An equilibrium of a micropolar elastic rectangle with mixed boundary conditions

The analytical method for solving of plane static problem in the micropolar elasticity theory in a rectangle region when normal stresses, tangential components of displacements and couple stresses are specified on a boundary is presented. In this method the original problem is reduced to the sequent...

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Bibliographic Details
Published in:Continuum mechanics and thermodynamics 2019-11, Vol.31 (6), p.1699-1718
Main Authors: Grigor’ev, Yu. M., Gavrilieva, A. A.
Format: Article
Language:English
Subjects:
Biharmonic equations
Boundary conditions
Boundary value problems
Classical and Continuum Physics
Dimensionless analysis
Dimensionless numbers
Elasticity
Engineering Thermodynamics
Exact solutions
Heat and Mass Transfer
Laplace equation
Original Article
Parametric analysis
Physics
Physics and Astronomy
Size effects
Stiffening
Stresses
Structural Materials
Theoretical and Applied Mechanics
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Summary:The analytical method for solving of plane static problem in the micropolar elasticity theory in a rectangle region when normal stresses, tangential components of displacements and couple stresses are specified on a boundary is presented. In this method the original problem is reduced to the sequent solution of scalar boundary value problems for the Laplace equation, the biharmonic equation and the Poisson equations. As an example the exact analytical solution expressed in terms of elementary functions in the case of particular boundary conditions is obtained. Numerical treatments with dimensionless parametric analysis show the values of micropolar effects such as size effect and stiffening.
ISSN:0935-1175
1432-0959
DOI:10.1007/s00161-019-00823-w