism

Contact Analysis Using Surface Green’s Functions for Isotropic Materials With Surface Stress and Surface Elasticity

2010 ◽  
Author(s):  
Hideo Koguchi ◽  
Naoki Nishi
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Amorphous Silicon ◽  
Green's Function ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Contact Analysis ◽  
Isotropic Materials ◽  
Stroh's Formalism ◽  
Stroh’S Formalism

Surface stress and surface elasticity are related to an organization of surface pattern and reconstruction of surface atoms. When the size of material reduces to a nanometer level, a ratio of surface to volume increases. Then, surface stress and surface elasticity influence on mechanical response near surface for an external force on the surface. Stroh formalism is very useful for analyzing the stress and displacement in anisotropic materials. When the Stroh’s formalism is applied to isotropic materials, the eigen matrix derived from equilibrium equation yields a triple root of i (i: imaginary unit), and then an independent eigen vector corresponding to the eigen value can not be determined. In this paper, surface Green function for isotropic materials is derived using Stroh’s formalism. The derived Green function considering neither surface stress nor surface elasticity agrees with the solution of Boussinesq. The surface Green’s function considering surface stress and surface elasticity is used for analyzing the displacement fields in amorphous silicon. It was found that the displacements obtained from the Green’s function were less than those from Boussinesq’s solution. Furthermore, the derived surface Green’s function is applied to a contact analysis for isotropic materials such as amorphous silicon. It is found that an apparent Young’s modulus determined from a force-indentation depth curve increases when surface stress and elasticity is taken into account in the analysis.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

2014 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
G. J. Lee ◽  
M. S. Shin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Surface Condition ◽  
Numerical Results ◽  
Forward Speed ◽  
Line Integral ◽  
Free Surface Condition ◽  
Surface Green Function

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

The Stroh Formalism

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
General Solution ◽  
Elastic Body ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Stroh Formalism ◽  
Two Dimensional ◽  
Stroh's Formalism ◽  
Elasticity Problems ◽  
Anisotropic Elastic ◽  
Stroh’S Formalism

In this chapter we study Stroh's sextic formalism for two-dimensional deformations of an anisotropic elastic body. The Stroh formalism can be traced to the work of Eshelby, Read, and Shockley (1953). We therefore present the latter first. Not all results presented in this chapter are due to Stroh (1958, 1962). Nevertheless we name the sextic formalism after Stroh because he laid the foundations for researchers who followed him. The derivation of Stroh's formalism is rather simple and straightforward. The general solution resembles that obtained by the Lekhnitskii formalism. However, the resemblance between the two formalisms stops there. As we will see in the rest of the book, the Stroh formalism is indeed mathematically elegant and technically powerful in solving two-dimensional anisotropic elasticity problems. The possibility of extending the formalism to three-dimensional deformations is explored in Chapter 15.

Free Surface Green Function Research Based on Cloud Computing for Ship Movement on the Water

2013 ◽  
Vol 344 ◽  
pp. 27-30
Author(s):  
Cong Zhang ◽  
Xin Wang ◽  
Jie Zhao ◽  
She Sheng Zhang
Keyword(s):  
Cloud Computing ◽  
Free Surface ◽  
Green Function ◽  
Point Source ◽  
Calculation Procedure ◽  
Green Functions ◽  
Two Dimensional ◽  
Surface Green Function ◽  
Cloud Computation ◽  
Control Equation

In order to easy use Green function on cloud computation, the author consider control equation of point source with free surface, and discuss the representation of Green function on cloud computation, and then propose the discrete calculation expression as well as the calculation procedure. Finally, the two-dimensional graphics of the Green functions real and imaginary parts are plotted.

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