EXACT SOLUTIONS OF SOME DYNAMIC PROBLEMS OF INDENTATION AND TRANSIENT LOADINGS OF AN ELASTIC HALF SPACE.
Civil engineering studies,
ILLINOIS UNIV URBANA DEPT OF CIVIL ENGINEERING
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In this report the method of self-similar potentials is used to solve certain problems which involve the frictionless indentation of a linearly elastic half space by a rigid die. Solutions which are exact within the limits of the classical theory of elasticity are obtained for the early stages of contact for any problem in which the surface of the die is smooth. For problems in which the die is wedge- or cone-shaped and indents the half space at a constant rate, the solution for the entire process is given. The stress and velocity fields for the wedge and cone problems are considered in detail. This report includes an exposition of the method of self-similar potentials and of the procedure based on this method for solving two- and three-dimensional problems involving transient loads acting at interior or surface points of a homogeneous linearly elastic half space. The asymptotic character of the disturbance near the wave fronts and near the surface wave is determined in detail for both the two- and three-dimensional problems in which the source of the disturbance is an impulse applied normal to the surface of the half space. Author