Contact Problem Of Conducting And Heated Punch On A Multifield Foundation

The solution for a multifield material subjected to temperature loading in a circular region is presented in an explicit analytical form. The study concerns the steady – state thermal loading infinite region (heated embedded inclusion), half – space region and two – constituent magneto – electro – thermo – elastic material region. The new mono – harmonic potential functions, obtained by the author, are used in the analysis of punch problem. The more interested case in which the contact region is annular is analyzed. By using the methods of triple integral equations and series solution technique the solution for an indentured multifield substrate over an annular contact region is given. The sensitivity analysis of obtained indentation parameters shows some interesting points. In particular, it shows that the increasing of the applied electric and magnetic potentials reduces the indentation depth in multifield materials.

Influence of Intermediate Principal Stress Effect on Flat Punch Problems

Using the finite difference code FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) and UST (Unified Strength Theory), the influence of the intermediate principal stress effect on the problems of flat punch are analyzed in this paper. The values of the ultimate bearing capacity resulting from numerical analyses and the analytical solution of Prandtl’s strip punch problem are compared. The three-dimensional problems of strip, rectangular, square and circular punches on a semi infinite metallic medium have been analyzed.

Punch Problem for Planar Anisotropic Elastic Half-Plane

ABSTRACTThe two dimensional punch problem for planar anisotropic elastic half-plane is revisited using the Lekhnitskii's formulation with aid of the Fourier transform and boundary integral equation. Four different conditions of contact problem for the rigid punch are analyzed in this study. From the combination of surface Green's function of half-plane and Hooke's law of anisotropic material, a set of Fredholm integral equations are obtained for mixed boundary value problems. After solving the integral equation according to specified contact condition, the explicit distributions of surface traction under the punch are obtained in closed-form. From the surface traction and Green's function of anisotropic half-plane, the full-field solutions of stresses are constructed. Numerical calculations of surface traction under the rigid punch are presented base on the analysis and are discussed in detail.

SINGULAR STRESS ANALYSIS IN FLAT PUNCH PROBLEM OF ELASTIC HALF-PLANE

Singular stress analysis in the flat punch problem of half-plane is carried out. The angle distribution for the stress components is also achieved in an explicit form. Followed a similar study in the punch analysis, the punch singular stress factor (abbreviated as PSSF) is defined from the singular stress distribution. For the problems of two punches or three punches, solutions in a closed form are obtained. The obtained solutions may depend on some complete elliptical integrals. Meantime, the exerting location of the resultant force for punches is also determined. Interactions between punches are also addressed. Several numerical examples with the calculated results are presented.

SINGULAR INTEGRAL EQUATION METHOD FOR MULTIPLE FLAT PUNCH PROBLEM FOR AN ELASTIC HALF-PLANE

When a flat punch is indented on elastic half-plane, the singular stress distribution at the vicinity of the punch corners is studied. The angle distribution for the stress components is also achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor is defined. The multiple punch problem can be considered as a superposition of many single punch problems. Taking the stress distribution under the punch base as the unknown function and the deformation under punch as the right-hand term, a set of the singular integral equations for the multiple punch problem can be achieved. After the singular integral equations are solved, the stress distributions under punches can be obtained. In addition, the exerting locations of the resultant forces under punches can also be determined. Two numerical examples with the calculated results are presented.