Skip to main content
SpringerLink
Log in

Mechanical Models and Finite-Element Approaches for the Structural Analysis of Photovoltaic Composite Structures: a Comparative Study

  • Published:
Mechanics of Composite Materials Aims and scope

In general, photovoltaic composite structures are three-layer laminates with a thin soft core layer. Due to the high contrast between the mechanical properties of skin and core layers, such structures have been studied by different theories. Finite-element models, continuum-based theories, and two-dimensional plate/shell theories are used in the analysis of laminated structures. The present study deals with the modeling and computational simulation of photovoltaic modules in the context of global structural mechanics. The focus is on the implementation of different elements in both two- and three-dimensional approaches to find the most efficient one for analyzing photovoltaic composite structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

References

  1. S.-H. Schulze, M. Pander, K. Naumenko, and H. Altenbach, “Analysis of laminated glass beams for photovoltaic applications,” Int. J. Solids Structures, 49, No. 15-16, 2027-2036 (2012).

    Article  CAS  Google Scholar 

  2. A. V. Duser, A. Jagota, and S. J. Bennison, “Analysis of glass/polyvinyl butyral laminates subjected to uniform pressure,” J. Eng. Mech., 125, No. 4, 435-442 (1999).

    Article  Google Scholar 

  3. L. Galuppi and G. Royer-Carfagni, “Enhanced effective thickness of multi-layered laminated glass,” Composites: Part B, 64, 202-213 (2014).

    Article  CAS  Google Scholar 

  4. M. M. e Costa, L. Valarinho, N. Silvestre, and J. R. Correia, “Modeling of the structural behavior of multilayer laminated glass beams: Flexural and torsional stiffness and lateral-torsional buckling,” Eng. Struct., 128, 265-282 (2016).

    Article  Google Scholar 

  5. L. Valarinho, J. R. Correia, M. M. e Costa, F. A. Branco, and N. Silvestre, “Lateral-torsional buckling behaviour of long-span laminated glass beams: Analytical, experimental and numerical study,” Mater. Des., 102, 264-275 (2016).

    Article  CAS  Google Scholar 

  6. G. Castori and E. Speranzini, “Structural analysis of failure behavior of laminated glass,” Composites: Part B., 125, 89-99 (2017).

    Article  CAS  Google Scholar 

  7. M. Aßmus, K. Naumenko, and H. Altenbach, “A multiscale projection approach for the coupled globallocal structural analysis of photovoltaic modules,” Compos. Struct., 158, 340-358 (2016).

    Article  Google Scholar 

  8. E. Reissner, “The effect of transverse shear deformation on the bending of elastic plates,” J. Appl. Mech., 12, 69-77 (1945).

    Google Scholar 

  9. R. D. Mindlin, “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates,” J. Appl. Mech., 18, 31-38 (1951).

    Google Scholar 

  10. M. Timmel, S. Kolling, P. Osterrieder, and P. D. Bois, “A finite element model for impact simulation with laminated glass,” Int. J. Impact Engineering, 34, No. 8, 1465-1478 (2007).

    Article  Google Scholar 

  11. P. D. Bois, S. Kolling, and W. Fassnacht, “Modelling of safety glass for crash simulation,” Computat. Mater. Sci., 28, No. 3-4, 675-683 (2003).

    Article  Google Scholar 

  12. M. Kim and A. Gupta, “Finite element analysis of free vibrations of laminated composite plates,” Int. J. Analytical and Experimental Modal Analysis, 5, No. 3, 195-203 (1990).

    Google Scholar 

  13. A. G. Niyogi, M. K. Laha, and P. K. Sinha, “Finite element vibration analysis of laminated composite folded plate structures,” Shock and Vibration, 6, No. 5-6, 273-283 (1999).

    Article  Google Scholar 

  14. M. K. Pandit, S. Haldar, and M. Mukhopadhyay, “Free vibration analysis of laminated composite rectangular plate using finite element method,” J. Reinforced Plastics and Compos., 26, No. 1, 69-80 (2007).

    Article  CAS  Google Scholar 

  15. R. Rikards, “Finite element analysis of vibration and damping of laminated composites,” Compos. Struct., 24, No. 3, 193-204 (1993).

    Article  Google Scholar 

  16. H. Altenbach, V. A. Eremeyev, and K. Naumenko, “On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer,” Zeitchrift für Angewandte Mathematik und Mechanik, 95, No. 10, 1004-1011 (2015).

    Article  Google Scholar 

  17. J. Eisenträger, K. Naumenko, H. Altenbach, and H. Köppe, “Application of the first-order shear deformation theory to the analysis of laminated glasses and photovoltaic panels,” Int. J. Mech. Sci., 96-97, 163-171 (2015).

    Article  Google Scholar 

  18. K. Naumenko and V. A. Eremeyev, “A layer-wise theory for laminated glass and photovoltaic panels,” Compos. Struct., 112, 283-291 (2014).

    Article  Google Scholar 

  19. M. Weps, K. Naumenko, and H. Altenbach, “Unsymmetric three-layer laminate with soft core for photovoltaic modules,” Compos. Struct., 105, 332-339 (2013).

