Abstract
Optimal material orientation problems of linear and non-linear elastic three-dimensional anisotropic materials are studied. Most commonly, the energy based formulation is applied for solving orientational design problems of anisotropic materials, considering elastic energy density as a measure of the stress strain state. The same approach is used in the current study, but the strength criteria based approaches are also discussed. A simple relation between the stationary conditions in terms of Euler angles and the optimality conditions in terms of strains is pointed out. The complexity analysis of the different existing optimality conditions has been performed. The solution of the posed optimization problem is decomposed into the strain level solution, search for global extremes and evaluation of Euler angles (parameters). The results obtained are extended to some nonlinear elastic material models.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Gupta AK, Kumar L (2008) Thermal effect on vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness. Meccanica 43:47–54
Gupta AK, Kaur H (2008) Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions. Meccanica 43:449–458
Banichuk NV (1981) Optimization problems for elastic anisotropic bodies. Arch Mech 33:347–363
Pedersen P (1989) On optimal orientation of orthotropic materials. Struct Optim 1:101–106
Pedersen P (1990) Bounds on elastic energy in solids of orthotropic materials. Struct Optim 2:55–62
Sacci Landriani G, Rovati M (1991) Optimal design for 2-D structures made of composite materials. ASME J Eng Mater Technol 113:88–92
Majak J (2001) Orientational design of nonorthotropic two-dimensional materials. Mech Compos Mater 37:27–38
Pedersen P, Taylor JE (1993) Optimal design based on power law nonlinear elasticity. In: Optimal design with advanced materials. Elsevier, Amsterdam, pp 51–66
Lellep J, Majak J (2000) Nonlinear constitutive behavior of orthotropic materials. Mech Compos Mater 36:261–266
Lellep J, Majak J (1997) On optimal orientation of nonlinear elastic orthotropic materials. Struct Optim 14:116–120
Seregin GA, Troitski VA (1982) On the best position of elastic symmetry planes in an orthotropic body. PMM USSR 45:139–142
Rovati M, Taliercio A (1989) Optimal orientation of the symmetry axes of orthotropic 3-D materials. Lect Notes Eng 63:127–134
Rovati M, Taliercio A (2003) Stationarity of the strain energy density for some classes of anisotropic solids. Int J Solids Struct 40:6043–6075
Cowin SC (1994) Optimization of the strain energy density in linear anisotropic elasticity. J Elast 34:45–68
Majak J (1995) On optimal material orientation of transversally isotropic and orthotropic 3D materials. In: Proc of the 8-th Nordic seminar on computational mechanics. Chalmers University of Technology, pp 39–42
Marannano G, Mariotti V (2008) Structural optimization and experimental analysis of composite material panels for naval use. Meccanica 43:251–262
Groenwold AA, Haftka RT (2006) Optimization with non-homogeneous failure criteria line Tsai-Wu for composite laminates. Struct Optim 32:183–190
Bassir DH, Zapico JL, Gonzales MP, Alonso R (2007) Identification of a spatial linear model based on earthquake-induced data and genetic algorithm with parallel selection. Int J Simul Multidiscipl Des Optim 1:39–48
Pohlak M, Majak J, Eerme M (2007) Optimization of car frontal protection system. Int J Simul Multidiscipl Des Optim 1:31–38
Majak J, Pohlak M (2009) Stationary of the strain energy density in anisotropic solids. In: Proc of the 8th World Congress on structural and multidisciplinary optimization (CD-ROM)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Majak, J., Pohlak, M. Optimal material orientation of linear and non-linear elastic 3D anisotropic materials. Meccanica 45, 671–680 (2010). https://doi.org/10.1007/s11012-009-9262-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-009-9262-7