Paper Titles
Programmable Shape Transformation of 4D Printed Fibre-Reinforced Composites
p.3
Numerical Simulation-Based Design of Conductive Polymer Composites
p.9
A Study on Maximum Friction Voltage and Half-Life of Composite Fiber Fabrics Containing Metal Oxide Particles
p.15
Multiscale Dispersity Analysis and Fatigue Life Prediction of Fiber-Reinforced Composites
p.23
Modal Parameter Control and Forward Dynamic Design of Laminates
p.31
Experimental Study on Model Fracture Toughness of Unidirectional Composite Laminates Using Digital Image Correlation (DIC) Technique
p.41
The Influence of a Finite Element Mesh on the Reliability of the Results of Dynamic Processes of Armor Penetration of a Steel Plate by a Bullet
p.47
Exact Analytical Solution of the Problem of Elastic Bending of a Multilayer Circular Arch under the Action of a Normal Uniform Load
p.59
Dependence of the Elastoplastic Properties of Compressed Concrete on its Strain Rate
p.73

Exact Analytical Solution of the Problem of Elastic Bending of a Multilayer Circular Arch under the Action of a Normal Uniform Load

Article Preview

Abstract:

An exact analytical solution is presented for the problem of plane transverse bending of a segment of a narrow multilayer circular arch subjected to a normal uniformly distributed load on its longitudinal surfaces. The solution is constructed using the superposition principle based on the general solutions obtained by the authors for the bending problems of multilayer cantilevers with a circular axis under the action of loads on the free end and a uniformly distributed normal load on the longitudinal surfaces. Methods for modelling different types of end restraints for multilayer arches are considered: rigid, hinged, and combined. Using the example of a five-layer arch with varying restraints at the end, the influence of transverse shear deformations on the deflection and normal stresses is analyzed. The obtained relations allow determining the stress-strain state of multilayer arches with an arbitrary number of homogeneous (orthotropic, isotropic) layers, taking into account transverse shear and compression deformations, and can be used to construct other important solutions to arch deformation problems and develop more universal methods for calculating such structural elements.

You might also be interested in these eBooks
Composite Materials and Mechanics of Structural Materials View Preview

Info:

Periodical:

Solid State Phenomena (Volume 381)

Pages:

59-72

DOI:

https://doi.org/10.4028/p-bIeu0j

Citation:

Cite this paper

Online since:

December 2025

Authors:

Stanislav Kovalchuk*, Oleksii Goryk, Serhii Yakhin, Oleksandr Brykun

Keywords:

Displacement, Elastic Bending, Multilayer Arch, Orthotropic Layer, Stress, Uniform Load

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2025 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

References

[1] V. Shvabyuk, H. Sulym, O. Mikulich, Stress state of plate with incisions under the action of oscillating concentrated forces, Acta Mech. Autom., 9 (3) (2015) 140–144.

DOI: 10.1515/ama-2015-0023

Google Scholar

[2] V. I. Shvabyuk, O. A. Mikulich, V. V. Shvabyuk, Stress state of foam media with tunnel openings under non-stationary dynamic loading, Strength Mater., 49 (6) (2017) 818–828.

DOI: 10.1007/s11223-018-9927-3

Google Scholar

[3] B. Kasal, R. Blass, Experimental and analytical investigation of crack development in composite reinforced laminated arch, Mater. Struct., 46 (1–2) (2013) 173–180.

DOI: 10.1617/s11527-012-9892-4

Google Scholar

[4] X. Li, C. Guedes Soares, Spectral finite element analysis of in-plane free vibration of laminated composite shallow arches, Compos. Struct., 132 (2015) 484–494.

DOI: 10.1016/j.compstruct.2015.05.060

Google Scholar

[5] M. Surianinov, Y. Krutii, A. Kovrov, V. Osadchiy, The solution of the problem of free circulation of circular arcs by numerical analytical boundary elements method, E3S Web Conf., 211 (2020) 02022.

DOI: 10.1051/e3sconf/202021102022

Google Scholar

[6] A. G. Chanda, S. O. Ojo, V. Oliveri, P. M. Weaver, Dynamic analysis of variable stiffness curved composite beams based on the inverse differential quadrature method, Compos. Struct., 363 (2025) 119087.

