Skip to main content
SpringerLink
Log in

Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element

  • Originals
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

Finite element static, free vibration and thermal analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices and the thermal load vector. Due to a strong analogy between the induced strain caused by the thermal field and the strain induced in a structure due to an electric field the present formulation is readily applicable for the analysis of structures excited by surface bonded or embedded piezoelectric actuators. The results are presented for (i) static analysis of (a) simply supported square plates under doubly sinusoidal load and uniformly distributed load (b) simply supported spherical shells under a uniformly distributed load, (ii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells; (iii) Thermal deformation analysis of (a) simply supported square plates, (b) simply supported-clamped square plate and (c) simply supported spherical shells. A numerical example is also presented demonstrating the application of the present formulation to analyse a symmetrically laminated graphite/epoxy laminate excited by a layer of piezoelectric polyvinylidene flouride (PVDF). The results presented are in good agreement with those available in the literature.

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

Similar content being viewed by others

References

  • Allman, D. J. 1984: A compatible triangular element including vertex rotations for plane elasticity analysis. Comput. Struct. 19: 1–8

    Google Scholar 

  • Allman, D. J. 1988: A quadrilateral finite element including vertex rotations for plane elasticity analysis. Int. J. Num. Meth. Eng. 26: 717–730

    Google Scholar 

  • Alvin, K.; Horacio, M. de la Fuente; Hhaugen, B.; Fellipa, C. A. 1992: Membrane triangles with corner drilling freedoms-I. EFF element. Finite elements in analysis and design. 12: 163–187

    Google Scholar 

  • Bathe, K. J.; Ho, L. W. 1981: A simple and effective element for analysis of general shell structures. Comput. Struct. 13: 673–681

    Google Scholar 

  • Batoz, J. L.; Bathe, K. J.; Ho, L. W. 1980: A study three noded triangular plate bending elements. Int. J. Num. Meth. Eng. 15: 1771–1812

    Google Scholar 

  • Bazeley, G. P.; Cheung, Y. K.; Irons, B. M.; Zienkiewicz, O. C. 1965: Triangular elements in plate bending-conforming and non-conforming solutions. Proc. Conf. Matrix Methods in Structural Mechanics: AFFDL-TR-66-80, Wright-Patterson Air Force Base, 547–576

  • Bergan, P. G.; Fellipa, C. A. 1985: A triangular membrane element with rotational degrees of freedom. Comput. Meth. Appl. Mech. Eng. 50: 24–69

    Google Scholar 

  • Bergan, P. G.; Nygard, M. K. 1984: Finite elements with increased freedom in choosing shape functions. Int. J. Num. Meth. Eng. 20: 643–664

    Google Scholar 

  • Carpenter, N.; Stolarski, H.; Belytschko, T. 1985: A flat triangular shell element with improved membrane interpolation. Comm. Appl. Num. Meth. 1: 161–168

    Google Scholar 

  • Cazzani, A.; Atluri, S. N. 1993: Four-noded mixed elements using unsymmetric stresses for linear analysis of membranes. Comput. Mech. 11: 229–251

    Google Scholar 

  • Chen, H. C. 1992: Evaluation of Allman triangular membrane element used in general shell analysis. Comput. Struct. 43: 881–887

    Google Scholar 

  • Chen, L. W.; Chen, L. Y. 1990: Thermal deformation and stress analysis of composite laminated plates by finite element method. Comput. Struct. 35: 41–49

    Google Scholar 

  • Cook, R. D. 1986: On the Allman triangle and related quadrilateral element. Comput. Struct. 22: 1065–1067

    Google Scholar 

  • Cook, R. D. 1987: A plane hybrid element with rotational DOF and adjustable stiffness. Int. J. Num.Meth. Eng. 24: 1499–1508

    Google Scholar 

  • Cook, R. D. 1987: Some options for plane triangular elements with rotational degrees of freedom. Finite elements in analysis and design. 6: 245–249

    Google Scholar 

  • Cook, R. D. 1991: Modified formulations for nine-D.O.F. plane triangles that include vertex rotations. Int. J. Num. Meth. Eng. 31: 825–835

    Google Scholar 

  • Cook, R. D. 1993: Further development of a three-node triangular shell element. Int. J. Num. Meth. Eng. 36: 1413–1425

    Google Scholar 

  • Dey, A.; Bandyopadhyay, J. N.; Sinha, P. K. 1992: Finite element analysis of laminated composite parabolaid of revolution shells. Comput. Struct. 44: 675–682

    Google Scholar 

  • Ertas, A.; Krafcik, J. T.; Ekwaro-Osire, S. 1992: Performance of an anisotropic Allman/DKT 3-node thin triangular flat shell element. Comp. Eng. 2: 269–280

    Google Scholar 

  • Fellippa, C. A.; Bergan, P. G. 1987: A triangular bending element based on energy orthogonal free formulation. Comp. Meth. Appl. Mech. Eng. 61: 129–160

