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Poisson Theory of Elastic Plates

Part of the Springer Tracts in Mechanical Engineering Book Series

DOI: 10.1007/978-981-33-4210-1

ISBN: 978-981-33-4209-5

Publisher: Springer Singapore - Springer Journals

Jan 26, 2021

Available

Poisson Theory of Isotropic Plates in Bending

Vijayakumar, Kaza; Ramaiah, Girish Kumar

Pages: 1 –29

[ Analysis of primary bending problems of homogeneous isotropic square plates is presented. Kirchhoff's theory and well-known shear deformation theories are briefly reviewed. The concept of lateral displacements as a face variable is introduced so that it is uncoupled from the determination of...
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Extension Problems: Higher-Order Approximations

Vijayakumar, Kaza; Ramaiah, Girish Kumar

Pages: 31 –48

[ The classical theory of extension problems is based on zero transverse stresses. The role of Airy’s stress function is discussed. It is a biharmonic function due to compatibility of strains.In-plane stresses are independent of material constants if the normal and shear stresses are prescribed...
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Homogeneous Anisotropic Plates

Vijayakumar, Kaza; Ramaiah, Girish Kumar

Pages: 49 –67

[Anisotropy of materials is sometimes called aeolotropy in old textbooks, for example, A. E. H. Love’s Classical book, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944). The application of Poisson theory in the previous two chapters is extended for the analysis of...
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Laminated Plates with Anisotropic Plies Part I: Single-Layer Theories

Vijayakumar, Kaza; Ramaiah, Girish Kumar

Pages: 69 –88

[In the literature, one finds several methods of (basically) approximate analysis of laminated composite plates. The present Poisson theory at the ply level is applied here with reference to Modified Homogeneous Plate Theories (MHPT) of Symmetric Laminates. It is adapted to eliminate...
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Laminated Plates with Anisotropic Plies Part II: Layerwise Theories

Vijayakumar, Kaza; Ramaiah, Girish Kumar

Pages: 89 –113

[There are several theories proposed and used extensively for the analysis of symmetric laminated plates. They are concerned with accurate estimation of stresses (more so for transverse stresses) along the interfaces of plies. Ply analysis is dependent on lamination. Generally, statically...
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Poisson Theory of Plates with Fourier Sinusoidal Series

Vijayakumar, Kaza; Ramaiah, Girish Kumar

Pages: 115 –126

[Analysis of elastic plates through the application of Poisson theory is quite sufficient for the practicing engineers even for thick plates. It involves solutions of Laplace, Poisson, and biharmonic equations (or their variants). In bending problems, solution of a complementary problem based on...

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