The non-linear theory of the pure bending of prismatic elastic solids. (Q2761298)

The authors study bending of the elastic body of the prismatic rod form. It is assumed that the elastic body is exposed to the finite strain described by the correlations NEWLINE\[NEWLINE \begin{gathered} X_1 = \alpha(x_1,x_2),\quad\,\,X_2 = \rho(x_1,x_2)\cos\beta x_3,\\ X_3 = \rho(x_1,x_2)\sin\beta x_3,\quad\,\,\beta = \text{ const}. \end{gathered} NEWLINE\]NEWLINE This problem is reduced to two-dimensional nonlinear boundary value problem for the region of the rod cross-section form. For some materials, using the Ditz method, an approximate solution is found for the large bending of the rod with rectangular cross-section.