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Cusped Beams

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Book cover Cusped Shell-Like Structures

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSAPPLSCIENCES))

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Abstract

If we consider the cylindrical bending of a plate, in particular, of a cusped one, with rectangular projection \(a\le x_{1} \le b,{\rm \; \; \; 0}\le x_{2} \le L\), then we, actually (if we take Poisson’s ratio equal to zero, they will exactly coincide), get the corresponding results also for cusped beams [see (Jaiani, Cylindrical bending of a rectangular plate with power law changing stiffness.Tbilisi University Press, Tbilisi, pp. 49–52, 1976, Boundary value problems of mathematical theory of prismatic shells with cusps. Tbilisi University Press, Tbilisi, pp. 126–142, 1984) , see also (Jaiani, ZAMM Z. Angew. Math. Mech. 81(3):147–173, 2001) and (Chinchaladze, Rep. Enlarged Sess. Semin. I. Vekua Appl. Math 10(1):21–23, 1995 , Rep. Enlarged Sess. Semin. I. Vekua Appl. Math 14(1):12–20, 1999, Proc. I. Vekua Inst. Appl. Math 52:30–48 2002)] . In the present chapter we briefly sketch all the papers devoted to both cusped Euler–Bernoulli beams and hierarchical models of cusped beams.

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Notes

  1. 1.

    Under (3.15)\(_0\) we mean the static system corresponding to (3.15). In what follows we use similar stipulation in other cases as well.

  2. 2.

    i.e., integrable on any interval contained in \(]0,L[\)

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Authors and Affiliations

  1. I. Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, University Street 2, 0186, Tbilisi, Georgia

    George Jaiani

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  1. George Jaiani
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Jaiani, G. (2011). Cusped Beams. In: Cusped Shell-Like Structures. SpringerBriefs in Applied Sciences and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22101-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-22101-9_5

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