Shear stresses in rectangular panels of ship structures in the calculations according to Reissner theory

Abstract

This study calculates and analyzes torsion moments of a rectangular panel with clamped edges as an element of ship structures under the action of uniform pressure with allowance for transverse shear deformation and examines the contribution of the corresponding shear stresses to the general stress state. In order to solve this problem, the method of infinite superposition of corrective functions of bending and stresses is applied. It involves an iterative process of mutually correcting the discrepancies from the said functions while meeting all boundary conditions. A particular solution for the bending function in the form of a quadratic polynomial is chosen as the initial approximation. It is established that torsion moment series diverge at the corner points of the plate going into infinity, which yields infinite values for the shear stresses at these points as well. Results of torsion moment calculation for square plates with different width ratios are provided. A 3D distribution diagram of moments is obtained. The computational experiment confirms the correctness of theoretical conclusions about infinite torsion moments at the corner points of the plate. Comparison with bending moments shows that torsion moments cannot be ignored during the assessment of the stress-strain state. The behavior of torsion moments near the corner points is qualitatively different from the simplified Kirchhoff theory, where they turn into zero.