Response of an elastic solid to nonuniformly expanding surface loads
TL;DR: In this paper, exact expressions for the displacement field in a homogeneous isotropic elastic half space whose surface is subjected to a unit normal pressure are obtained in the form of triple integrals over finite ranges.
About: This article is published in International Journal of Engineering Science.The article was published on 1979-01-01. It has received 6 citations till now. The article focuses on the topics: Displacement field & Isotropy.
Citations
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TL;DR: In this article, an exact analytical solution has been constructed for the plane problem on action of a non-stationary load on the surface of an elastic semiplane for conditions of a'mixed' boundary problem when normal stress and tangent displacement are specified on the boundary Laplace and Fourier integral transforms are used Their inversions were obtained with the help of tabular relationships and the convolution theorem for a wide range of acting nonstationary loads Expressions for stresses (displacements) were obtained in explicit form.
Abstract: An exact analytical solution has been constructed for the plane problem on action of a non-stationary load on the surface of an elastic semiplane for conditions of a 'mixed' boundary problem when normal stress and tangent displacement (the fourth boundary problem) are specified on the boundary Laplace and Fourier integral transforms are used Their inversions were obtained with the help of tabular relationships and the convolution theorem for a wide range of acting non-stationary loads Expressions for stresses (displacements) were obtained in explicit form The obtained expressions allow determining the wave process characteristics in any point of the object at an arbitrary point of time Some variants of non-stationary loads acting on an area with fixed boundaries or an area with boundaries changing by a known function are considered For a particular case, computed numerical results are compared with the solution of the first boundary problem Constructing exact analytical solutions, even if infrequently used in practice, besides being significant on their own, can also help refine various numerical and approximate approaches, for which the types of boundary conditions are not critical
7 citations
06 Dec 2019
TL;DR: Linear and Non-Linear Deformations of Elastic Solids as discussed by the authors aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics.
Abstract: Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.
5 citations
TL;DR: In this paper, a study is made of the generation of SH-type waves at the free surface of a layered anisotropic elastic medium due to a stress discontinuity moving with non-uniform velocity along the interface of the layered half-space.
Abstract: A study is made of the generation of SH-type waves at the free surface of a layered anisotropic elastic medium due to a stress discontinuity moving with non-uniform velocity along the interface of the layered half-space. The exact solution for the displacement function is obtained by the Laplace and Fourier transforms method combined with the modified Cagniard method. Solution is discussed on the basis of ray theory. Formations of different wave pattern are also illustrated with figures. Some special cases are also derived.
4 citations
TL;DR: In this article, the authors present analytical and numerical-analytic approaches to solving the problem of the action of an arbitrarily distributed axisymmetric load applied instantly to the surface of an isotropic elastic half-space.
Abstract: This paper presents analytical and numerical-analytic approaches to solving the problem of the action of an arbitrarily distributed axisymmetric load applied instantly to the surface of an isotropic elastic half-space. The first approach is built around the Laplace and Hankel integral transforms whose inversion is performed jointly with Cagniard’s technique, and as a result, exact analytical expressions are obtained for computing stresses along an axis of symmetry. The second approach uses the Laplace integral transform and the expansion of sought for values into the Fourier–Bessel series to reduce the problem to a numerical solution of a series of Volterra integral equations. Concrete numerical analysis was performed for cases where the domain of application of a distributed load is fixed or expands in time with both constant and variable velocity.
2 citations
TL;DR: In this paper, an approach to study nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed.
Abstract: An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads
2 citations
References
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TL;DR: In this paper, a numerical example is presented in which Rayleigh stresses at various depths and locations are given; use for practical design purposes, such as in design of underground facilities.
Abstract: Analysis of stresses and displacements due to Rayleigh waves that are produced by nuclear burst on surface of semi-infinite elastic half space causing time decaying pressure pulse that acts over circular surface area of increasing radius; numerical example is presented in which Rayleigh stresses at various depths and locations are given; use for practical design purposes, such as in design of underground facilities.
8 citations
TL;DR: In this article, the response of an elastic half space to a realistic model of faulting is considered, where a dislocation is developed along a line of finite length and then moves nonuniformly along an inclined plane (fault) surface.
8 citations