A Novel Semi-Analytical Approach to the Assessment of the Equivalent Stiffness of a Beam

Zámečníková, Tereza; Mareš, Tomáš; Kulíšek, Viktor; Padovec, Zdeněk; Malá, Anna; Kropík, Bohumil

doi:10.2478/scjme-2022-0033

Abstract

This paper introduces several new approaches to stiffness calculation of the composite beam with a circular cross-section. The paper poses the problem of calculating the stiffness of the fibre-reinforced winded beam and introduces a new way of stiffness calculation. The novel semi-analytical calculation represents an approach that is less time consuming than conventional calculation methods or FEA methods. The expected application of the new method of calculation is in preliminary design and design calculations.

References

[1] Barbero, Ever J. “Finite element analysis of composite materials using Abaqus”, Boca Raton: CRC Press/Taylor & Francis Group; 2013. 413 p. ISBN 978-14-6651-661-8
Search in Google Scholar Back to article
[2] Barbero, Ever J. “Introduction to composite materials design”, 2nd. Boca Raton: CRC Press, 2011. ISBN 9781420079159;1420079158
Search in Google Scholar Back to article
[3] Berthelot, Jean-Marie “Composite materials: Mechanical behavior and structural analysis”, New York: Springer, 1999. Mechanical engineering series. ISBN 0-387-98426-7.
Search in Google Scholar Back to article
[4] Lekhnitskii, S. G., Brandstatter, J. “Theory of elasticity of an anisotropic elastic body”, San Francisco: HOLDEN-DAY, 1963.
Search in Google Scholar Back to article
[5] Karama, M., Afaq, K. S., Mistou, S. “Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity”, International Journal of Solids and Structures 40, pp. 1525 – 1546, 2003.
Search in Google Scholar Back to article
[6] Jiann-Quo, T., Wang, Y-M. “Laminated composite tubes under extension, torsion, bending, sparing and pressuring: a state-space approach”, International Journal of Solids and Structures 38, pp. 9053 – 9075, 2001.
Search in Google Scholar Back to article
[7] Wen, S. Ch., Demirhan, K. C. “A Simple Closed-Form Solution of Bending Stiffness for laminated Composite Tubes”, Journal of Reinforced Plastics and Composites 19 (4), pp. 278 – 291, 2000.
Search in Google Scholar Back to article
[8] Zhanming, Q., Librescu, L. “On a shear-deformable theory of anisotropic thin-walled beams: further contribution and validations”, Composite Structures 56 (4), pp. 345 – 358, 2002.
Search in Google Scholar Back to article
[9] Zvi, H., Rosen, B. W. “The Elastic Moduli of Fiber-Reinforced Materials”, Journal of Applied Mechanics 31 (86), Trans. ASME, Series E, pp. 223 – 232, 1964.
Search in Google Scholar Back to article
[10] Shadmehri, F., Derisi, B., HOA, S. V. “On bending stiffness of composite tubes”, Composite Structures 93 (9), pp. 2173 – 2179, 2011.
Search in Google Scholar Back to article
[11] Kim, Nam-Il et al. “Coupled deflection analysis of thin-walled Timoshenko laminated composite beams”, Computational Mechanics 43 (4), pp. 493 – 514, 2009.
Search in Google Scholar Back to article
[12] Claude, J., Cardou, A. “Analytical Solution for Bending of Coaxial Orthotropic Cylinders”, Journal of Engineering Mechanics 120 (12), pp. 2556 – 2574, 1994.
Search in Google Scholar Back to article
[13] Chouchaoui, C. S., Ochoa, O. O. “Similitude study for a laminated cylindrical tube under tensile, torsion, bending, internal and external pressure Part I: governing equations”, Composite structures 44, pp. 221 – 229, 1999.
Search in Google Scholar Back to article
[14] Chouchaoui, C. S., Ochoa, O. O. “Similitude study for a laminated cylindrical tube under tensile, torsion, bending, internal and external pressure Part II: scale models”, Composite structures 44, pp. 231 – 236, 1999.
Search in Google Scholar Back to article
[15] Librescu, L., Song, O. “Thin-walled composite beams: theory and application”, Springer, 2006. ISBN 9781402042034; 1402042035
Search in Google Scholar Back to article
[16] Ting, T. C. T. “Pressuring, shearing, torsion and extension of a circular tube or bar of cylindrically anisotropic material”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 452.1954: pp. 2397 – 2421, 1996.
Search in Google Scholar Back to article
[17] Ting, T. C. T. “New solutions to pressuring, shearing, torsion and extension of a cylindrically anisotropic elastic circular tube or bar”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 455.1989, pp. 3527 – 3542, 1999.
Search in Google Scholar Back to article
[18] Chen, T., Chung, Ch-T., Lin, W-L. “A revisit of a cylindrically anisotropic tube subjected to pressuring, shearing, torsion, extension and a uniform temperature change”, International Journal of Solids and Structures 37 (37), pp. 5143 – 5159, 2000.
Search in Google Scholar Back to article
[19] Bhaskar, V., Srinivas, K., Rao, D. “Investigation on Physical and Mechanical Properties of Banana and Palmyra Fiber Reinforced Epoxy Composites”, Strojnícky časopis – Journal of Mechanical Engineering 70(2), pp. 167 – 180, 2020. DOI: 10.2478/scjme-2020-0029
Search in Google Scholar Back to article
[20] Andrii, D. et al. “Modeling of a Stress-Strain State of Detachable Connection in Details of Reinforced Composite Materials with Cea Method”, Strojnícky časopis – Journal of Mechanical Engineering 70 (1), pp. 17 – 28, 2020. DOI: 10.2478/scjme-2020-0002
Open DOI Search in Google Scholar Back to article
[21] Zámečníková, T. et al. “Comparison of methods for calculation of composite wound tube deflection”, Materials Today: Proceedings 32, pp. 224 – 231. 2020.
Search in Google Scholar Back to article
[22] Zavřelová, T. “Analysis of composite beam bending. Diploma thesis (Ing.)”, Czech Technical University in Prague. Faculty of Mechanical Engineering, Department of mechanics, biomechanics and mechatronics. Prague, CZ, 2015.
Search in Google Scholar Back to article

A Novel Semi-Analytical Approach to the Assessment of the Equivalent Stiffness of a Beam

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