Fracture and Structural Integrity e-ISSN 1971-8993 Open access
Structural Integrity and Durability of Structures Vol. 14, No. 53 (2020)

Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length

Author and affiliation details
  • Victor Rizov Corresponding author Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy V_RIZOV_FHE@UACG.BG
  • Holm Altenbach Lehrstuhl für Technische Mechanik und Geschäftsführender Leiter Institut für Mechanik G10/58, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg
DOI
10.3221/IGF-ESIS.53.04
Pages
38-50
Published
Licence
CC BY 4.0
Published inVol. 14, No. 53 (2020)Go to the issue

Abstract

Analyses of longitudinal fracture behavior of inhomogeneous beams which have continuously varying sizes of the cross-section along the beam length are carried-out. Beams of a rectangular cross-section are studied. It is assumed that beams exhibit continuous (smooth) material inhomogeneity along the width and height of the cross-section. A longitudinal crack located arbitrary along the beam height is analyzed. First, a cantilever beam with linearly varying width and height along the beam length is considered. The material of the beam has non-linear elastic mechanical behavior. The external loading consists of one bending moment applied at the free end of the lower crack arm. The fracture behavior is analyzed in terms of the strain energy release rate assuming that the modulus of elasticity is distributed continuously in the beam cross-section. The balance of the energy is considered in order to derive the strain energy release rate. A solution to the strain energy release rate is obtained also by considering the complementary strain energy for verification. The longitudinal fracture behavior of the inhomogeneous non-linear elastic cantilever beam configuration is studied also for the cases when the variation of the width and height of the cross-section is described by sine and power laws.       

Keywords

Article history

  1. ReceivedUntil the next stage: 121 days
  2. Revision requestedUntil the next stage: 11 days
  3. RevisedUntil the next stage: 1 day
  4. AcceptedUntil the next stage: 90 days
  5. Published

Statements

Funding

DAAD

About the authors

Victor Rizov

Department of Technical Mechanics

Prof. Dr.

How to cite

APA

Rizov, V., & Altenbach, H. (2020). Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length. Fracture and Structural Integrity, 14(53), 38–50. https://doi.org/10.3221/IGF-ESIS.53.04

IEEE

V. Rizov and H. Altenbach, “Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length,” Fracture and Structural Integrity, vol. 14, no. 53, pp. 38–50, 2020, doi: 10.3221/IGF-ESIS.53.04.

MLA

Rizov, Victor, and Holm Altenbach. “Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length.” Fracture and Structural Integrity, vol. 14, no. 53, 2020, pp. 38–50. https://doi.org/10.3221/IGF-ESIS.53.04.

Chicago

Rizov, Victor, and Holm Altenbach. 2020. “Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length.” Fracture and Structural Integrity 14 (53): 38–50. https://doi.org/10.3221/IGF-ESIS.53.04.

Harvard

Rizov, V. and Altenbach, H. (2020) ‘Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length’, Fracture and Structural Integrity, 14(53), pp. 38–50. doi: 10.3221/IGF-ESIS.53.04.

Vancouver

Rizov V, Altenbach H. Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length. Fracture and Structural Integrity. 2020;14(53):38-50. doi:10.3221/IGF-ESIS.53.04

BibTeX

@article{rizov2020, author = {Rizov, Victor and Altenbach, Holm}, title = {Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length}, journal = {Fracture and Structural Integrity}, year = {2020}, volume = {14}, number = {53}, pages = {38--50}, doi = {10.3221/IGF-ESIS.53.04}, url = {https://doi.org/10.3221/IGF-ESIS.53.04}, issn = {1971-8993} }

RIS

TY - JOUR AU - Rizov, Victor AU - Altenbach, Holm TI - Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length JO - Fracture and Structural Integrity T2 - Fracture and Structural Integrity PY - 2020 DA - 2020/07/19 VL - 14 IS - 53 SP - 38 EP - 50 DO - 10.3221/IGF-ESIS.53.04 UR - https://doi.org/10.3221/IGF-ESIS.53.04 SN - 1971-8993 ER -

Licence

Creative Commons Attribution 4.0 International

May be shared and adapted, provided appropriate credit is given. Copyright © 2020 Victor Rizov, Holm Altenbach.

Copyright 
Authors are allowed to retain both the copyright and the publishing rights of their articles without restrictions.  

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