Abstract
The problem of minimization (or maximization) of the elastic energy density is solved in the two-dimensional case for a nonlinear elastic solid. The material behaviour is simulated on the basis of a power law stress-strain relation. Closed-form solutions which include corresponding solutions for a linear elastic solid are obtained. The latter may give local as well as global maxima and minima, respectively.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jones, R. 1975:Mechanics of composite materials. New York: Mc Graw-Hill
Malmeister, A.; Tamuzs, V.; Teters, G. 1980:Strength of polymer and composite materials (in Russian). Riga: Zinatne
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, 55–63
Pedersen, P. 1991: On thickness and orientational design with orthotropic materials.Struct. Optim. 3, 69–78
Pedersen, P.; Bendsøe, M. 1995:On strain-stress fields resulting from optimal orientation. In: Olhoff, N.; Rozvany, G.I.N. (eds.)WCSMO-1. Proc. First World Congress of Structural and Multidisciplinary Optimization, pp. 243–250. Oxford: Pergamon
Pedersen, P.; Taylor, J.E. 1993: Optimal design based on power law non-linear elasticity. In: Pederson, P. (ed.)Optimal design with advanced materials, pp. 51–66. Amsterdam: Elsevier
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lellep, J., Majak, J. On optimal orientation of nonlinear elastic orthotropic materials. Structural Optimization 14, 116–120 (1997). https://doi.org/10.1007/BF01812513
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01812513