journal article·2022-11-03Open access

Derivation and Verification of Laminated Composite T-Beam Theory

Yu-Ting Lyu, Tsung-Pin Hung, Herchang Ay, Hsiu-An Tsai, Yih-Cherng Chiang, Ah-Der Lin

Applied Sciences· Volume 12· Issue 21

Abstract

This study analyzes the composite laminated T-beams using the composite beam and laminated composite plate theories. The theoretical formula was derived assuming that the composite T-beam has one- and two-dimensional (1D and 2D) structures. The 1D analysis was performed according to the Kirchhoff-Love hypothesis, thereby considering only the axial strain to derive a relationship between the strain and displacement. The 2D analysis was performed considering the T-beam as a combination of two composite sheets. The effective stiffness of the beam was derived from the stress-strain and moment-curvature relationships. Furthermore, the deflection of the beam and the stress of each laminate were calculated. A simple support beam, made of AS4/3501-6 carbon/epoxy, was used as a composite laminated T-beam. MSC/NASTRAN finite element software was used for analysis. The accuracy of the theoretical formula and limitations of its use was verified using the finite element analysis. Higher accuracy of the theoretical formula was obtained at a composite beam aspect ratio greater than 15. The formula derived in this study is suitable for thin and long beams.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Structural Load-Bearing Analysis · Composite Structure Analysis and Optimization · Structural Analysis and Optimization

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Mold and Die Engineering, National Kaohsiung University of Science and Technology, Kaohsung 807618, Taiwan

Department of Mechanical Engineering, Center for Environmental Toxin and Emerging-Contaminant Research, Super Micro Mass Research & Technology Center, Cheng Shiu University, Kaohsiung 833301, Taiwan

Metal Industries Research and Development Centre (MIRDC), Kaohsiung 811020, Taiwan

Department of Mechanical Engineering, Chinese Culture University, Taipei 11114, Taiwan

Funding

Metal Industries Research and Development Centre (MIRDC)

References (31)

Show source-provided references
1. Modifications to beam theory for bending and twisting of open-section composite beams10.1016/0263-8223(90)90001-U ↗
2. Shear coefficients for thin-walled composite beams10.1016/0263-8223(87)90015-8 ↗
3. A beam theory for thin-walled composite beams10.1016/0266-3538(88)90065-6 ↗
4. The Shear Coefficient in Timoshenko’s Beam Theory10.1115/1.3625046 ↗
5. Stress Analysis of Laminated Composite and Sandwich Beams using a Novel Shear and Normal Deformation Theory10.1590/1679-78251470 ↗
6. Effect of Transverse Shear and Transverse Normal Strain on Bending Analysis of Cross-Ply Laminated Beams
7. Elastic wave propagation in heterogeneous plates10.1016/0020-7683(66)90045-X ↗
8. Chandra, R., and Chopra, I. (1991). Experimental and Theoretical Analysis of Composite I-Beams with Elastic Couplings. Proceedings of the 32th AIAA/ASME/ASCE/ASC Structures, Structural Dynamics and Materials Conference, AIAA.10.2514/6.1991-1024 ↗
9. A Vlasov Theory for Fiber Reinforced Beams with Thin-Walled Open Cross-Sections10.1016/0020-7683(84)90039-8 ↗
10. Experiment and Analysis for Composite Blades Under Large Deflections Part 1: Static Behavior10.2514/3.25255 ↗
11. Rios, G. (2009). A Unified Analysis of Stiffener Reinforced Composite Beams with Arbitrary Cross-Section. [Ph.D. Thesis, The University of Texas at Arlington].
12. Stress Analysis of Laminated Composite Beam by Using MATLAB Software
13. Trigonometric-series solution for analysis of laminated composite beams10.1016/j.compstruct.2016.10.033 ↗
14. Flexure analysis of laminated composite and sandwich beams using Timoshenko beam theory
15. A Beam Theory for Anisotropic Materials,” Transactions of the American Society of Mechanical Engineers10.1115/1.3169063 ↗
16. Kosmatka, J. (1989, January 3–5). Extension, bending, and torsion of anisotropic beams with initial twist. Proceedings of the 30th Structures, Structural Dynamics and Materials Conference, Mobile, AL, USA.10.2514/6.1989-1364 ↗
17. Finite-Element Model for Composite Beams with Arbitrary Cross-Sectional Warping10.2514/3.48797 ↗
18. Kosmatka, J., and Friedmann, P. (1987, January 6–8). Structural dynamic modeling of advanced composite propellers by the finite element method. Proceedings of the 28th Structures, Structural Dynamics and Materials Conference, Monterey, CA, USA.10.2514/6.1987-740 ↗
19. Finite Element Approach to Rotor Blade Modeling10.4050/JAHS.32.60 ↗
20. Bending of thick angle-ply bimodular composite plates10.2514/3.10515 ↗
21. Structural design and analysis of a composite wing with high aspect ratio10.1631/jzus.A1900271 ↗
22. Topological designing and analysis of the composite wing rib10.32620/aktt.2020.6.01 ↗
23. Structural Analysis and Testing of an Ultralight Un-manned-Aerial-Vehicle Carbon-Composite Wing10.2514/1.36415 ↗
24. Abhiram, D.R., Ganguli, R., and Harursampath, D.K. (2019, January 13–16). Sturcture Optimization of Composite Rotor Blade for Un-manned Helicopter using Variational Asymptotic Beam Sectional Analysis and Multi-Objective Bat Algorithm. Proceedings of the Vertical Flight Society 75th Annual Forum & Techonolgy Display, Philadelphia, PA, USA.
25. Design and Analysis of a Composite Beam for Side Impact Protection of a Car Door
26. Dynamic modelling and analysis of smart carbon nano-tube-based hybrid composite beams: Analytical and finite element study
27. Swanson, S.R. (1997). Advanced Composite Material, Prentice Hall.
28. Ugural, C. (1991). Mechanics of Materials, McGraw-Hill.
29. (2022, October 25). MSC/NASTRAN Application Manual. Available online: https://www.academia.edu/9977854/MSC_Nastran_2001_Numerical_Methods_Users_Guide.
30. (2022, October 25). MSC/NASTRAN Linear & Nonlinear Static Analysis User’s Guide. Available online: https://help.hexagonmi.com/bundle/MSC_Nastran_2021.3_Linear_Static_Analysis_User_Guide/resource/MSC_Nastran_2021.3_Linear_Static_Analysis_User_Guide.pdf.
31. Lyu, Y.-T., Hung, T.-P., Ay, H.-C., Tsai, H.-A., and Chiang, Y.-C. (2022). Evaluation of Laminated Composite Beam Theory Accuracy. Materials, 15.10.3390/ma15196941 ↗