An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates
TL;DR: In this paper, a 3D linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates.
About: This article is published in Journal of Sound and Vibration.The article was published on 1970-06-01. It has received 444 citations till now. The article focuses on the topics: Plate theory & Isotropy.
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11 Aug 2014
TL;DR: The semi-analytical finite element method (SAFE) has been used for guided wave modeling as discussed by the authors, which has been shown to be useful in the analysis and display of non-destructive testing.
Abstract: Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.
823 citations
TL;DR: In this article, a unified exact analysis for the statics and dynamics of a class of thick laminates is presented, which leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems.
770 citations
TL;DR: In this paper, a higher-order shear deformation theory of plates accounting for the von Karman strain was presented, which contains the same dependent unknowns as in the Hencky-Mindlin type first-order deformation theories and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
695 citations
TL;DR: A review of the reported studies in the area of thermo-elastic and vibration analyses of functionally graded (FG) plates with an emphasis on the recent works published since 1998 is presented in this paper.
695 citations
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TL;DR: In this article, a higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia.
629 citations
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
4,554 citations
Book•
01 Jan 1969
TL;DR: In this article, elementary differential equations and boundary value problems are studied in the context of boundary value problem, where boundary value is defined as a function of the boundary value of the elementary differential equation.
Abstract: Elementary differential equations and boundary value problems , Elementary differential equations and boundary value problems , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
1,575 citations
156 citations
TL;DR: In this article, a three-dimensional linear deformation theory of elasticity solution by the direct method is given for the flexure of simply supported homogeneous, isotropic, thick rectangular plates under arbitrary loading.
Abstract: A three-dimensional, linear, small deformation theory of elasticity solution by the direct method is given for the flexure of simply supported homogeneous, isotropic, thick rectangular plates under arbitrary loading. This solution, in terms of infinite series is formally exact and yields accurate numerical results without undue effort. Numerical results are presented for uniformly distributed normal load on the top surface. The results from Reissner's theory of thick plates and the predictions of thin plate theory are compared with the values from the present exact solution. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for a three-ply laminate under uniformly distributed normal load on the top surface, and are used to assess the accuracy of thin plate theory predictions for laminates.
Fur das Biegeproblem einer einfach unterstutzten, homogenen, isotropen, dicken, beliebig belasteten Rechteckplatte wird auf direktem Wege uber eine dreidimensionale lineare Theorie kleiner elastischer Verformungen eine Losung gewonnen. Sie erscheint in der Gestalt unendlicher Reihen, ist formal exakt und liefert ohne unzumutbaren Aufwand genaue numerische Resultate. Solche werden fur den Fall einer uber die obere Randflache gleichformig verteilten Normallast angegeben und mit den Ergebnissen der Reissnerschen Theorie dicker Platten und mit den Voraussagen einer Theorie dunner Platten verglichen. Die verwendete Analysis last sich leicht auf geschichtete Platten aus isotropen Materialien ausdehnen. Fur eine Dreischichtplatte, auf deren obere Randflache eine gleichformig verteilte Normallast wirkt, werden die numerischen Ergebnisse mitgeteilt und dazu benutzt, die Genauigkeit der von der Theorie dunner Platten gemachten Voraussagen einzuschatzen.
96 citations