A New Main Matrix to Find the Principal Stresses, Strains and the Max - Shear Stress, Strain by MATLAB Simulation

Abstract:

In this research, a main matrix has been derived from the stress components in the inclined plane with an angle θ that calculates the normal stresses and shear stress in the inclined plane to be used in calculating the main stresses and the maximum shear stress in one step, this is done using the principal stress angle which is calculated from known stress compounds. As well as calculating the maximum shear stress after using the correction factor. The inverse of this derived matrix can be used to calculate the stress compounds through the known principal stresses and this applies to the components of the principal strain and strain, and the maximum shear strain. All this is done through MATLAB simulation Keywords: Normal Stresses and Strains, Shear, Principal Stresses, max. Shear Stress

• Periodical: Engineering Headway (Volume 8)
• Pages: 121-132
• DOI: https://doi.org/10.4028/p-cLVS2s
• Online since: June 2024
• Authors: Abdullah Dhayea Assi*
• Keywords: Max. Shear Stress, Normal Stresses, Principal Stresses, Shear, Strains

References

[1] Mariano, C.A.; Sattari, S.; Maghsoudi-Ganjeh, M.; Tartibi, M.; Lo, "Eskandari, M. Novel Mechanical Strain Characterization of Ventilated ex vivo Porcine and Murine Lung using Digital Image Correlation", Front. Physiol. 2020, 11.

DOI: 10.3389/fphys.2020.600492

[2] David Roylance," Transformation of Stresses and Strains", Cambridge, MA 02139 May 14, 2001.

[3] Fernández, M.P.; Kao, A.P.; Witte, F.; Arora, H.; Tozzi, G. Low-cycle full-field residual strains in cortical bone and their influence on tissue fracture evaluated via in situ stepwise and continuous X-ray computed tomography. J. Biomech. 2020, 113, 110105.

DOI: 10.1016/j.jbiomech.2020.110105

[4] Robert M. Jones, "mechanics of composite materials ", second edition, Taylor & Francis, (1999)

[5] Tozzi, G.; Fernández, M.P.; Davis, S.; Karali, A.; Kao, A.P.; Blunn, G.W. Full-Field Strain Uncertainties and Residuals at the Cartilage-Bone Interface in Unstained Tissues Using Propagation-Based Phase-Contrast XCT and Digital Volume Correlation.Materials 2020, 13, 2579.

DOI: 10.3390/ma13112579

[6] George Z. Voyiadjis Peter I. Kattan, "Mechanics of Composite Materials with MATLAB', Springer-Verlag Berlin Heidelberg 2005.

[7] Nicolaie Dan Cristescu, Eduard-Marius Craciun, Eugen Soós, "Mechanics of Elastic Composites", 2004 by Chapman & Hall/CRC.

[8] Kelly, M.; Arora, H.; Worley, A.; Kaye, M.; Del Linz, P.; Hooper, P.A.; Dear, J.P. Sandwich panel cores for blast applications: Materials and graded density. Exp. Mech. 2015, 1–22.

DOI: 10.1007/s11340-015-0058-5

[9] Arora, H.; Del Linz, P.; Dear, J.P. Damage and deformation in composite sandwich panels exposed to multiple and single explosive blasts. Int. J. Impact Eng. 2017, 104, 95–106. 51. Rolfe, E.; Quinn, R.; Sancho, A.; Johnson, A.; Liu, H.

DOI: 10.1016/j.ijimpeng.2017.01.017

[10] Hooper, P.A.; Dear, J.P.; Arora, H. Blast resilience of composite sandwich panels with hybrid glass-fibre and carbon-fibre skins. Multiscale Multidiscip. Modeling Exp. Des. 2018, 1, 197–210.

DOI: 10.1007/s41939-018-0025-9

[11] Rolfe, E.; Quinn, R.; Irven, G.; Brick, D.; Dear, J.P.; Arora, H. Underwater blast loading of partially submerged sandwich composite materials in relation to air blast loading response. Int. J. Light. Mater. Manuf. 2020, 3, 387–402.

DOI: 10.1016/j.ijlmm.2020.06.003

[12] Koshiyama, K.; Nishimoto, K.; Ii, S.; Sera, T.;Wada, S. Heterogeneous structure and surface tension effects on mechanical response in pulmonary acinus: A finite element analysis. Clin. Biomech. 2019, 66, 32–39.

DOI: 10.1016/j.clinbiomech.2018.01.001

[13] Laszlo P. Kollari, "Mechanics of Composite Materials", Springer-Verlag Berlin Heidelberg 2003.

[14] David Roylance. Mechanics of Materials , Open Education Resource (OER) LibreTexts Project, https://libretexts.org/, 2023.

[15] Ferdinand P. Beer, E. Russell Johnston, Jr. John T. Dewolf . Mechanics of Materrials, Five Edition, 2020 Elsevier Ltd.

[16] Leckie, F.A., Bello, D.J.D. (2009). Transformation of Stress and Strain. In: Strength and Stiffness of Engineering Systems. Mechanical Engineering Series. Springer, Boston, MA.

DOI: 10.1007/978-0-387-49474-6_8

[17] Abdullah Dhayea Assi. Design Support System by MATLAB for Selection Steel Alloys. Journal of University of Babylon, Vol. 23, No. 1, 2015.

[18] Abdullah Dhayea Assi. Study of Transverse and Longitudinal Crack Propagation in Human Bone using the Finite Element Method with MATLAB, Al-Khwarizmi Engineering Journal, Vol. 15,No. 2, (2019)

DOI: 10.22153/kej.2019.01.001

[19] Autar K. Kaw, "Mechanics of Composite Materials", the Taylor & Francis ,2006.

[20] Đbrahim Fadıl SOYKÖK," Failure Analysis of Bolted and Pinned Composite Joints Under Temperature Effects ", A Thesis Submitted to the Graduate School of Natural and Applied Sciences of Dokuz Eylül University, October, 2012,ĐZMĐR.

[21] Abdullah Dhayea Assi. Solve the Cubic Equation in a New Method with Engineering Application. Al-Qadisiyah Journal for Engineering Sciences, Vol. 13, No.3,(2020)

DOI: 10.30772/qjes.v13i3.659