Home The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
Article
Licensed
Unlicensed Requires Authentication

The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading

  • I. I. Andrianov , J. Awrejcewicz EMAIL logo and A.A. Diskovsky
Published/Copyright: March 13, 2019

Abstract

Optimization of parameters of the corrugated shell aims to achieve its minimum weight while keeping maximum stiffness ability. How an introduction of functionally graded corrugations resulted in improved efficiency of this thin-walled structure is demonstrated. The corrugations are graded varying their pitch. The effect of variation in pitch is studied. Homogenization approach gives explicit expressions to calculate the equivalent shell properties. Then well-elaborate methods of optimal design theory are used. The illustrative examples for hydrostatic load demonstrate a high efficiency of the used method.

MSC 2010: 65Kxx; 74Kxx; 74Qxx

Acknowledgments

The authors thank the anonymous referees whose valuable comments and suggestions favored improvement of the paper.

References

[1] I. Dayyani, A. D. Shaw, E. I. Saavedra Flores and M. I. Friswell, The mechanics of composite corrugated structures: A review with applications in morphing aircraft, Comp. Struct. 133 (2015), 358–380.10.1016/j.compstruct.2015.07.099Search in Google Scholar

[2] S. Rawat, A. Narayanan, T. Nagendiran and A. K. Upadhyay, Collapse behavior and energy absorption in elliptical tubes with functionally graded corrugations, Proc. Eng. 173 (2017), 1374–1381.10.1016/j.proeng.2016.12.194Search in Google Scholar

[3] F. Guinea, M. I. Katsnelson and M. A. H. Vozmediano, Midgap states and charge inhomogeneities in corrugated graphene, Phys. Rev. B 77 (7) (2008), 075422.10.1103/PhysRevB.77.075422Search in Google Scholar

[4] I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Sensitivity analysis in design of constructions made of functionally graded materials, Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sc. 227 (1) (2013), 19–28.10.1177/0954406212445139Search in Google Scholar

[5] I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Optimal design of a functionally graded corrugated rods subjected to longitudinal deformation, Arch. Appl. Mech. 85 (2015), 303–314.10.1007/s00419-014-0914-2Search in Google Scholar

[6] I. V. Andrianov, A. A. Diskovsky and E. Syerko, Optimal design of a circular diaphragm using the homogenization approach, Math. Mech. Sol. 22 (3) (2017), 283–303.10.1177/1081286515586278Search in Google Scholar

[7] I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Optimal design of a functionally graded corrugated cylindrical shell subjected to axisymmetric loading, Arch. Appl. Mech. 88 (2018), 1027–1039.10.1007/s00419-018-1356-zSearch in Google Scholar

[8] A. G. Kolpakov, Design of corrugated plates with extreme stiffnesses, J. Appl. Mech. Tech. Phys. 58 (3) (2017), 495–502.10.1134/S0021894417030142Search in Google Scholar

[9] Y. S. Tian and T. J. Lu, Optimal design of compression corrugated panels, Thin-Wall. Struct. 43 (1) (2005), 477–498.10.1016/j.tws.2004.07.014Search in Google Scholar

[10] T. Flatscher, T. Daxner, D. H. Pahr and F. G. Rammerstorfer, Optimization of corrugated paperboard under local and global buckling constraints, Lect. Notes Appl. Comput. Mech. 55 (2011), 329–346.10.1007/978-90-481-9809-2_17Search in Google Scholar

[11] N. V. Banichuk and B. L. Karihaloo, On the solution of optimization problems with non-smooth extremals, Int. J. Sol. Struct. 13 (8) (1977), 725–733.10.1016/0020-7683(77)90109-3Search in Google Scholar

[12] A. F. Arkhangelskii and V. I. Gorbachev, Effective characteristics of corrugated plates, Mech. Sol. 42 (2007), 447–462.10.3103/S0025654407030132Search in Google Scholar

[13] A. G. Kolpakov and S. I. Rakin, Calculation of the effective stiffness of the corrugated plate by solving the problem on the plate cross-section, J. Appl. Mech. Tech. Phys. 57 (4) (2016), 757–767.10.1134/S0021894416040209Search in Google Scholar

[14] E. Syerko, A. A. Diskovsky, I. V. Andrianov, S. Comas-Cardona and C. Binetruy, Corrugated beams mechanical behavior modeling by the homogenization method, Int. J. Sol. Struct. 50 (2013), 928–936.10.1016/j.ijsolstr.2012.11.013Search in Google Scholar

[15] Y. Zheng, V. L. Berdichevsky and W. Yu, An equivalent classical plate model of corrugated structures, Int. J. Sol. Struct. 51 (11) (2014), 2073–2083.10.1016/j.ijsolstr.2014.02.025Search in Google Scholar

[16] D. Briassoulis, Equivalent orthotropic properties of corrugated sheets, Comput. Struct. 23 (1986), 129–138.10.1016/0045-7949(86)90207-5Search in Google Scholar

[17] Y. Xia, M. I. Friswell and E. I. Saavedra Flores, Equivalent models of corrugated panels, Int. J. Sol. Struct. 49 (13) (2012), 1453–1462.10.1016/j.ijsolstr.2012.02.023Search in Google Scholar

[18] I. V. Andrianov, A. A. Diskovsky and E.G. Kholod, Homogenization method in the theory of corrugated plates, Tech. Mech. 18 (1998), 123–133.Search in Google Scholar

[19] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, 1959.Search in Google Scholar

[20] M. V. Pryjmak, Periodic functions with variable period, arXiv:1006.2792v1 [math.GM].Search in Google Scholar

[21] A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.Search in Google Scholar

Received: 2018-05-31
Accepted: 2019-02-20
Published Online: 2019-03-13
Published in Print: 2019-05-26

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
  4. Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
  5. Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
  6. Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
  7. Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
  8. A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
  9. New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
  10. Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach
  11. Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
  12. A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems
  13. The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach
  14. Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
  15. The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
  16. Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
  17. Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
  18. Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
  19. Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
  20. Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
  21. Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
  22. Results on Controllability of Nonlinear Hilfer Fractional Stochastic System
  23. Effects of Different Turbulence Models on Three-Dimensional Unsteady Cavitating Flows in the Centrifugal Pump and Performance Prediction
Downloaded on 21.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ijnsns-2018-0156/html
Scroll to top button