Quasi-static response of a layered viscoelastic half-space to general surface loading

1991 ◽  
Vol 28 (6) ◽  
pp. A343
Author(s):  
Z.Y. Ding ◽  
Y.Q. Shen
Keyword(s):  
Half Space ◽  
Static Response ◽  
Surface Loading ◽  
General Surface

scholarly journals Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Supakorn Tirapat ◽  
Teerapong Senjuntichai ◽  
Jaroon Rungamornrat
Keyword(s):  
Surface Energy ◽  
Half Space ◽  
Integral Transform ◽  
Integral Form ◽  
Form Solution ◽  
Numerical Results ◽  
Stress Fields ◽  
Surface Loading ◽  
Elastic Fields ◽  
Analytical Technique

This paper presents the analysis of a layered elastic half space under the action of axisymmetric surface loading and the influence of the surface energy effects. The boundary value problems for the bulk and the surface are formulated based on classical linear elasticity and a complete Gurtin-Murdoch constitutive relation. An analytical technique using Love’s representation and the Hankel integral transform is employed to derive an integral-form solution for both displacement and stress fields. An efficient numerical quadrature is then applied to accurately evaluate all involved integrals. Selected numerical results are presented to portray the influence of various parameters on elastic fields. Numerical results indicate that the surface stress displays a significant influence on both displacement and stress fields. It is also found that the layered half space becomes stiffer with the presence of surface stresses. In addition, unlike the classical elasticity solution, size-dependent behavior of elastic fields is noted. The present analytical solutions provide fundamental understanding of the influence of surface energy on layered elastic materials. It can also be used as a benchmark solution for the development of numerical techniques such as FEM and BEM, for analysis of more complex problems involving a layered medium under the influence of surface energy effects.

EXPLICIT SOLUTIONS FOR AN ANISOTROPIC PIEZOELECTRIC HALF-SPACE SUBJECT TO LINEARLY-VARYING SURFACE LOADINGS ALONG x3-DIRECTION

2014 ◽  
Vol 06 (06) ◽  
pp. 1450074 ◽  
Author(s):  
M. Y. CHUNG
Keyword(s):  
Half Space ◽  
Explicit Solution ◽  
Efficient Solution ◽  
Displacement Vector ◽  
Polynomial Solution ◽  
Three Dimensional ◽  
Stroh Formalism ◽  
Explicit Solutions ◽  
Surface Loading ◽  
Space Problem

Explicit results for a piezoelectric half-space x2 ≥ 0 subject to linearly-varying surface loadings along x3 axis are derived. The extended Stroh formalism is employed to provide three-dimensional solutions with the generalized displacement vector u expressed as a function of (z, x2, x3). A general polynomial solution for u with order of m in x3 is suggested and it provides a particularly efficient solution for half-space problem with loadings on the surface. A simple uniform surface loading is considered first to clarify the derivations. Then explicit solution in case of a linearly-varying surface loading along x3-direction is obtained. In addition, the Green's function for a piezoelectric half-space with a linearly-varying surface line loading along x3-axis is constructed.

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