Rectangular plate problems, often solved using trigonometric series, are analyzed here using power series expansions. The governing equations and the boundary conditions are immediately reduced to algebraic equations that are readily solved. The method is shown to be accurate for several challenging cases involving complications such as variable thickness, material anisotropy, unsymmetric lamination and shear deformation. © 2008 Elsevier Ltd. All rights reserved.

K. Bhaskar

Department of Aerospace Engineering

J. Dhaoya

Fourier series

Algebraic equations

Analytical Solution

Governing equations

MATERIAL ANISOTROPIES

MODERATELY THICK PLATES

POWER SERIES SOLUTIONS

POWER-SERIES EXPANSIONS

Rectangular plates

TRIGONOMETRIC SERIES

Variable thickness

Plates (structural components)

Anisotropy

Deformation

laminate

mathematical analysis

shear property

Structural analysis

Thickness

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Composite Structures

Clamped cross-ply plates are analyzed here using a higher-order theory based on a realistic thickness-wise displacement field that accounts for a zig-zag variation of the in-plane displacements. Rigorous analytical solutions are obtained for this difficult problem using a methodology developed recently wherein simple Fourier series solutions of a corresponding simply-supported plate are superposed, each such component solution being summed without truncation using MATHEMATICA. Numerical results, for square homogeneous and three-layer plates under uniform and central point loads, are compared with those based on the classical and first-order theories. © 2005 Elsevier Ltd. All rights reserved.

Analytical solutions for flexure of clamped rectangular cross-ply plates using an accurate zig-zag type higher-order theory

Based on the idea developed in an earlier work on orthotropic rectangular plates [Compos. Struct. 63 (2004) 63], it is shown here that exact double Fourier series solutions can be easily obtained for simply supported rectangular unsymmetrically laminated cross-ply plates subjected to various edge forces and moments, and that these can be superposed to yield a simple solution for the title problem considered difficult hitherto. Numerical results, based on the summation of the infinite series without truncation using MATLAB, are presented for a set of symmetric and antisymmetric cross-ply laminates under uniform and central concentrated loads. © 2004 Elsevier Ltd. All rights reserved.

Analysis of clamped unsymmetric cross-ply rectangular plates by superposition of simple exact double Fourier series solutions

A rigorous analytical solution for the title problem is presented here using the method of superposition. The derivation of tedious Levy-type solutions, commonly used in such an approach, is obviated by the ingenious use of their infinite series counterparts, which are summed without truncation so as to retain accuracy. The methodology is fast convergent and yields accurate results without excessive computation. Tabulated results are presented for two cross-ply plates for future comparisons. © 2005 SAGE Publications.

Journal of Reinforced Plastics and Composites

Accurate flexural analysis of clamped moderately thick cross-ply rectangular plates by superposition of exact untruncated infinite series solutions

Rectangular plates with arbitrary clamped edges are not easily amenable to exact analysis. Available solutions are either approximate or mathematically complex. The purpose of this paper to present an exact solution methodology for such problems based on superposition of double sine series solutions easily derived using the principle of virtual work. The paper includes tabulated results for two laminates for all possible combinations of clamped-simply supported edges, which would be valuable for future comparisons. © 2003 Elsevier Ltd. All rights reserved.

Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges

Mechanics of Composite Materials

Introduction to Composite Materials

Straightforward power series solutions for rectangular plates

Journal	Composite Structures
ISSN	02638223
Open Access	No