Original scientific paper
Optimal design and hyperbolic problems
Full text: english pdf 147 Kb
APA 6th Edition
Antonić, N. & Vrdoljak, M. (1999). Optimal design and hyperbolic problems. Mathematical Communications, 4 (1), 121-129. Retrieved from https://hrcak.srce.hr/1750
MLA 8th Edition
Antonić, N. and M. Vrdoljak. "Optimal design and hyperbolic problems." Mathematical Communications, vol. 4, no. 1, 1999, pp. 121-129. https://hrcak.srce.hr/1750. Accessed 31 Mar. 2023.
Chicago 17th Edition
Antonić, N. and M. Vrdoljak. "Optimal design and hyperbolic problems." Mathematical Communications 4, no. 1 (1999): 121-129. https://hrcak.srce.hr/1750
Antonić, N., and Vrdoljak, M. (1999). 'Optimal design and hyperbolic problems', Mathematical Communications, 4(1), pp. 121-129. Available at: https://hrcak.srce.hr/1750 (Accessed 31 March 2023)
Antonić N, Vrdoljak M. Optimal design and hyperbolic problems. Mathematical Communications [Internet]. 1999 [cited 2023 March 31];4(1):121-129. Available from: https://hrcak.srce.hr/1750
N. Antonić and M. Vrdoljak, "Optimal design and hyperbolic problems", Mathematical Communications, vol.4, no. 1, pp. 121-129, 1999. [Online]. Available: https://hrcak.srce.hr/1750. [Accessed: 31 March 2023]
Quite often practical problems of optimal design have no solution. This situation can be alleviated by relaxation, where one needs generalised materials which can mathematically be defined by using the theory of homogenisation.
First mathematical results in this direction for general (nonperiodic) materials were obtained by Murat and Tartar.
We present some results in optimal design where the equation of state is hyperbolic. The control function is related to the response of vibrating material under the given external force.
As the problem under consideration has no solution, we consider its relaxation to H-closure of the original set of controls.
optimal design, homogenisation, relaxation, H-convergence, stratified materials
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