Abstract
For the first time, the finite integral transform method is introduced to explore the accurate bending analysis of orthotropic rectangular thin plates with two adjacent edges free and the others clamped or simply supported. Previous solutions mostly focused on plates with simply supported and clamped edges, but the existence of free corner makes the solution procedure much complex to solve by conventional inverse/semi-inverse methods. Compared with the conventional methods, the employed method eliminates the need to preselect the deflection function, which makes it more reasonable and theoretical for calculating the mechanical responses of the plates. Moreover, the approach used can also analyze static problems of moderately thick plates and thick plates with the same boundary conditions investigated in this article. Finally, comprehensive analytical results obtained in this paper illuminate the validity of the proposed approach by comparing with the previous literature and finite element method by using (ABAQUS) software.
Highlights
Due to the better structural performance such as superior strength-to-weight ratios and stiffness-to-weight ratios, composite materials are widely applied in engineering fields such as mechanical engineering, civil and structural engineering, naval, and aerospace
Orthotropic rectangular plate is considered as the fundamental structural application of composite materials. us, the research on the mechanical behavior of orthotropic plate aroused the interest of scientists and engineers for more than a century
For the rectangular plate clamped at edge x 0, y b, the undetermined unknowns Jm will be zero, and the supported at edge y 0, and free at edges x a and deflection of the plate reduces to
Summary
Due to the better structural performance such as superior strength-to-weight ratios and stiffness-to-weight ratios, composite materials are widely applied in engineering fields such as mechanical engineering, civil and structural engineering, naval, and aerospace. Analytical solution is relatively sparse, which is due to the mathematical complexity in choosing proper trial function to satisfy the governing equation and the boundary conditions simultaneously. Among the combinations of boundary conditions of rectangular plate, it is very difficult to obtain analytical solution for plate with at least two adjacent edges free. The finite integral transform method [33], an effective mathematical method, is developed which is successfully implemented to solve the bending [34,35,36,37] and free vibration [38,39,40] plate problems with different boundary conditions. A semi-inverse method normally fails to yield a unified solution procedure since it requires case-by-case trial functions to satisfy both the governing equation and boundary conditions. X a o q z b y Figure 1: Schematic illustration of thin plate
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