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Analog-discrete approach for the solution of a class of rigid-contact problems

A combined application of electrical analog model and finite-difference technique is presented to determine stresses and displacements produced in a semi-infinite elastic solid by a rigid footing (or punch) of any arbitrary shape at its plane boundary

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Abstract

This investigation consists in finding stresses and displacements produced by a rigid footing (or punch) at the plane boundary of a semi-infinite elastic solid. The proposed method is a combined application of electrical analog and finite-difference technique and can be applied to any arbitrary shape of rigid footing (or punch). The experimental setup is very simple and the numerical-analysis part is easily amenable to computer programming. The method has been exemplified by 3 cases: (1) rigid strip footing (or punch); (2) rigid circular footing (or punch); and (3) rigid square footing (or punch) on a three-dimensional semi-infinite solid. The results, wherever possible, have been compared with exact solutions and have been found to be in close agreement.

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Abbreviations

A :

some linear dimension of footing

B :

half width of strip or half of side of square

E :

modulus of elasticity

a tog :

finite-difference-equation coefficients

H :

nodal spacing

l,m :

nodal-spacing coefficients

q :

applied pressure

R :

dimensionless distance from origin

S :

summation of potentials

u, v, w :

displacement components inx, y, z directions

V :

inverse potential (nondimensional)

w 0 :

depression under loading area

x, y, z :

cartesian coordinates

X, Y, Z :

nondimensional cartesian coordinates

ζ:

depth variable

γxy, γxz, γyz :

shear-strain components

ε x , ε y , ε z :

unit elongation alongx, y, z directions

ξ, η:

loading-area coordinates

θ:

logarithmic potential

ν:

Poisson's ratio

σ x , σ y , σ z :

normal-stress components

τ xy , τ yz , τ zx :

shear-stress components

ψ:

nondimensional logarithmic potential

∇2 :

Laplacian operator

References

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  3. Prakash, I., “Analog-discrete Approach for Rigid-footing Problems,”M. Tech. Thesis, Department of Civil Engineering, Indian Institute of Technology, Kanpur, India (August 1971).

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  4. Scarborough, J. B., Numerical Mathematical Analysis, John Hopkins Press, Baltimore (1958).

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  5. Timoshenko, S. andGoodier, J. N., Theory of Elasticity, McGraw-Hill Book Co., Inc, Tokyo (1951).

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology, Kanpur, India

    N. S. V. Kameswara Rao (Assistant Professor) & I. Prakash (Graduate Student)

Authors
  1. N. S. V. Kameswara Rao
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  2. I. Prakash
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Kameswara Rao, N.S.V., Prakash, I. Analog-discrete approach for the solution of a class of rigid-contact problems. Experimental Mechanics 12, 564–569 (1972). https://doi.org/10.1007/BF02320600

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  • DOI: https://doi.org/10.1007/BF02320600

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