Dynamical Problems in Elasticity (Progress in Solid Mechanics, vol. III)

Abstract

A LEADING authority in the field presents an original mathematical treatment of the problem of propagation of errors in the numerical integration of systems of differential equations by difference methods. A short, technical monograph, it constitutes a sequel or companion volume to the author's "Discrete Variable Methods in Ordinary Differential Equations" (Wiley, 1962). In this new work, the author extends his results on error propagation for linear multistep methods to systems of ordinary differential equations.

The method of fundamental solutions for annular shaped domains

“…Their error bounds can be derived. In this paper, we integrate the analysis of [2] with [5,21], as well as [22], to provide the error bounds of the method of fundamental solutions (MFS) [11] for the Dirichlet problem of bounded simply-connected domains, and the error bounds are improved by removing a factor √ n from those of [2]. Next, we extend our analysis to the annular domain S a .…”

Some results concerning the state of bending for transversely isotropic plates

“…Such representation is very useful in the study of solutions under concentrated loads and for the existence of solutions through the method of potentials [20]. To this end, we rewrite Equations (11), (13), (14) …”

“…In the last section, we give a Galerkin representation of solution of the field equations. This representation can be used in the study of solutions corresponding to concentrated loads and for the existence of solutions through the method of potentials [20].…”

Shape reconstruction of a 2D-elastic penetrable object via the L-curve method

“…For r ∈ B i the following integral representation [13] holds For r ∈ B i the following integral representation [13] holds…”