Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates

Abstract

In this work, the problem of first order shear deformable solid circular plate under transverse load was solved mathematically. The problem considered was assumed axisymmetric. The plate and loading were considered axisymmetric. The problem was defined as a boundary value problem of a system of differential equations of equilibrium in terms of the stress resultants and the stress-resultants-displacement relations. The set of equations were considered simultaneously to express them in variable separable form. The mathematical technique of separation of variables was then used to obtain solutions for the unknown generalised displacements. Specific problems of clamped edge plates and simply supported edge plates under uniformly distributed load and point load at the centre were considered and solved using the same technique of separation of variables. The mathematical expressions obtained showed that in all cases, the deflection was expressible in terms of flexural and shear components. The maximum deflection was found to occur at the plate centre as is expected from the symmetrical nature of the problem. The shear component of the transverse deflection was found to significantly increase with significant increase in the ratio of the plate thickness to the radius (ℎ ⁄).

A third-order shear deformation plate bending formulation for thick plates: first principles derivation and applications

“…Ike [20], [22] studied Mindlin's first order shear deformable plates. Nwoji et al [21] obtained satisfactory solutions for the flexural analysis of simply supported rectangular Mindlin plates subjected to sinusoidal transverse load distribution using the Navier's double trigonometric series method.…”

“…The main disadvantage of the KPT is the inability to consider transverse shear deformations, thus limiting the scope of applicability to thin plates where transverse shear deformations are ignorable without significant errors [17][18][19][20][21][22]. Despite the disadvantages, KPT has been found to be satisfactory for thin plates and various methods for solving KPT are found in references and [23][24].…”

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

“…The limitations of KLPT led to the development of shear deformation theories by Mindlin [4], Reddy [5][6] and refined theories by Shimpi [7] and Shimpi et al [8] to account for shear deformation and render the formulations applicable to thick plates. Mindlin's firstorder shear deformation plate problems were studied by Nwoji et al [9][10], Ike [11][12]; Norouzzadeh et al [13] and Bao et al [14].…”