scholarly journals TRANSIENT PLANE WAVES IN MULTILAYERED HALF-SPACE

2013 ◽  
Vol 7 (1) ◽  
pp. 53-57
Author(s):  
Ihor Turchyn ◽  
Olga Turchyn
Keyword(s):  
Half Space ◽  
Normal Load ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Boundary Surface ◽  
Fourier Integral ◽  
Theory Of Elasticity ◽  
Mechanical Contact ◽  
Space Boundary ◽  
And Function

Abstract Considered the dynamic problem of the theory of elasticity for multilayered half-space. Boundary surface of inhomogeneous half-space loaded with normal load, and the boundaries of separation layers are in conditions of ideal mechanical contact. The formulation involves non-classical separation of equations of motion using two functions with a particular mechanical meaning volumetric expansion and function of acceleration of the shift. In terms of these functions obtained two wave equation, written boundary conditions and the conditions of ideal mechanical contact of layers. Using the Laguerre and Fourier integral transformations was obtained the solution of the formulated problem. The results of the calculation of the stress-strain state in the half-space with a coating for a local impact loading are presented.

Reflection of plane waves from the boundary of an initially stressed incompressible half-space

2017 ◽  
Vol 24 (2) ◽  
pp. 406-433 ◽  
Author(s):  
M Shams
Keyword(s):  
Initial Stress ◽  
Half Space ◽  
Plane Waves ◽  
Strain Energy Function ◽  
Prototype Strain ◽  
Incompressible Material ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Plane Boundary ◽  
Infinitesimal Deformations

In this paper, nonlinear theory of elasticity is used to study the effect of initial stress on plane waves in an incompressible material. For this problem, the initial stress is not associated with a finite elastic deformation and the material is assumed to be isotropic in the absence of the initial stress. The theory of superposition of infinitesimal deformations on finite deformation is applied to a problem of plane incremental motions in an initially stressed incompressible homogeneous elastic half-space. The general formulation of the problem is presented first and then specialized using a prototype strain energy function. Homogeneous plane waves are considered and the analysis is carried out for incompressible materials in both the deformed and the undeformed reference configurations. In addition to this, problems for the reflection of small amplitude homogeneous waves from the plane boundary of an initially stressed half-space are also considered and graphical results are included, which show the effect of initial stress on reflection. It is noted that the reflection coefficients in this case behave in a similar fashion when the initial stress is a pre-stress.

Load Buckling of a Layer Bonded to a Half-Space With an Interface Crack

1995 ◽  
Vol 62 (1) ◽  
pp. 64-70 ◽  
Author(s):  
Wen-Xue Wang ◽  
Yoshihiro Takao
Keyword(s):  
Half Space ◽  
Interface Crack ◽  
Integral Transform ◽  
Local Buckling ◽  
Compressive Load ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Theory Of Elasticity ◽  
Layered System ◽  
Cauchy Type

An analytical solution is presented for local buckling of a model of delaminated composites, that is, a layer bonded to a half-space with an interface crack. The layered system is subjected to compressive load parallel to the free surface. Basic stability equations derived from the mathematical theory of elasticity are employed to study this local buckling behavior. They are different from the conventional buckling equations used in most previous studies and based on the classical structural mechanics of beams and plates. A system of homogeneous Cauchy-type singular integral equations of the second kind is formulated by means of the Fourier integral transform and is solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for the buckling load and shape are presented for various delamination geometries and material properties of both the layer and half-space.

scholarly journals Doublel-robot coordination workspace Analysis based on Matlab

2018 ◽  
Vol 232 ◽  
pp. 03057
Author(s):  
Wei Wang ◽  
Yong Xu
Keyword(s):  
Boundary Surface ◽  
Value Theory ◽  
Working Space ◽  
The Monte Carlo Method ◽  
Workspace Analysis ◽  
Solution Equation ◽  
Space Boundary ◽  
Robot Cooperation ◽  
Limit Position ◽  
Cooperation System

Aiming at the requirements of dual robot collaborative operation, a dual robot cooperation system model is established in SolidWorks2012 software to study the dual robot cooperation space. The D-H parameters are established, and the kinematics positive solution equation is obtained. The dual robot cooperative kinematics model is given. Based on the Monte Carlo method, the workspace of the dual robot is solved. The extreme value theory method is used to analyze and calculate, so as to extract the precise boundary contour of the common area of the dual robot workspace, and the collaborative space boundary surface and limit position of the dual robot are determined. The optimal coordinated working space of the dual robot end effector is obtained, which lays a theoretical foundation for the coordinated trajectory planning of the dual robot.

Bounds on the Maximum Contact Stress of an Indented Elastic Layer

1971 ◽  
Vol 38 (3) ◽  
pp. 608-614 ◽  
Author(s):  
Y. C. Pao ◽  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Elastic Layer ◽  
Theory Of Elasticity ◽  
Contact Conditions ◽  
Practical Applications ◽  
Method Of Solution ◽  
Elastic Layers ◽  
Maximum Contact ◽  
Contact Stress Distribution

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.

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