Application of Differential Equations to Calculations of Large Deformations of Structural Members

Abstract:

The article discusses the application of differential equations to solve large deformations of the designed slender structural elements. The structural element under design has a variable circular cross-section in longitudinal direction. It is made of a composite material based on carbon fiber and is capable of large deformations. In the solution it was necessary to consider the nonlinear deformation theory, which led to the solution of a nonlinear differential equation of second order. The creation of the differential equation describing the line of elastic deformation of a significantly curved structural element required the formulation of input equations and boundary conditions for its solution. The results obtained by means of a differential equation were compared with the numerical solution applying the finite element method. The solution presented and methodology can be used for practical application in the engineering design of fishing rods.

• Periodical: Applied Mechanics and Materials (Volume 611)
• Pages: 400-404
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.611.400
• Online since: August 2014
• Authors: Oskar Ostertag*, Ladislav Novotný, Eva Ostertagová
• Keywords: Beam, Differential Equation, Finite Element Analysis (FEA), Large Deformations

References

[1] A.S. Berdyshev, A. Cabada, E.T. Karimov and N.S. Akhtaeva, On the Volterra property of a boundary problem with integral gluing condition for mixed parabolic-hyperbolic equation, in: Boundary Value Problems, 2013, 2013: 94.

DOI: 10.1186/1687-2770-2013-94

[2] A.S. Berdyshev, E.T. Karimov and N. Akhtaeva, Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation, in: International Journal of Differential Equations, Vol. 2011, Article ID 268465, 10 p., (2011).

DOI: 10.1155/2011/268465

[3] A. Vega, S. Rashed, Y. Tango, M. Ishiyama, H. Murakawa, Analysis and prediction of multi-heating lines effect on plate forming by line heating. CMES Journal: Computer Modeling in Engineering & Sciences, CMES, Vol. 28, No. 1, pp.1-14, (2008).

[4] G. Fedorko, Determination of the Material Characteristics of Pipe Conveyor Belts for Mathematical Modeling. Doprava a logistika (CD-ROM), Vol. 9, 2011, pp.474-483.

[5] E. Parente and L. E. Vaz, On evaluation of shape sensitivities of non-linear critical loads. International journal for numerical methods in engineering, No. 56, pp.809-846, (2003).

DOI: 10.1002/nme.587

[6] K. Semrád, Fatigue and Buckling Strength Analysis of the Wing Hinge in the Creo Simulation Environment, Journal of Mechanics Engineering and Automation. Vol. 3, no. 4, pp.247-250.

DOI: 10.17265/2159-5275/2013.04.008