    Google Scholar 

  • Fillipa, C. A.; Militello, C. 1992: Membrane triangles with corner drilling freedoms-II. ANDES Element, Finite elements in analysis and design. 12: 189–201

    Google Scholar 

  • Fellipa, C. A.; Alexander, S. 1992: Membrane triangles with corner drilling freedoms-III. Implementation and performance evaluation. Finite elements in analysis and design. 12: 203–239

    Google Scholar 

  • Fish, J.; Belytschko, T. 1992: Stabilized rapidly convergent 18-degrees of freedom flat shell triangular element. Int. J. Num. Meth. Eng. 33: 149–162

    Google Scholar 

  • Hrabok, M. M.; Hrudey, T. M. 1984: A review and catalogue of plate bending finite elements. Comput. Struct. 19: 479–495

    Google Scholar 

  • Huang, B. Z.; Shenoy, V. B.; Atluri, S. N. 1994: A quasi-conforming triangular laminated composite shell element based on a refined first-order theory. Comput. Mech. 13: 295–314

    Google Scholar 

  • Hughes, T. R. J.; Brezzi, F. 1989: On drilling degrees of freedom Comput. Meth. Appl. Mech. Eng. 72: 105–121

    Google Scholar 

  • Ibrahimbegovic, A. 1990: A novel membrane finite element with an enhanced displacement interpolation. Finite elements in analysis and design. 7: 167–179

    Google Scholar 

  • Iura, M.; Atluri, S. N.: Formulation of a membrane finite element with drilling degrees of freedom. Comput. Mech. 9: 417–428

  • Jeyachandrabose, C.; Kirkhope, J. 1985: An alternative explicit formulation for the DKT plate bending element. Int. J. Num. Meth. Eng. 21: 1289–1293

    Google Scholar 

  • Jeyachandrabose, C.; Kirkhope, J. 1986: Construction of new efficient three-node triangular thin plate bending elements. Comput. Struct. 23: 587–603

    Google Scholar 

  • Jonnalagadda, K. D.; Blandford, G. E.; Tauchert, T. R. 1994: Piezothermoelastic composite plate analysis using first-order shear deformation theory. Comput. Struct. 51: 79–89

    Google Scholar 

  • Kapania, R. K.; Singhvi, S. 1991: Free vibration analysis of generally laminated tapered skew plates. Enhancing analysis techniques for composite materials. ASME NDE-Vol. 10: 159–168

    Google Scholar 

  • Meek, J. L.; Tan, H. S. 1986: A faceted shell element with loof nodes. Int. J. Numer. Meth. Eng. 23: 49–67

    Google Scholar 

  • Phan, N. D.; Reddy, J. N. 1985: Analysis of laminated composite plates using a higher order shear deformation theory. Int. J. Num. Meth. Eng. 21: 2201–2219

    Google Scholar 

  • Reddy, J. N. 1984: Exact solutions of moderately thick laminated shells. J. Eng. Mech. Div. ASCE. 110: 794–807

    Google Scholar 

  • Specht, B. 1988: Modified shape functions for the three node plate bending element passing the patch test. Int. J. Num. Meth. Eng. 26: 705–715

    Google Scholar 

  • Yunus, S. M.; Saigal, S.; Cook, R. D. 1989: On improved hybrid finite element with rotational degrees of freedom. Int. J. Num. Meth. Eng. 28: 785–800

    Google Scholar 

  • Whitney, J. M.; Leissa, A. W. 1969: Analysis of anisotropic heterogeneous plates. J. Appl. Mech. 36: 261–266

    Google Scholar 

  • Wu, C. H.; Tauchert, T. R. 1980: Thermoelastic analysis of laminated plates. 1: Symmetric specially orthotropic laminates. J. Thermal Stresses. 3: 247–259

    Google Scholar 

  • Wu, C. H.; Tauchert, T. R. 1980: Thermoelastic analysis of laminated plates. 2: Antisymmetric cross-ply and angle-ply laminates. J. Thermal Stresses. 3: 365–378

    Google Scholar 

  • Yang, T. Y. 1986: Finite element structural analysis. Prentice-Hall, Inc

  • Zienkiewicz, O. C. 1977: The finite element method, edition, McGraw-Hill, London

    Google Scholar 

  • Zienkiewicz, O. C.; Taylor, R. L.; Papadopoulos, P.; Onate, E. 1990: Plate bending elements with discrete constraints: New triangular elements. Comput. Struct. 35: 505–522

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, 24061-0219, Blacksburg, VA, USA

    R. K. Kapania & P. Mohan

Authors
  1. R. K. Kapania
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S. N.Atluri, 4 October 1995

The work was partly sponsored by a grant (DAAHO4-95-1-0175) from the army research office with Dr. Gary Anderson as the grant monitor.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kapania, R.K., Mohan, P. Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element. Computational Mechanics 17, 343–357 (1996). https://doi.org/10.1007/BF00368557

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00368557

Keywords

Search

Navigation