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Arthur W. Leissa

Bio: Arthur W. Leissa is an academic researcher from Colorado State University. The author has contributed to research in topics: Ritz method & Normal mode. The author has an hindex of 48, co-authored 154 publications receiving 11097 citations. Previous affiliations of Arthur W. Leissa include Ohio State University & NASA Headquarters.


Papers
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Book•
Arthur W. Leissa1•
01 Jan 1969
TL;DR: The fundamental equation of classical plate theory can be found in this article, where anisotropic and variable-thickness versions of the classical plates are considered, as well as other considerations.
Abstract: : Contents: Fundamental Equations of Classical Plate Theory; Circular Plates; Elliptical Plates; Rectangular Plates; Parallelogram Plates; Other Quadrilateral Plates; Triangular Plates; Plates of Other Shapes; Anisotropic Plates; Plates With Inplane Forces; Plates With Variable Thickness; and Other Considerations.

2,137 citations

Book•
01 Jan 1973
TL;DR: In this paper, the vibrational characteristics and mechanical properties of shell structures are discussed, including the fundamental equations of thin shell theory, the characteristics of thin circular cylindrical shells, the complicating effects of noncircular cylinders, the properties of spherical shells and the solution of three-dimensional equations of motion for cylinders.
Abstract: The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.

1,114 citations

Journal Article•DOI•
TL;DR: In this article, the free vibration of rectangular plates is analyzed using the Ritz method with 36 terms containing the products of beam functions, including clamped, simply-supported, and free edge conditions.

1,076 citations

Journal Article•DOI•

367 citations

Journal Article•DOI•

296 citations


Cited by
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Book•
01 Jan 1938
TL;DR: This chapter discusses the Behavior of Bodies Under Stress, which involves tension, Compression, Shear, and Combined Stress, and the role of Fasteners and Joints in this Behavior.
Abstract: Chapter 1. Introduction Chapter 2. Stress and Strain: Important Relationships Chapter 3. The Behavior of Bodies Under Stress Chapter 4. Principles and Analytical Methods Chapter 5. Numerical Methods Chapter 6. Experimental Methods Chapter 7. Tension, Compression, Shear, and Combined Stress Chapter 8. Beams Flexure of Straight Bars Chapter 9. Curved Beams Chapter 10. Torsion Chapter 11. Flat Plates Chapter 12. Columns and Other Compression Members Chapter 13. Shells of Revolution Pressure Vessels Pipes Chapter 14. Bodies under Direct Bearing and Shear Stress Chapter 15. Elastic Stability Chapter 16. Dynamic and Temperature Stresses Chapter 17. Stress Concentration Chapter 18. Fatigue and Fracture Chapter 19. Stresses in Fasteners and Joints Chapter 20. Composite Materials Chapter 21. Solid Biomechanics Appendix A. Properties of a Plane Area Appendix B. Mathematical Formulas and Matrices Appendix C. Glossary Index

2,050 citations

Journal Article•DOI•
N. J. Pagano1•
TL;DR: In this article, three-dimensional elasticity solutions for rectangular laminates with pinned edges are constructed for three dimensional elasticity problems, including a sandwich plate, and compared to the analogous results in classical laminated plate theory.
Abstract: In a continuing study, three-dimensional elasticity solutions are constructed for rectangular laminates with pinned edges. The lamination geometry treated consists of arbitrary numbers of layers which can be isotropic or orthotropic with material symmetry axes parallel to the plate axes. Several specific example problems are solved, including a sandwich plate, and compared to the analogous results in classical laminated plate theory.

1,730 citations

Book•
01 Jan 1973
TL;DR: In this article, the authors consider bending waves, which are a special combination of compressional and shear waves, and for some special cases (quasi-) longitudinal waves and torsional waves also have to be considered.
Abstract: Although sound waves in structures cannot be heard directly, and only be felt at low frequencies, they play an important role in noise control, because many sound signals are generated or transmitted in structures before they are radiated into the surrounding medium. In several respects sound waves in structures and sound waves in gases or liquids are similar, there are, however, also fundamental differences, which are due to the fact that solids have a certain shear stiffness, wheras gases or liquids show practically none. As a consequence acoustic energy can be transported not only by the normal compressional waves but also by shear waves and many combinations of compressional (sometimes loosely called longitudinal) and shear waves . For noise control purposes bending waves (which are a special combination of compressional and shear waves) are of primary importance; for some special cases (quasi-) longitudinal waves and torsional waves also have to be considered.

1,085 citations

Journal Article•DOI•
TL;DR: In this article, the free vibration of rectangular plates is analyzed using the Ritz method with 36 terms containing the products of beam functions, including clamped, simply-supported, and free edge conditions.

1,076 citations

Journal Article•DOI•
TL;DR: A review of the Zig-Zag theories for multilayered structures can be found in this article, where the authors refer to these three theories by using the following three names: Lekhnitskii Multi-layered Theory, ~LMT!, Ambartsumian Multi-Layered Theory ~AMT!, and Reissner Multilayed Theory ~RMT.
Abstract: This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1! Lekhnitskii ~1935! was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2! Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian ~1958!, who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner ~1984!, who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3 ! On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, ~LMT!, Ambartsumian Multilayered Theory ~AMT!, and Reissner Multilayered Theory ~RMT!. As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4! LMT although very promising, has almost been ignored in the open literature. 5! Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6! RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references. @DOI: 10.1115/1.1557614#

972 citations