Original scientific paper
https://doi.org/https://doi.org/10.32762/zr.27.1.8
Analytical solution for the problem of pure bending of orthotropic micropolar plate
Damjan Jurković
; University of Rijeka, Faculty of Civil Engineering
*
Gordan Jelenić
; University of Rijeka, Faculty of Civil Engineering
Sara Grbčić Erdelj
; University of Rijeka, Faculty of Civil Engineering
* Corresponding author.
Abstract
When analysing the problem of pure bending of a plate, it can be noticed that, for cylindrical bending, a spatial problem collapses into a plane-strain problem. For such a boundary-value problem of the Cosserats' continuum, three engineering parameters are required: Young’s modulus, Poisson’s ratio and the characteristic length for bending. Here we consider an orthotropic form of such a problem, whereby two Young’s moduli, four Poison’s ratios and one characteristic length for bending are found to be sufficient to propose a mathematical model of this problem. General equations of the isotropic micropolar continuum are introduced, and the analytical solution for the pure bending of an isotropic micropolar plate is generalized to the case of orthotropic microstructure. By defining the ratio of a distributed force and a distributed moment boundary conditions required for the pure-bending state, a closed-form solution to this problem is obtained in terms of displacement, strains and stress functions. It is shown that the derived results reduce to the isotropic ones if a material isotropy is assumed.
Keywords
orthotropic micropolar continuum; analytical solution of pure bending; characteristic length for bending
Hrčak ID:
324024
URI
Publication date:
18.12.2024.
Visits: 0 *