Boundary Integral Equations for Arbitrary Geometry Shells
Theory of shells has numerous applications in engineering fields such as civil, aerospace, chemical, mechanical, naval, nuclear, and microelectronics. Different aspects of the theory of shells have been discussed in numerous publications of theoretical and applied nature (Guliaev et al. 1978), (Kil’chevski 1963), (Vekua 1982). However, there are still some problems that have not been solved or even properly understood. A fundamental problem of the theory of shells is reduction of the 3-D equations of the solid mechanics to 2-D equations of shells. It is necessary for the 2-D equations to be as simple as possible, and their solution should make it possible to reconstruct the three-dimensional stress–strain state as accurately as possible. The existing theory of shells appeared by way of a compromise between these mutually exclusive requirements.
KeywordsFundamental Solution Boundary Integral Equation Shell Theory Middle Surface Arbitrary Geometry
Unable to display preview. Download preview PDF.
- [ArGr02]Artyuhin, Yu.P., Gribanov, A.P.: Solution of the Problems of Nonlinear Deformation of Plates and Shallow Shells by Boundary Element Method, Kazan University Publisher House, Kazan (2002) (Russian). Google Scholar
- [Be91]Beskos, D.E.: Boundary Element Analysis of Plates and Shells, Springer, Berlin, 93–140 (1991). Google Scholar
- [GuBL78]Guliaev, V.I., Bajenov, V.A., Lizunov, P.P.: Nonclassical Shell Theory and Its Application for Engineering Problems Solution, Vyshcha shkola, Lviv (1978) (Russian). Google Scholar
- [Ho83-85]Hormander, L.: The Analysis of Linear Partial Differential Operators, vols. I–IV, Springer Verlag, Berlin (1983–1985). Google Scholar
- [Ki63]Kil’chevski, N.A.: Foundation of Analytical Theory of Shells, Publisher House of ANUkrSSR, Kiev (1963) (Russian). Google Scholar
- [Pa91]Paymushin, V.I., Sidorov, I.N.: Variant of boundary integral equation method for solution of static problems for isotropic arbitrary geometry shells. Mech. Solids, 1, 60–169 (1991). Google Scholar
- [Ve78]Vekua, I.N.: Fundamental of Tensor Analysis and Theory of Covariants, Nauka, Moskow (1978) (Russian). Google Scholar
- [Ve82]Vekua, I.N.: Some General Methods of Construction Various Variants of Shell Theory, Nauka, Moskow (1982) (Russian). Google Scholar
- [Zo07]Zozulya, V.V.: Mathematical modeling of pencil-thin nuclear fuel rods, in: Structural Mechanics in Reactor Technology (Editor: A. Gupta), SMIRT, Toronto, C04–C12, (2007). Google Scholar