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afallingbomb
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Where can I find the derivation of the Boussinesq problem of elasticity (point load on an isotropic elastic infinite half-plane)? Besides the original 19th century paper, of course. Thanks!
afallingbomb said:Where can I find the derivation of the Boussinesq problem of elasticity (point load on an isotropic elastic infinite half-plane)? Besides the original 19th century paper, of course. Thanks!
The Boussinesq Elasticity Problem is a mathematical model that describes the deformation and stress distribution in an elastic material subject to a concentrated force or load. It was first proposed by French mathematician Joseph Valentin Boussinesq in the 19th century.
The derivation of the Boussinesq Elasticity Problem is based on several assumptions, including:
The Boussinesq Elasticity Problem is a fundamental model in the field of elasticity and is commonly used in engineering to analyze the stress and deformation of structures subject to concentrated loads. It has applications in various fields, including civil engineering, mechanical engineering, and geotechnical engineering.
The Boussinesq Elasticity Problem is typically solved using analytical methods, such as the method of superposition or the Fourier transform method. In some cases, numerical methods may also be used, such as the finite element method.
While the Boussinesq Elasticity Problem is a useful model for analyzing elastic materials, it has some limitations. It assumes a linearly elastic material, which may not accurately describe the behavior of some materials under high loads. It also does not take into account the effects of shear stress, which may be significant in some cases. Additionally, the assumptions made in the derivation may not hold true for all materials and loading conditions.