    Article  Google Scholar 

  20. J. Eisenträger, K. Naumenko, H. Altenbach, and J. Meenen, “A user-defined finite element for glass and photovoltaic panels based on a layer-wise theory,” Compos. Struct., 133, 265-277 (2015).

    Article  Google Scholar 

  21. L. P. Lebedev, M. J. Cloud, and V. A. Eremeyev, Tensor Analysis with Applications in Mechanics, World Scientific, (2010).

  22. H. Altenbach, Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen, 3rd Edition, Springer, Berlin, Heidelberg (2015).

    Book  Google Scholar 

  23. A. Bertram, Elasticity and Plasticity of Large Deformations: An Introduction, 3rd Edition, Springer, Berlin, Heidelberg (2012).

    Book  Google Scholar 

  24. E. Carrera, “Theories and finite elements for multilayered, anisotropic, composite plates and shells,” Archives of Computational Methods in Engineering, 9, No. 2, 87-140 (2002).

    Article  Google Scholar 

  25. Simulia, ABAQUS® Analysis User’s Guide, ABAQUS® 6.14 Documentation, Volume IV: Elements, Dassault Systmes, (2014).

  26. Simulia, ABAQUS® Theory Guide, ABAQUS® 6.14 Documentation, Dassault Systmes, (2014).

  27. E. Ellobody, R. Feng, and B. Young, Finite Element Analysis and Design of Metal Structures, Butterworth-Heinemann, Boston (2014).

    Google Scholar 

  28. J. N. Reddy, “On refined computational models of composite laminates,” International Journal for Numerical Methods in Engineering, 27, No. 2, 361-382 (1989).

    Article  Google Scholar 

  29. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd Edition, CRC Press, Boca Raton, (2003).

    Google Scholar 

  30. Y. Zhang and C. Yang, “Recent developments in finite element analysis for laminated composite plates,” Compos. Struct., 88, No. 1, 147-157 (2009).

    Article  Google Scholar 

  31. M. Aßmus, J. Nordmann, K. Naumenko, and H. Altenbach, “A homogeneous substitute material for the core layer of photovoltaic composite structures,” Composites: Part B., 112, 353-372 (2017).

    Article  Google Scholar 

  32. M. Aßmus, S. Bergmann, K. Naumenko, and H. Altenbach, “Mechanical behaviour of photovoltaic composite structures: A parameter study on the influence of geometric dimensions and material properties under static loading,” Compos. Communic., 5, 23-26 (2017).

    Article  Google Scholar 

  33. M. Aßmus, S. Bergmann, J. Eisenträger, K. Naumenko, and H. Altenbach, in : H. Altenbach, R. Goldstein, and E. Murashkin (eds.), Mechanics for Material and Technologies. Advanced Structural Materials, Springer, Cham, 46, 73-122 (2017).

Download references

Acknowledgement

This research was supported financially by the European Structural and Investment Funds (ESF) under the program ‘Sachen-Anhalt WISSENSCHAFT Internationalisierung’ (project no. ZS/2016/08/80646) in context of the Inretnational Graduatr School at Otto von Guericke University (OVGU) MEMoRIAL and by the German Research Foundation (DFG) within the framework of the research training group 1554 ‘Micro-Macro-Interactions of Structured Media and Particle Systems’ (RTG 1554). This support is highly acknowledged.

Author information

Authors and Affiliations

  1. Chair of Engineering Mechanics, Institute of Mechanics, Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Germany

    M. Haghi, M. Aßmus, K. Naumenko & H. Altenbach

Authors
  1. M. Haghi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Aßmus
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Naumenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Altenbach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Haghi.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 54, No. 4, pp. 609-630, July-August, 2018.

Appendix

Appendix

During the convergence study, the mesh density was varied by changing element edge length. As can be seen in following tables, the aspect ratio of 2D elements was kept constant, at AR = 1. In the 3D elements, the aspect ratio was changed, but the number of elements across the plate thickness was kept constant for three different models.

The number of elements in the plate (NE) and across its thickness (NE (X3)), the total number of degrees of freedom (NDoF), and the total number of integration points are indicated in the tables for the different elements used in this work.

Table 2. Solid Brick Element (Full Integration)
Full size table
Table 3. Solid Brick Element (Reduced Integration)
Full size table
Table 4. Continuum Shell Element
Full size table
Table 5. Conventional Composite Shell Element
Full size table
Table 6. Conventional Shell Element (Tied Model)
Full size table
Table 7. XLWT Element (Full Integration)
Full size table
Table 8. XLWT Element (Reduced Integration)
Full size table
Table 9. XLWT Element (Selective Integration)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haghi, M., Aßmus, M., Naumenko, K. et al. Mechanical Models and Finite-Element Approaches for the Structural Analysis of Photovoltaic Composite Structures: a Comparative Study. Mech Compos Mater 54, 415–430 (2018). https://doi.org/10.1007/s11029-018-9752-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-018-9752-6

Keywords

Search

Navigation