Bending of a ribbed plate under complex loading

D. P. Goloskokov, A. V. Matrosov

Research output: Contribution to journalArticlepeer-review

Abstract

The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. An analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.

Original languageEnglish
Pages (from-to)120-130
Number of pages11
JournalVestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya
Volume17
Issue number2
DOIs
StatePublished - 2021

Scopus subject areas

  • Computer Science(all)
  • Control and Optimization
  • Applied Mathematics

Keywords

  • Dirac function
  • Fourier series
  • Heaviside function
  • Mathematical model
  • Numerical-analytical methods
  • Orthogonal series
  • Plate
  • Special discontinuous functions
  • Stiffeners

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