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Steel and Composite Structures Volume 39, Number 1, April10 2021 , pages 1-20 DOI: https://doi.org/10.12989/scs.2021.39.1.001 |
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Exact third-order static and free vibration analyses of functionally graded porous curved beam |
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Mirza S. Beg, Hasan M. Khalid, Mohd Y. Yasin and L. Hadji
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| Abstract | ||
| An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1+z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1+z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies. | ||
| Key Words | ||
| refined third-order theory; functionally graded material; deep curved beams; porosity; Mori-Tanaka; analytical solution | ||
| Address | ||
| Mirza S. Beg, Hasan M. Khalid and Mohd Y. Yasin: Smart Structures Lab, Department of Mechanical Engineering, Z. H. College of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India L. Hadji: Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria | ||