A Viscoelastic Analysis on Saturated Axial Symmetrical Problem

Explicit equations of stress, displacement and pore-water pressure are derived by solving Biot’s consolidation equations through Laplace and Hankel transforms. A numetical analysis is developed on the semi-infinite viscoelastic body with Burgers model. Reasonable results show that the present theory is correct and with high accuracy and efficiency.

The axisymmetric Boussinesq-type problem for a half-space under optimal heating of arbitrary profile

A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically.

A Relation between Laplace and Hankel Transforms

The Laplace transform of a function f(t) ∈ L(0, ∞) is defined by the equationand its Hankel transform of order v is defined by the equationThe object of this note is to obtain a relation between the Laplace transform of tμf(t) and the Hankel transform of f(t), when ℛ(μ) > − 1. The result is stated in the form of a theorem which is then illustrated by an example.