Static response of laminated plate using new parabolic higher order shear deformation theory: A finite element approach
Document Type : Research Paper
Authors
- Sumit Khare 1
- Rahul Kumar 2
- Harish K Sharma 3
- Ram Bilas Prasad 4
- Kanif Markad 5
- Suraj Singh 2
- Ashutosh K. Tiwari 2
- Sourabh Ven 6
1 Department of Mechanical Engineering, SVNIT, Surat (GJ), India
2 Department of Mechanical Engineering, IET, DDU, Gorakhpur, India
3 Department of Mechanical Engineering, GLA University, Mathura, India
4 Department of Mechanical Engineering, MMMUT, Gorakhpur, U.P, India
5 Department of Mechanical Engineering, DVVP College of Engineering, Ahmednagar, India
6 Department of Civil, Computer Science and Aeronautical Technologies Engineering, Roma Tre University, Via Vito Volterra 62, Rome, 00146, Italy
Abstract
This study presents a new exponential higher-order shear deformation theory (NEHSDT) to examine the flexural analysis of multi-layered laminated composite plates. The novel parabolic shear deformation function is developed to analyze the bending response of laminated plates. A new shear deformation theory eliminates the need for shear correction factors. The present theory gives an exact parabolic distribution of transverse shear stress over the thickness and fulfills the traction-free boundary conditions on the outer surfaces of multi-layered laminated plates. The governing equations are solved using the finite element method. In this finite element method, a nine-nodded isoperimetric element with seven degrees of freedom per node is formed especially for this purpose. Illustrative examples are presented to demonstrate the predictive capability of the proposed finite element method. The presented numerical results are compared with the existing results to illustrate the correctness and robustness of the finite element method. The proposed analysis is accurate, converges rapidly, and is valid for thin and thick laminated plates based on comparisons with earlier higher-order shear deformation theories. In addition, the present results may be taken as the benchmark for further studies.
Keywords
Main Subjects
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[23] K. Soldatos, A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mechanica, Vol. 94, No. 3, pp. 195-220, 1992.
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[30] J. Mantari, A. Oktem, C. G. Soares, Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory, Composite structures, Vol. 94, No. 1, pp. 37-49, 2011.
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[32] J. N. Reddy, A simple higher-order theory for laminated composite plates, 1984.
[33] R. Shimpi, H. Patel, A two variable refined plate theory for orthotropic plate analysis, International Journal of Solids and Structures, Vol. 43, No. 22-23, pp. 6783-6799, 2006.
[34] S.-E. Kim, H.-T. Thai, J. Lee, Buckling analysis of plates using the two variable refined plate theory, Thin-Walled Structures, Vol. 47, No. 4, pp. 455-462, 2009.
[35] J. Mantari, A simple polynomial quasi-3D HSDT with four unknowns to study FGPs. Reddy’s HSDT assessment, Composite Structures, Vol. 137, pp. 114-120, 2016.
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Volume 56, Issue 1
January 2025Pages 101-126
- Receive Date: 29 May 2024
- Revise Date: 16 June 2024
- Accept Date: 20 June 2024