On a Description of Deformable Junction in the Resultant Nonlinear Shell Theory
The virtual work principle for two regular shell elements joined together along a part of their boundaries is proposed within the general nonlinear resultant shell theory. It is assumed that translations across the junction curve are smooth, but no restri
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Abstract The virtual work principle for two regular shell elements joined together along a part of their boundaries is proposed within the general nonlinear resultant shell theory. It is assumed that translations across the junction curve are smooth, but no restrictions are enforced on the rotations. For stiff and hinge type junctions, the curvilinear integral along the junction curve vanishes identically. In the case of deformable junction, the 1D constitutive type relation is proposed, where the constitutive function should be established by experiments for each particular engineering construction of the junction.
1 Introduction By junctions of shells we mean design elements used for assembling regular shell parts along some of their boundaries into the complex multi-shell structure. It follows from the review by Pietraszkiewicz and Konopi´nska (2015) that different shell models available in the literature require special forms of jump conditions at the singular surface curves modelling the shell junctions. Jump conditions corresponding to different shell models may lead to different stress and strain distributions near the junction. But the review also indicates that almost in all descriptions of shell junctions available in the literature the stiff junction conditions were enforced. Deformability of the junction itself was explicitly indicated and used in only a few papers based on the simplest shell models. This is in sharp contrast to the analyses and design of one-dimensional steel framed structures, where various semi-rigid beam-to-column connections were discussed in a number of papers, summarised in several books e.g. (Chen et al. 1996; Faella et al. 1999) and were even introduced into Eurocode 3 (1993). Within the resultant nonlinear six-field shell model, the mechanical theory of compound multi-shell structures was initiated by Makowski and Stumpf (1994) and W. Pietraszkiewicz (B) Institute of Fluid-Flow Machinery, PASci, ul. Gen. J. Fiszera 14, 80-231 Gda´nsk, Poland e-mail: [email protected] © Springer Science+Business Media Singapore 2016 K. Naumenko and M. Aßmus (eds.), Advanced Methods of Continuum Mechanics for Materials and Structures, Advanced Structured Materials 60, DOI 10.1007/978-981-10-0959-4_25
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developed in the book by Chró´scielewski et al. (2004). In this approach several regular shell elements may be joined at the common junction, deformability of any of the shell branches at the junction may individually be defined, and the junction curve itself may be equipped with additional mechanical properties independent from the adjacent shell branches. Unfortunately, the BVP of such a general theory became extremely complex and virtually useless for engineering applications. Even relatively simple cases of branching and self-intersecting shells developed in Konopi´nska and Pietraszkiewicz (2007) and Pietraszkiewicz and Konopi´nska (2011) led to complex shell relations, which were still hardly readable for engineering community. This explains why in the review
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