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.
Highlights
Modern ship structures widely use metallic and non-metallic materials with high interlaminar shear strength
Numerical results for torsion moments are obtained for a rectangular plate (γ = 1) with fully clamped edges (CCCC plate according to the international nomenclature) under the effect of uniform pressure according to the refined Reissner theory
After the 10th iteration, discrepancies in the fulfillment of boundary conditions, which are printed after each iteration, are practically zero
Summary
Modern ship structures widely use metallic and non-metallic materials with high interlaminar shear strength. This requires using more accurate methods of analysis during calculation that would reduce the weight of the structure without compromising its strength. The linear plate-bending theory, which qualitatively specifies the classical theory, was first introduced by Reissner [1], who obtained new differential equations of plate bending and the corresponding boundary conditions with allowance for the effects of the transverse shear. The system of two differential equations consists of a fourth-order equation with respect to the bending function and an additional second-order equation with respect to the stress function. This makes it possible to meet three boundary conditions (instead of two in the classical theory) on each edge of the plate
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