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Titlebook: Elasticity; J. R. Barber Textbook 2022Latest edition The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer

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Gladstone and the Ulster question,8, except for a few important differences — notably that (i) the ends of the beam constitute two new boundaries on which boundary conditions (usually weak boundary conditions) are to be applied and (ii) it is no longer necessary to enforce continuity of displacements (see §9.3.1), since a suitable p
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Ice-Wedge Polygons of Northern Alaskas are defined by equations of the form . .. A wide range of such problems can be treated using stress functions which are polynomials in ., .. In particular, polynomial solutions can be obtained for ‘Mechanics of Materials’ type beam problems in which a rectangular bar is bent by an end load or by a distributed load on one or both faces.
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https://doi.org/10.1007/978-1-4613-3793-5eak sense of force resultants, through equations (5.29–5.31). In general, if a rectangular beam is loaded by tractions of finite polynomial form, a finite polynomial solution can be obtained which satisfies the boundary conditions in the strong (i.e. pointwise) sense on two edges and in the weak sense on the other two edges.
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,The birth of Arall (1945–1981),dimensional stress states that satisfy the elasticity equations exactly is that in which the in-plane displacements . are everywhere zero, whilst the out-of-plane displacement . is independent of . — i.e.
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Problems in Rectangular Coördinatess are defined by equations of the form . .. A wide range of such problems can be treated using stress functions which are polynomials in ., .. In particular, polynomial solutions can be obtained for ‘Mechanics of Materials’ type beam problems in which a rectangular bar is bent by an end load or by a distributed load on one or both faces.
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