DOI: 10.1016/j.compstruct.2025.119087

Google Scholar

[7] Z. Zhang, A. Liu, J. Yang, Y.-L. Pi, Y. Huang, J. Fu, Nonlinear in-plane buckling of shallow laminated arches incorporating shear deformation under a uniform radial loading, Compos. Struct., 252 (2020) 112732.

DOI: 10.1016/j.compstruct.2020.112732

Google Scholar

[8] M. Y. Yasin, H. M. Khalid, M. S. Beg, Exact solution considering layerwise mechanics for laminated composite and sandwich curved beams of deep curvatures, Compos. Struct., 244 (2020) 112258.

DOI: 10.1016/j.compstruct.2020.112258

Google Scholar

[9] M. S. Beg, M. Y. Yasin, Bending, free and forced vibration of functionally graded deep curved beams in thermal environment using an efficient layerwise theory, Mech. Mater., 159 (2021) 103919.

DOI: 10.1016/j.mechmat.2021.103919

Google Scholar

[10] S. P. Timoshenko, J.N. Goodier, Theory of Elasticity, 3rd Edition. McGraw Hill, New York, 1970.

Google Scholar

[11] S. G. Lekhnitskii, Anisotropic Plate, Gordon and Breach, New York, 1968.

Google Scholar

[12] S. G. Lekhnitskii, On the bending of a plane inhomogeneous curved beam, J. Appl. Math. Mech., 43 (1) (1979) 198–200.

Google Scholar

[13] G. Tolf, Stresses in a curved laminated beam, Fibre Sci. Technol., 19 (4) (1983) 243–267.

DOI: 10.1016/0015-0568(83)90012-x

Google Scholar

[14] W. L. Ko, R. H. Jackson, Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments, Compos. Struct., 5 (1989) 173–198.

DOI: 10.1007/978-94-009-1125-3_7

Google Scholar

[15] G. A. Kardomateas, Bending of a cylindrically orthotropic curved beam with linearly distributed elastic constants, Q. J. Mech. Appl. Math., 43 (1990) 43–55.

DOI: 10.1093/qjmam/43.1.43

Google Scholar

[16] G. A. Kardomateas, End force loading of generally anisotropic curved beams with linearly varying elastic constants, Int. J. Solids Struct., 27 (1) (1991) 59–71.

DOI: 10.1016/0020-7683(91)90145-6

Google Scholar

[17] J. Dryden, Bending of inhomogeneous curved bars, Int. J. Solids Struct., 44 (11–12) (2007) 4158–4166.

DOI: 10.1016/j.ijsolstr.2006.11.021

Google Scholar

[18] S. B. Koval'chuk, A. V. Goryk, Elasticity theory solution of the problem on bending of a narrow multilayer cantilever with a circular axis by loads at its end, Mech. Compos. Mater., 54 (5) (2018) 605–620.

DOI: 10.1007/s11029-018-9768-y

Google Scholar

[19] M. Wang, Y. Liu, Elasticity solutions for orthotropic functionally graded curved beams, Eur. J. Mech. A Solids, 37 (2013) 8–16.

DOI: 10.1016/j.euromechsol.2012.04.005

Google Scholar

[20] S. B. Koval'chuk, Analytical solution to the plane bending task of the multilayer beam with a circular axis under normal uniform loading, Strength Mater., 52 (5) (2020) 762–778.

DOI: 10.1007/s11223-020-00230-6

Google Scholar

[21] S. Koval'chuk, A. Goryk, Exact solution of the problem of elastic bending of a multilayer beam under the action of a normal uniform load, Mater. Sci. Forum, 968 (2019) 475–485.

DOI: 10.4028/www.scientific.net/msf.968.475

Google Scholar

[22] S. Koval'chuk, O. Goryk, S. Yakhin, A. Antonets, Exact analytical solution of the problem of elastic bending of a multilayer beam with a normal trapezoidal load, Key Eng. Mater., 1005 (2024) 107–119.

DOI: 10.4028/p-mzjc71

Google Scholar