Modeling of fiber circumplacement around a hole using a streamline approach

Stefan Hartmann; Ali Kheiri Marghzar

doi:10.32323/ujma.398481

EN

Modeling of fiber circumplacement around a hole using a streamline approach

Abstract

The insertion of holes into laminates can be done by producing a fiber reinforced composite plate and, subsequently, drilling the borehole. Alternatively, we can bypass the fibers around the final hole before injecting the matrix material. In the first case, the spatial distribution of the axis of anisotropy, and the structural tensor concerned, are spatially constant. In the second case, i.e. the fiber circumplacement around the hole, a space-dependent anisotropy has to be considered. Instead of the common approach of defining region-wise constant fiber orientations, we propose a continuous formulation of fiber orientations using streamlines. To estimate the final stress and strain state for a unidirectional composite plate, three-dimensional finite element simulations are performed, where spatially constant transverse isotropy is compared to inhomogeneously distributed fiber orientation around the hole. It will turn out that the resulting stress states lead to both reduced stress amplitudes in loading direction as well as compressive strains in lateral direction. A detailed mathematical derivation of the basic equations accompanies the investigations.

Keywords

Borehole,Composite,Streamline,Finite element analysis,Transverse isotropy

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Stefan Hartmann ^*
Germany

Ali Kheiri Marghzar This is me

Publication Date

March 11, 2018

Submission Date

February 25, 2018

Acceptance Date

March 6, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

DOI

https://doi.org/10.32323/ujma.398481

IZ

https://izlik.org/JA22WC43JW

APA

Hartmann, S., & Kheiri Marghzar, A. (2018). Modeling of fiber circumplacement around a hole using a streamline approach. Universal Journal of Mathematics and Applications, 1(1), 17-28. https://doi.org/10.32323/ujma.398481

AMA

1.Hartmann S, Kheiri Marghzar A. Modeling of fiber circumplacement around a hole using a streamline approach. Univ. J. Math. Appl. 2018;1(1):17-28. doi:10.32323/ujma.398481

Chicago

Hartmann, Stefan, and Ali Kheiri Marghzar. 2018. “Modeling of Fiber Circumplacement Around a Hole Using a Streamline Approach”. Universal Journal of Mathematics and Applications 1 (1): 17-28. https://doi.org/10.32323/ujma.398481.

EndNote

Hartmann S, Kheiri Marghzar A (March 1, 2018) Modeling of fiber circumplacement around a hole using a streamline approach. Universal Journal of Mathematics and Applications 1 1 17–28.

IEEE

[1]S. Hartmann and A. Kheiri Marghzar, “Modeling of fiber circumplacement around a hole using a streamline approach”, Univ. J. Math. Appl., vol. 1, no. 1, pp. 17–28, Mar. 2018, doi: 10.32323/ujma.398481.

ISNAD

Hartmann, Stefan - Kheiri Marghzar, Ali. “Modeling of Fiber Circumplacement Around a Hole Using a Streamline Approach”. Universal Journal of Mathematics and Applications 1/1 (March 1, 2018): 17-28. https://doi.org/10.32323/ujma.398481.

JAMA

1.Hartmann S, Kheiri Marghzar A. Modeling of fiber circumplacement around a hole using a streamline approach. Univ. J. Math. Appl. 2018;1:17–28.

MLA

Hartmann, Stefan, and Ali Kheiri Marghzar. “Modeling of Fiber Circumplacement Around a Hole Using a Streamline Approach”. Universal Journal of Mathematics and Applications, vol. 1, no. 1, Mar. 2018, pp. 17-28, doi:10.32323/ujma.398481.

Vancouver

1.Stefan Hartmann, Ali Kheiri Marghzar. Modeling of fiber circumplacement around a hole using a streamline approach. Univ. J. Math. Appl. 2018 Mar. 1;1(1):17-28. doi:10.32323/ujma.398481