Exploration of the high order theory for functionally graded beams based on Legendre's polynomial expansion
Autor: | V. V. Zozulya |
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Rok vydání: | 2019 |
Předmět: |
Materials science
Order theory Series (mathematics) Mechanical Engineering Multiphysics Mathematical analysis 02 engineering and technology Elasticity (physics) 010402 general chemistry 021001 nanoscience & nanotechnology 01 natural sciences Industrial and Manufacturing Engineering Finite element method 0104 chemical sciences Mechanics of Materials Ceramics and Composites Boundary value problem Composite material 0210 nano-technology Polynomial expansion Legendre polynomials |
Zdroj: | Composites Part B: Engineering. 158:373-383 |
ISSN: | 1359-8368 |
Popis: | A high order theory for functionally graded (FG) beams based on expansion of the two dimensional (2-D) equations of elasticity for functionally graded materials (FGMs) into Legendre's polynomials series has been developed. The 2-D equations of elasticity have been expanded into Legendre's polynomials series in terms of a thickness coordinate. In the same way functions that describe functionally graded relations also has been expanded. Thereby all equations of elasticity including Hook's law have been transformed to corresponding equations for coefficients of Legendre's polynomials expansion. Then system of differential equations in term of displacements and boundary conditions for the coefficients of Legendre's polynomials expansion coefficients has been obtained. Cases of the first and second approximations have been considered in more detail. For the obtained boundary-value problems solution, a finite element method (FEM) has been used and numerical calculations have been done with MATHEMATICA, MATLAB and COMSOL Multiphysics software. Numerical results are presented and discussed. |
Databáze: | OpenAIRE |
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