Ranjit S. Dhaliwal

On the theory of elssticity of a nonhomogeneous medium

In this paper the equation of equilibrium for a nonhomogeneous isotropic elastic solid under shear has been solved in rectangular Cartesian coordinates as well as in cylindrical polar coordinates. The modulus of rigidity of the material is assumed to vary in lateral as well as vertical directions. As an example, the above solution has been used to solve the problem of a Griffith crack in an infinite solid under shear.

A heat-flux dependent theory of thermoelasticity with voids

SummaryA thermoelasticity theory for elastic materials with voids is formulated. This theory includes the heat-flux among the constitutive variables and assumes an evolution equation for the heat-flux. A class of mixed initial boundary value problems is defined and the uniqueness is established.

The axisymmetric boussinesq problem for a thick elastic layer under a punch of arbitrary profile

Abstract A solution of the axisymmetric Boussinesq problem is obtained, for an elastic layer lying over an elastic foundation, from which are deduced simple formulae for the depth of penetration of the tip of a punch of arbitrary profile and the total load which must be applied to the punch to achieve this penetration. Simple expressions are also deduced for the shape of the deformed surface outside the punch and the distribution of pressure under the punch. Particular results are obtained for cylindrical, conical, spherical, paraboloidal and ellipsoidal punch shapes.

Punch problem for an elastic layer overlying an elastic foundation

Abstract The title problem is equivalent to an axisymmetric mixed boundary value problem in the theory of elasticity in which the nor4mal displacement is specified inside the circular area r ⩽ a , the normal stress is zero outside and the shearing stress is zero on the whole face z = − h ; the continuity of the normal and radial displacements and the normal and shearing stresses is assumed at the interface z = 0 between the elastic layer and the elastic foundation having different elastic constants. The problem is reduced to the solution of a Fredholm integral equation of the second kind; for a flat circular punch its iterative solution has been obtained valid for large values of h; for small values of h it has been solved numerically. Some interesting conclusions have been drawn.

ONE-DIMENSIONAL THERMAL SHOCK PROBLEM WITH TWO RELAXATION TIMES

The theory of generalized thermoelasticity with two relaxation times is used to solve a boundary value problem of an isotropic elastic half-space with its plane boundary either held rigidly fixed or stress-free and subjected to a sudden temperature increase. An approximate small-time solution is obtained by using the Laplace transform method. Numerical values of displacement, stress, and temperature are obtained and displayed graphically. Two discontinuities in both the displacement and temperature functions and that the stress has infinite discontinuities at these two wave fronts were noted

Domain of influence theorem in the theory of elastic materials with voids

Abstract A domain of influence theorem in the linear theory of elastic materials with voids, proposed by Cowin and Nunziato, has been established. The theorem shows that for a finite time t > 0 , the displacement field u i and the change in volume fraction ϑ generate no disturbance outside a bounded domain Ω t .

Axisymmetric contact and crack problems for an initially stressed neo-Hookean elastic layer

Abstract A solution of the contact problem for an initially stressed neo-Hookean infinite layer is obtained. The layer is assumed to be bonded to a rigid foundation. The punch is taken to be axisymmetric and in particular, the conical and cylindrical shapes of the punch are considered in detail. The expression for the total load applied to the punch to maintain a given displacement is obtained. We have also considered the penny-shaped crack in the layer under an initial stress. The crack is taken to lie in the central plane of the layer. The surfaces of the layer are considered to be either stress free or fixed. Expressions for the stress intensity factors are obtained. Numerical values of the physical quantities are exhibited graphically.

The axisymmetric boussinesq problem of an initially stressed neo-hookean half-space for a punch of arbitrary profile☆

Abstract A solution of the axisymmetric Boussinesq problem for an initially stressed neo-Hookean half-space is obtained in the closed form, from which are deduced simple formulae for the depth of penetration of the tip of a rigid punch of arbitrary profile and the total load which must be applied to the punch to achieve this penetration. Simple closed form expressions are also deduced for the shape of the deformed surface outside the punch and the distribution of pressure under the punch. The corresponding results are obtained for cylindrical, conical, paraboloidal, ellipsoidal and spherical punch shapes.

Stress intensity factor for the cylindrical interface crack between nonhomogeneous coaxial finite elastic cylinders

Abstract The problem of determining the stress intensity factor for a cylindrical interface crack between two dissimilar nonhomogeneous coaxial finite elastic cylinders under axially symmetric longitudinal shear stress is considered. The mixed boundary conditions lead to a pair of dual series equations which are reduced to a Fredholm integral equation of the second kind and then finally to a system of algebraic equations. Numerical values of the stress intensity factor are presented graphically.

ONE-DIMENSIONAL GENERALIZED THERMOELASTIC PROBLEM FOR A HALF SPACE

In this paper the theory of generalized thermoelasticity is used to solve a boundary-value problem of an isotropic elastic half-space with its plane boundary held rigidly fixed and subjected to a sudden temperature increase. Approximate small time solution is obtained by using the Laplace transform method. Numerical values of stress and temperature have been obtained. It has been noticed that the displacement is continuous and that there are two discontinuities in both the stress and temperature functions.