Definition of Critical Loading on Three-Layered Plate with Cuts by Transition from Static Problem to Stability Problem

Abstract:

In the paper stated method that is grounded on the following idea, firstly applied in the work [1]. The critical state equation of compression plate is obtained from according equations of lateral bending of same plate, if is made the substitution -P=T10Wx''+2S0T10Wxy''+T20Wy'' where T10, S°, T20-are the components of external compressive loading. Further the obtained differential equations are transferred into algebraic equations by approximation of deflection by system of preliminary selected functions and application of one of variation methods. From the obtained algebraic equations are defined the parameters of critical loading. The applied in the work method is that firstly is solved the static problem and are found deflection functions, subjected to concentrated loading in the point x=ξ, y=η, corresponding for al singularities, arising due the cuts influence. Actually at this are found the Green’s functions. This task is solved analytically and due the application of special discontinuous functions, the function of deflection is expressed as rapidly convergence series. Practically for the definition of deflection is sufficient the keeping of one term of series. Due the stated above [2] also is considered the solution in the refined formulation. The definition of critical loading on three-layered plate on grounded on the accordingly static problem.

• Periodical: Advanced Materials Research (Volume 1020)
• Pages: 143-150
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1020.143
• Online since: October 2014
• Authors: Gela Kipiani*
• Keywords: Bending, Critical Load, Parameter, Plate, Stability

References

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