Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume -, Issue -, Pages -Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/10812865231201623
Keywords
Implicit constitutive theories; Nonlinear elasticity; Rock mechanics; Incremental method
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This paper calculates the shear stresses for a two-dimensional beam by modifying the classical method. It studies the cases of a cantilever beam with a point load and a three-point flexural test for a beam of rectangular cross-section, comparing the results with the classical theory of strength of materials.
Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.
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