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Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading

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Abstract
A variational approach based on the minimization of complementary energy is developed to determine accurately a complete solution for both free-edge stress and displacement distributions of a laminate with arbitrary lay-ups (possibly un-symmetric and made of thin plies) under combined in-plane, bending and thermal loading. The key idea is partitioning the total stresses/displacements in a laminate with free edges into unperturbed (without free edges) and unknown perturbation stresses/displacements caused by the presence of free edges. It enables the theory of variational stress-transfer to deal easily with both applied traction and displacement boundary conditions. A methodology is introduced to obtain displacement fields for a stress-based variational approach. The resulting stress and displacement fields exactly satisfy local equilibrium equations, strain-displacement relations together with all traction/displacement boundary and continuity conditions. By comparing the results with those obtained from the finite element method, the accuracy and computational efficiency of the developed model, is confirmed.
Keywords
INTERLAMINAR STRESSES, COMPOSITES, CRACKING, MODEL, PLATES, PREDICTION, Laminates, Stress concentrations, stress transfer, Analytical modelling

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Chicago
Hajikazemi, Mohammad, and Wim Van Paepegem. 2018. “Variational Analysis of Free-edge Stress and Displacement Fields in General Un-symmetric and Thin-ply Laminates Under In-plane, Bending and Thermal Loading.” Composites Part A-applied Science and Manufacturing 113: 220–232.
APA
Hajikazemi, M., & Van Paepegem, W. (2018). Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading. COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING, 113, 220–232.
Vancouver
1.
Hajikazemi M, Van Paepegem W. Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading. COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING. Oxford: Elsevier Sci Ltd; 2018;113:220–32.
MLA
Hajikazemi, Mohammad, and Wim Van Paepegem. “Variational Analysis of Free-edge Stress and Displacement Fields in General Un-symmetric and Thin-ply Laminates Under In-plane, Bending and Thermal Loading.” COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING 113 (2018): 220–232. Print.
@article{8612387,
  abstract     = {A variational approach based on the minimization of complementary energy is developed to determine accurately a complete solution for both free-edge stress and displacement distributions of a laminate with arbitrary lay-ups (possibly un-symmetric and made of thin plies) under combined in-plane, bending and thermal loading. The key idea is partitioning the total stresses/displacements in a laminate with free edges into unperturbed (without free edges) and unknown perturbation stresses/displacements caused by the presence of free edges. It enables the theory of variational stress-transfer to deal easily with both applied traction and displacement boundary conditions. A methodology is introduced to obtain displacement fields for a stress-based variational approach. The resulting stress and displacement fields exactly satisfy local equilibrium equations, strain-displacement relations together with all traction/displacement boundary and continuity conditions. By comparing the results with those obtained from the finite element method, the accuracy and computational efficiency of the developed model, is confirmed.},
  author       = {Hajikazemi, Mohammad and Van Paepegem, Wim},
  issn         = {1359-835X},
  journal      = {COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING},
  language     = {eng},
  pages        = {220--232},
  publisher    = {Elsevier Sci Ltd},
  title        = {Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading},
  url          = {http://dx.doi.org/10.1016/j.compositesa.2018.07.030},
  volume       = {113},
  year         = {2018},
}

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