Constrained thickness optimization of rectangular orthotropic fiber-reinforced plate for fundamental frequency maximization

详细信息    查看全文

• 作者：Reza Moradi (1)
  Omid Vaseghi (1)
  Hamid Reza Mirdamadi (1)
  
• 关键词：Composite plate ; Constrained optimization ; Thickness optimization ; Orthotropic plate ; Rosen’s conjugate gradient projection method ; Fundamental frequency maximization ; Fiber ; reinforced plate ; Angle ; ply ; Nonlinear programming
• 刊名：Optimization and Engineering
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：15
• 期：1
• 页码：293-310
• 全文大小：1,760 KB
• 参考文献：1. Arora JS (2004) Introduction to optimum design. The University of Iowa, Iowa City
  2. Hinton E, Ozakca M, Siez J (1993) Optimum shape of vibrating axisymmetric plates and shells. J Sound Vib 167(3):511-28 CrossRef
  3. Kaw AK (2006) Mechanics of composite materials, 2nd edn. Taylor & Francis, London
  4. Kemal Apalak M, Yildirim M, Ekici R (2007) Layer optimisation for maximum fundamental frequency of laminated composite plates for different edge conditions. Compos Sci Technol 68:537-50 CrossRef
  5. Manickarajah D, Xie YM, Steven GP (1998) An evolutionary method for optimization of plate buckling resistance. Finite Elem Anal Des 29:205-30 CrossRef
  6. Narita Y (2003) Layerwise optimization for the maximum fundamental frequency of laminated composite plates. J Sound Vib 263(5):1005-016 CrossRef
  7. Ozakca M, Hinton E (1994a) Free vibration analysis and optimisation of axisymmetric plates and shells—finite element formulation. Comput Struct 52(6):181-97
  8. Ozakca M, Hinton E (1994b) Free vibration analysis and optimisation of axisymmetric plates and shells-shape optimisation. Comput Struct 52(6):197-11
  9. Rao SS (2009) Engineering optimization theory and practice. Hoboken, New Jersey
  10. Seyranian AP, Mailybaev AA (2003) Multiparameter stability theory with mechanical applications. World Scientific, Singapore
  11. Seyranian AP, Lund E, Olhoff N (1994) Multiple eigenvalues in structural optimization problems. Struct Multidiscip Optim 8(4):207-27 CrossRef
  12. Topal U, Uzman U (2008) Frequency optimization of laminated composite angle-ply plates with circular hole. Mater Des 29:1512-517 CrossRef
  13. Topal U, Uzman U (2009) Frequency optimization of laminated skew plates. Mater Des 30:3180-185 CrossRef
  14. Ugural AC (1981) Stresses in plates and shells. McGraw-Hill, New York
  15. Xu ZS, Huang QB, Zhao ZG (2010) Topology optimization of composite material plate with respect to sound radiation. Eng Anal Bound Elem 35:61-7 CrossRef
  16. Yang XY, Xie YM, Steven GP, Querin OM (1999) Topology optimization for frequencies using an evolutionary method. J Struct Eng 125(12)
  17. Zhao C, Steven GP, Xie YM (1996) Evolutionary natural frequency optimization of thin plate bending vibration problems. Struct Optim 11:244-51 CrossRef
  
• 作者单位：Reza Moradi (1)
  Omid Vaseghi (1)
  Hamid Reza Mirdamadi (1)
  
  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran
  
• ISSN：1573-2924

文摘

This paper addresses the thickness optimization of rectangular orthotropic fiber-reinforced composite plates by using mathematical programming theory of nonlinear constrained optimization. We optimize the thickness distribution of various composite plates for reaching a maximum in the plate natural frequency, subject to an equality constraint in a plate volume and a number of inequality constraints on the lower and upper bounds of allowable range of thicknesses. For the modeling part of our optimization algorithm, we formulate the kinematical hypothesis of the classical plate theory (CPT), reduced plane stress theory of linearized elasticity, and Hamilton’s principle. For the solution part, we implement the Rayleigh-Ritz semi-analytical solution technique to spatially discretize the weak form of the plate partial differential equation (PDE), and transforming it to a generalized algebraic eigen-problem. For the design optimization part, we use a conjugate Rosen’s gradient projection method. The design variables of the optimization design space are thicknesses of an arbitrary but rectangular partition of the plate into constant-thickness subdivisions. After simulating our algorithm, we noticed many interesting and impressive results, and tried to justify them. The most impressive finding is that, as the fiber orientation of the composite plate rotates, the plate thickness distribution rotates also in the same way, but with different manifestations for different boundary conditions. For parametric studies, we analyze the sensitivity of the algorithm against parameters, like, the degree of fineness in the number of plate partitions into constant-thickness sub-plates, the degree of plate anisotropy, the fiber orientation, the rectangular plate aspect ratio, the upper to lower bounds of allowable thickness ratio, and boundary conditions.