Vibration of Mindlin plates: programming the p-version Ritz Method

K.M. Liew, Y. Xiang, S. Kitipornchai, C.M. Wang9780080433417, 0-08-043341-3

Over the last several years, the four authors have jointly conducted research into the analysis of vibrating Mindlin plates as a collaborative project between Nanyang Technological University, The National University of Singapore, and The University of Queensland. The research was prompted by the fact that there is a dearth of vibration results for Mindlin plates when compared to classical thin plate solutions. To generate the vibration results, the authors have successfully employed the Ritz method for general plate shapes and boundary conditions. The Ritz method, once thought to be awkward for general plate analysis, can be automated through suitable trial functions (for displacements) that satisfy the geometric plate boundary conditions a priori . This work has been well-received by academics and researchers, as indicated by the continual requests for the authors’ papers and the Ritz software codes. This monograph is written with the view to share this so-called p -Ritz method for the vibration analysis of Mindlin plates and its software codes with the research community. To the authors’ knowledge, the monograph contains the first published Ritz plate software codes of its kind.

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Table of contents :
0080433413……Page 1
Copyright Page……Page 5
Contents……Page 10
Foreword……Page 6
Preface……Page 8
1.2 Plate vibration……Page 12
1.3 About this monograph……Page 14
2.1 Mindlin plate theory……Page 16
2.2 Relations between Kirchhoff and Mindlin plates……Page 26
2.3 Shear correction factor……Page 34
2.4 Ritz method……Page 35
3.1 Introduction……Page 38
3.2 Energy functionals……Page 44
3.3 Eigenvalue equation……Page 46
3.4 Computer program……Page 51
3.5 Benchmark checks……Page 85
4.1 Introduction……Page 100
4.2 Energy functionals……Page 103
4.3 Eigenvalue equation……Page 104
4.4 Computer program……Page 107
4.5 Benchmark checks……Page 129
5.2 Skew coordinates transformation……Page 144
5.3 Energy functional in skew coordiantes……Page 145
5.4 Eigenvalue equation……Page 146
5.5 Computer program……Page 148
5.6 Benchmark checks……Page 167
6.2 Initial inplane stresses……Page 176
6.3 Elastic foundations……Page 178
6.4 Stiffeners……Page 180
6.5 Nonuniform thickness……Page 184
6.6 Line/curved/loop internal supports……Page 186
6.7 Point supports……Page 187
6.8 Mixed boundary conditions……Page 188
6.9 Reentrant corners……Page 189
6.11 Sandwich construction……Page 190
References……Page 194
Relevant Reference Books……Page 200
Appendix I – Gaussian Quadrature Subroutines……Page 202
Appendix II – Subroutines for Mathematical Operations on Polynomials……Page 208
Subject Index……Page 212