Numerical Analysis of Large Deflections of a Flat Textile Structure with Variable Bending Rigidity and Verification of Results Using Fem Simulation

• Autorzy: Szablewski Piotr

Identyfikatory

DOI

10.2478/aut-2020-0033

• Języki publikacji: EN

Abstrakty

EN

The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method.

Słowa kluczowe

EN

textile structure; large deflection; heavy elastica; variable bending rigidity; numerical methods; finite element method

PL

struktura tekstyliów; ugięcie duże; sztywność zginania; metody numeryczne; metoda elementów skończonych

• Wydawca: Lodz University of Technology, Faculty of Material Technologies and Textile Design
• Czasopismo: Autex Research Journal
• Rocznik: 2021
• Tom: Vol. 21, no. 1
• Strony: 108--114
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Szablewski Piotr

• Department of Mechanical Engineering, Informatics and Chemistry of Polymer Materials, Lodz University of Technology, Lodz, Poland

Bibliografia

• [1] Gere, J. M. (2004). Mechanics of materials. (6th ed.). Brooks/Cole-Thomson Learning (Belmont, CA).
• [2] Lee, B. K., Wilson, J. F., Oh, S. J. (1993). Elastica of cantilevered beams with variable cross sections. International Journal of Non-Linear Mechanics, 28, 579–589.
• [3] Baker, G. (1993). On the large deflections of non-prismatic cantilevers with a finite depth. Computers & Structures, 46(2), 365–370.
• [4] Dado, M., AL-Sadder, S. (2005). A new technique for large deflection analysis of non-prismatic cantilever beams. Mechanics Research Communications, 32(6), 692–703.
• [5] Shatnawi, A., AL-Sadder, S. (2007). Exact large deflection analysis of non-prismatic cantilever beams of nonlinear bimodulus material subjected to tip moment. Journal of Reinforced Plastics and Composites, 26(12), 1253–1268.
• [6] Shvartsman, B. S. (2007). Large deflections of a cantilever beam subjected to a follower force. Journal of Sound and Vibration, 304(3–5), 969–973.
• [7] Szablewski, P., Kobza, W. (2003). Numerical analysis of Peirce's cantilever test for the bending rigidity of textiles. Fibres & Textiles in Eastern Europe, 11(4), 54–57.
• [8] AL-Sadder, S., AL-Rawi, R. (2006). Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings. Archive of Applied Mechanics, 75(8), 459–473.
• [9] Ibrahimbegovic, A. (1995). On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements. Computer Methods in Applied Mechanics and Engineering, 122, 11–26.
• [10] Lewis, G., Monasa, F. (1981). Large deflections of cantilever beams of nonlinear materials. Computers & Structures, 14(5–6), 357–360.
• [11] Lee, K. (2002). Large deflections of cantilever beams of non-linear elastic material under a combined loading. International Journal of Non-Linear Mechanics, 37(3), 439–443.
• [12] Szablewski, P., Korycki, R. (2019). Numerical analysis of free folding of flat textile products and proposal of new test concerning bending rigidity. Indian Journal of Fibre & Textile Research, 44, 180–187.
• [13] Rezazadeh, G. (2008). A comprehensive model to study nonlinear behavior of multilayered micro beam switches. Microsystem Technologies, 14(1), 135–141.
• [14] Antman, S. (1984). Large lateral buckling of nonlinearly elastic beams. Archive for Rational Mechanics and Analysis, 84(4), 293–305.
• [15] Cesnik, C., Sutyrin, V., Hodges, D. (1996). Refined theory of composite beams: The role of short-wavelength extrapolation. International Journal of Solids and Structures, 33(10), 1387–1408.
• [16] Szablewski, P. (2006). Analysis of the stability of a flat textile structure. AUTEX Research Journal, 6(4), 204–215.
• [17] Seames, A. E., Conway, H. D. (1957). A numerical procedure for calculating the large deflections of straight and curved beams. Journal of Applied Mechanics, 24, 289–294.
• [18] Rhode, F. V. (1953). Large deflections of cantilever beams with uniformly distributed load. Quarterly of Applied Mathematics, 11, 337–338.
• [19] Lee, H., Durelli A. J., Parks, V. J. (1969). Stress in largely deflected cantilever beams subjected to gravity. Journal of Applied Mechanics, 36, 323–325.
• [20] Szablewski, P., Korycki, R. (2016). Shape determination of elastica subjected to bending by means of displacements. Fibres & Textiles in Eastern Europe, 24(6), 138–142.
• [21] Belendez, T., Perez-Polo, M., Neipp, C., Belendez, A. (2005). Numerical and experimental analysis of large deflections of cantilever beams under a combined load. Physica Scripta, T118, 61–65.
• [22] Frisch-Fay, R. (1962). Large deflections of a cantilever beam under two concentrated loads. Journal of Applied Mechanics, 29(1), 200–201.
• [23] Bisshopp, K. E., Drucker, D. C. (1945). Large deflections of cantilever beams. Quarterly of Applied Mathematics, 3, 272–275.
• [24] Belendez, T., Neipp, C., Belendez, A. (2002). Large and small deflections of a cantilever beam. European Journal of Physics, 23(3), 371–379.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).