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Membrane Theory Of Shells
The membrane theory of shells, or membrane theory for short, describes the mechanical properties of shells when twisting and bending moments are small enough to be negligible. The spectacular simplification of membrane theory makes possible the examination of a wide variety of shapes and supports, in particular, tanks and shell roofs. There are heavy penalties paid for this simplification, and such inadequacies are apparent through critical inspection, remaining within the theory, of solutions. However, this theory is more than a first approximation. If a shell is shaped and supported so as to carry the load within a membrane stress system it may be a desirable solution to the design problem, i.e., thin, light and stiff.Wilhelm Flügge Gottfried Wilhelm Flügge (March 18, 1904 – March 19, 1990) was a German engineer, and Professor of Applied Mechanics at Stanford University.J.J. O'Connor and E.F. Robertson.Gottfried Wilhelm Flügge" at ''history.mcs.st-and.ac.uk.'' School of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shell (structure)
A shell is a type of structural element which is characterized by its geometry, being a three-dimensional solid whose thickness is very small when compared with other dimensions, and in structural terms, by the stress resultants calculated in the middle plane displaying components which are both coplanar and normal to the surface. Essentially, a shell can be derived from a plate by two means: by initially forming the middle surface as a singly or doubly curved surface, and by applying loads which are coplanar to a plate's plane which generate significant stresses. Thin-shell structures (also called plate and shell structures) are lightweight constructions using shell elements. These elements, typically curved, are assembled to make large structures. Typical applications include aircraft fuselages, boat hulls, and the roofs of large buildings. Definition A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bending Moment
In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple or fixed). In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely. The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Flügge
Gottfried Wilhelm Flügge (March 18, 1904 – March 19, 1990) was a German engineer, and Professor of Applied Mechanics at Stanford University.J.J. O'Connor and E.F. Robertson.Gottfried Wilhelm Flügge" at ''history.mcs.st-and.ac.uk.'' School of Mathematics and Statistics University of St Andrews, 2015. Accessed 2017-09-20.James Gere, George Herrmann, Charles R. Steele." at website Historical Society, Stanford University, 2004. He is known as recipient of the 1970 Theodore von Karman Medal in Engineering Mechanics, and the 1970 Worcester Reed Warner Medal.''Engineers of Distinction,'' Volume 2. 1973, p. 101 In 1934 Flügge published his most noted work ''Statik und Dynamik der Schalen'' in German, in 1960 translated it into English, entitled ''Stresses in shells.'' In those days this work evolved into the international standard work on shell theory. As Gere et al. (2004) put it, that work "served as the handbook for designers of concrete roofs, pressure vessels for storage and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Plates And Shells
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draws on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions.Timoshenko, S. and Woinowsky-Krieger, S. "Theory of plates and shells". McGraw–Hill New York, 1959. The typical thickness to width ratio of a plate structure is less than 0.1. A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two-dimensional problem. The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads. Of the numerous plate theories that have been developed since the late 19th century, two are widely accepted and used in engineering. These are * the Kirchhoff–Love theory of plates (classical plate theory) * The Uflyand-Mindlin theory of plates (first-order shear plate theory) Kirchhoff–Love theory for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress Resultants
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions. As a consequence the three traction components that vary from point to point in a cross-section can be replaced with a set of resultant forces and resultant moments. These are the stress resultants (also called '' membrane forces'', '' shear forces'', and ''bending moment'') that may be used to determine the detailed stress state in the structural element. A three-dimensional problem can then be reduced to a one-dimensional problem (for beams) or a two-dimensional problem (for plates and shells). Stress resultants are defined as integrals of stress over the thickness of a structural element. The integrals are weighted by integer po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Theories
A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge. A scientific theory differs from a scientific fact or scientific law in that a theory explains "why" or "how": a fact is a simple, basic observation, whereas a law is a statement (often a mathematical equation) about a relationship between facts. For example, Newton’s Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain ''how'' gravity works. Step ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
