Abstract
A new, practical method is proposed for solving the partial differential equations describing the dynamic behavior of either linear elastic or nonlinear inelastic multi-dimensional continua. The ultimate application of the method is the prediction of the dynamic response of foundations to loads having a broad range of intensities. Stresses, particle velocities and partial derivatives are computed numerically for points within the medium giving a detailed description of dynamic response. Since few approximations are introduced, solutions are accurate. The method is applied to the equations describing the axisymmetric torsional behavior of a three-dimensinal medium. Multi-dimensional linear and nonlinear torsional solutions are obtained. Examples in which one-dimensional behavior is approximated are discussed. Linear solutions agree with theory. Nonlinear solutions, for which theoretical solutions are not found, satisfy energy balance requirements. The effects of shearing nonlinear inelasticity on dynamic response are found to be significant.
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