10th International Congress of the Serbian Society of Mechanics (18-20. 06. 2025, Niš) [pp. 124-131]
AUTHOR(S) / АУТОР(И): Emilija V. Jočić
, Milica Z. Živković
, Miroslav S. Marjanović 
Download Full Pdf 
DOI: 10.46793/ICSSM25.124J
ABSTRACT / САЖЕТАК:
This paper deals with the 3D analysis of free-edge stresses in laminated composite plates using Reddy’s full-layerwise-theory-based finite element model (FLWT-FEM). The theory assumes a piece-wise linear variation of all displacement components and quadratic variation of interlaminar stresses within each layer. The free-edge effects are related to singular stress states at the interfaces between dissimilar layers along the free edges of the laminar composite. Stress concentrations at free edges can further lead to delamination and the significant drop in stiffness, with failure occurring at lower loads than expected.
Starting from the strong formulation of the FLWT, a family of layered finite elements has been derived and implemented in original object-oriented MATLAB code. Free-edge stress field under axial strain has been analyzed. A validation example of cross-ply composite has been presented, and the results are compared against the existing analytical solutions and those obtained using the commercial software. The accuracy of the model is verified, and the possibilities for the further improvement and applications are provided.
KEYWORDS / КЉУЧНЕ РЕЧИ:
free-edge stresses, full layerwise theory, laminate, composite, plate
ACKNOWLEDGEMENT / ПРОЈЕКАТ:
The financial support of the Ministry of Education, Science and Technological Development of the Republic of Serbia, through the project 200092 is acknowledged.
REFERENCES / ЛИТЕРАТУРА:
- Jočić, E., Marjanović, M., Progressive failure analysis of open-hole composite laminates using FLWT-SCB prediction model, International Journal of Mechanical Sciences, Vol. 227, 107407, 2022.
- Carrera, E., Theories and finite elements for multilayered, anisotropic, composite plates and shells, Archives of Computational Methods in Engineering, Vol. 9, No. 2, 87-140, 2002.
- Liew, K. M., Pan, Z. Z., Zhang, L. W., An overview of layerwise theories for composite laminates and structures: Development, numerical implementation and application, Composite Structures, Vol. 216, 240-259, 2019.
- Reddy, J. N., Mechanics of laminated composite plates and shells: theory and analysis, CRC Press, Boca Raton, Florida, 2004.
- Mittelstedt, C., Becker, W., Reddy’s layerwise laminate plate theory for the computation of elastic fields in the vicinity of straight free laminate edges, Materials Science and Engineering: A, Vol. 498(1-2), 76-80, 2008.
- Phillips, E. A., Herakovich, C. T., Graham, L. L., Damage development in composites with large stress gradients, Composites Science and Technology, Vol. 61(15), 2169–2182, 2001.
- Tahani, M., Nosier, A., Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading, Composite Structures, Vol. 60, 91-103, 2003.
- Riepl, C., FEM-Modeling of Composite Laminates considering Free Edge Effects, Diploma Thesis, TU Wien, 2023.
- Mittelstedt, C., Becker, W., Interlaminar stress concentrations in layered structures: part I – a selective literature survey on the free edge effect since 1967, Journal of Composite Materials, Vol. 38(12), 1037–1062, 2004.
- D’Ottavio, M., Vidal, P., Valot, E., Polit, O., Assessment of plate theories for free-edge effects, Composites Part B: Engineering, Vol. 48, 111-121, 2013.
- Byron Pipes, R., Pagano, N. J., Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension, Journal of Composite Materials, Vol. 4, 538, 1970.
- Li, D. H., Wu, P. X., Wan, A. S., A three-scale layerwise multiscale analysis method for composite laminated plates, Mechanics of Materials, Vol. 185, 104769, 2023.
- Savoia, M., Reddy, J. N., A variational approach to three-dimensional elasticity solutions of laminated composite plates, Journal of Applied Mechanics, Vol. 59(2S), 166–175, 1992.
- Liang, W. Y., Ju, S. H., Tarn, J. Q., Analytic determination of stress fields in cross-ply symmetric composite laminates, International Journal of Solids and Structures, Vol. 94-95, 87-99, 2016.
- Becker, W., Closed-form solution for the free-edge effect in cross-ply laminates, Composite Structures, Vol. 26(1), 39–45, 1993.
- Nosier, A., Bahrami, A., Free-edge stresses in antisymmetric angle-ply laminates in exten- sion and torsion, International Journal of Solids and Structures, Vol. 43, 6800–6816, 2006.
- Nosier, A., Maleki, M., Free-edge stresses in general composite laminates, International Journal of Mechanical Sciences, Vol. 50(10), 1435–1447, 2008.
- Marjanović, M., Meschke, G., Damnjanović, E. Object-oriented framework for 3D bending and free vibration analysis of multilayer plates: Application to cross-laminated timber and soft-core sandwich panels, Composite Structures, Vol. 255, 112859, 2021.
- Gao, S., Cai, C. S., Zhang, S. Q., A compressible layerwise third-order shear deformation theory with transverse shear stress continuity for laminated sandwich plates, Composite Structures, Vol. 338, 118108, 2024.
- Gao, Y., Zhang, S., Hu, W., Songyun, M. A., Markert, B., Layerwise third-order shear deformation theory with transverse shear stress continuity for piezolaminated plates, Chinese Journal of Aeronautics, Vol. 37(9), 490-505, 2024.
- Bouteiller, P., Bleyer, J., Sab, K., Continuum damage analysis of delamination in composite laminates using a stress-based layerwise plate model, International Journal of Solids and Structures, Vol. 246–247, 111611, 2022.
- MATLAB R2011b, The MathWorks, , Natick, Massachusetts, USA.
- GiD Customization Manual. CIMNE – International Center for Numerical Methods in Engineering, 2016.
- https://github.com/miregrf/FLWTFEM
- ABAQUS User Manual 9. DS SIMULIA Corp., Providence, Rhode Island, USA, 2009.
- Damnjanović, E., Marjanović, M. Three-dimensional stress analysis of laminated composite plates using FLWT-based finite elements, 7th International Congress of Serbian Society of Mechanics, Sremski Karlovci, Serbia, June 24-26 2019.
- Marjanović, M., Marković, N., Damnjanović, E., Cvetković, R. Three-dimensional stress analysis and design of cross-laminated timber panels using full-layerwise-theory-based finite element method, Thin-Walled Structures, Vol. 157, 107156, 2020.
- Dhondt, G., The Finite Element Method for Three-Dimensional Thermomechanical Applications, Wiley, 2004.