Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Abstract

This paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving boundary value problems of governing partial differential equations of plate. Based on the integral transform theory, the title problem is transformed into solving regular linear algebraic simultaneous equations, which provides a more rational and theoretical solution process than traditional inverse/semi‐inverse approaches. The acquired comprehensive results of critical buckling load factors and mode shapes are in excellent agreement with the ones obtained by finite element method, which verifies the validity and accuracy of the present approach. In addition, classical boundary conditions, such as simply supported and clamped edges, can be investigated by choosing different rotational fixity factors. Furthermore, the features of the employed method that no preselection of trial function and the generality for various boundary conditions enable one to analytically solve static problems for moderately thick plates and thick plates.

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

“…On this basis, displacements expressed in terms of ∑ ∞ m=1,2,3,••• κ1 m sin(α m x) and ∑ ∞ m=1,2,3,••• κ2 m sin(α m x) are applied to the y = 0 and y = b sides of the plate in subproblem (1), respectively; displacements expressed in terms of ∑ ∞ n=1,2,3,••• κ3 n sin(β n y) and ∑ ∞ n=1,2,3,••• κ4 n sin(β n y) are applied to the x = 0 and x = a sides of the plate in subproblem (2), where α m = mπ/a, β n = nπ/b, κ1 m , κ2 m , κ3 n and κ4 n are the parameters to be determined (m = 1, 2, 3, . .…”

“…The mechanics of plates and shells have been studied by many scholars [1,2]. Rectangular plates supported by corner point are commonly used in various engineering applications, including building structures, mechanical components, and aerospace vehicles.…”

Performance Evaluation of Aged Asphalt Pavement Binder through Rejuvenators

“…The steric hardening is structural reconstruction and reorganization at the intermolecular level produced because of temperature variations during the service life. It is also a complex nonrecoverable process that is produced by ultraviolet (UV) light, oxygen, and heating effect due to temperature changes [21][22][23][24]. Numerous analytical techniques have been developed to investigate and link the physical and rheological properties with the performance characteristics of asphalt binders.…”

“…Numerous analytical techniques have been developed to investigate and link the physical and rheological properties with the performance characteristics of asphalt binders. For this reason, it is essential to introduce a collaboration among material engineers, pavement specialists, highway agencies, and asphalt industries [24]. Meanwhile, there may be durable adhesion and film between aggregate and asphalt binder in the existence of moisture to decrease stripping that can be achieved through modification of asphalt binders [25,26].…”

Mechanical buckling analysis of functionally graded composite laminated plates reinforced with temperature dependent graphene sheets resting on elastic foundation

“…Awrejcewicz et al [16] studied on the free vibrations of FG plates and shallow shells with cutout in thermal environment. Zhang et al [17] employed the finite Fourier integral transform technique to examine the buckling treatment of rectangular thin plates with two opposite edges free and the others rotationally restrained.…”