A Minimum Norm Interpolation Method for Determining the Displacement Field of a Homogeneous Isotropic Elastic Body from Discrete Data

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Abstract
A minimum norm interpolation method is proposed for solving the classical displacement boundary value problem of elastostatics from discretely defined boundary displacement vectors. A stability theorem is developed which is dependent on the spacing of the data on the boundary, and convergence is established for the case in which the data points become dense. A basic tool is a new vectorial generalization of the addition theorem for spherical harmonics.

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