Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions
| Autor: | Yu. M. Volchkov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Materials science
Differential equation Mechanical Engineering Mathematical analysis 02 engineering and technology Equilibrium equation Condensed Matter Physics Orthotropic material 01 natural sciences Maximum error 010305 fluids & plasmas 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials 0103 physical sciences Boundary value problem Elasticity (economics) Legendre polynomials |
| Zdroj: | Journal of Applied Mechanics and Technical Physics. 58:904-913 |
| ISSN: | 1573-8620 0021-8944 |
| DOI: | 10.1134/s0021894417050170 |
| Popis: | This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|