A perturbation solution of von-Kármán circular plates with different moduli in tension and compression under concentrated force

ABSTRACT

By modifying classical von-Kármán equations, we established bimodular von-Kármán equations of thin plates with different moduli in tension and compression. Adopting central deflection as a perturbation parameter, we used a perturbation method to solve the equations under various boundary conditions, including rigidly clamped, loosely clamped, simply hinged, and simply supported. The relation of load versus central deflection and stress formulas were derived via the perturbation solution obtained. The numerical simulation also shows that the perturbation solution based on central deflection is overall valid. The results indicate that when the compressive modulus of materials is greater than the tensile one, the bearing capacity of the plate will be further strengthened, which should be considered in the analysis and design of plate-like structures with obvious bimodular effect. Moreover, by comparing with the case under uniformly distributed load, the plate-membrane transition under centrally concentrated force presents discontinuity to some extent.

KEYWORDS:

• tension and compression
• bimodulus
• von-Kármán equations
• perturbation
• concentrated force
• thin plates

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11572061) and also by the Fundamental Research Funds for the Central Universities, P.R. China (Grant No. 106112014CDJZR200021).