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Modern interpretation of Saint-Venant’s principle and semi-inverse method
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In: Structural Mechanics of Engineering Constructions and Buildings, Vol 16, Iss 5, Pp 390-413 (2020) (2020)
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Abstract:
Relevance. The progressive development of views on the Saint-Venant formulated principles and methods underlying the deformable body mechanics, the growth of the mathematical analysis branch, which is used for calculation and accumulation of rules of thumb obtained by the mathematical results interpretation, lead to the fact that the existing principles are being replaced with new, more general ones, their number is decreasing, and this field is brought into an increasingly closer relationship with other branches of science and technology. Most differential equations of mechanics have solutions where there are gaps, quick transitions, inhomogeneities or other irregularities arising out of an approximate description. On the other hand, it is necessary to construct equation solutions with preservation of the order of the differential equation in conjunction with satisfying all the boundary conditions. Thus, the following aims of the work were determined: 1) to complete the familiar Saint-Venants principle for the case of displacements specified on a small area; 2) to generalize the semi-inverse Saint-Venants method by finding the complement to the classical local rapidly decaying solutions; 3) to construct on the basis of the semi-inverse method a modernized method, which completes the solutions obtained by the classical semi-inverse method by rapidly varying decaying solutions, and to rationalize asymptotic convergence of the solutions and clarify the classical theory for a better understanding of the classic theory itself. To achieve these goals, we used such methods , as: 1) strict mathematical separation of decaying and non-decaying components of the solution out of the plane elasticity equations by the methods of complex variable theory function; 2) construction of the asymptotic solution without any hypotheses and satisfaction of all boundary conditions; 3) evaluation of convergence. Results. A generalized formulation of the Saint-Venants principle is proposed for the displacements specified on a small area of a body. A method of constructing asymptotic analytical solutions of the elasticity theory equations is found, which allows to satisfy all boundary conditions.
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Keyword:
Architectural engineering. Structural engineering of buildings; complete solution; contraction mapping principle; elasticity; fixed point theorem; saint-venant; strip; TH845-895
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URL: https://doaj.org/article/dd155ff02d4e4decb22290bc3045ad6d
https://doi.org/10.22363/1815-5235-2020-16-5-390-413
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| 11 |
Fully-Functional Bidirectional Burrows-Wheeler Indexes and Infinite-Order De Bruijn Graphs
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Belazzougui, Djamal; Cunial, Fabio. - : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2019. : LIPIcs - Leibniz International Proceedings in Informatics. 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019), 2019
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| 12 |
SYNTACTIC VARIATION AND AUXILIARY CONTRACTION: THE SURPRISING CASE OF SCOTS
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| 13 |
Словообразовательные модели топонимов немецкого языка в динамическом аспекте ; Word-Formation Patterns in German Toponymy: A Dynamic Perspective
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Sonority bias in Rugao di-syllabic syllable contraction
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In: Proceedings of the Linguistic Society of America; Vol 3 (2018): Proceedings of the Linguistic Society of America; 28:1–13 ; 2473-8689 (2018)
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| 20 |
The functions of external voices in hard news Appraisal: A dialogic perspective
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In: Topics in Linguistics, Vol 18, Iss 2, Pp 63-80 (2017) (2017)
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