| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
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| Research Abstract |
Various morphogenesis problems were arranged mathematically, and a cellular automaton was proposed as a mathematical model of the optimization for these problems. Development of the local rule of the cellular automaton as a method of analyzing a non-linear optimization problem and application to some problems was performed as the result Furthermore, the local rule called "neuron model" developed here was extended, and validity of the method to the form finding problem under periodic external forces became clear. Moreover, the possibility to various problems, such as a form finding problem of the optimum design of structures with frequency constraints, has been examined. The results of the project are summarized as follows.
1)Mathematical model for structural morphogenesis
The minimum weight problem, the maximum rigidity problem, the frequency optimization problem, etc.were arranged on the assumption that those problems would be analyzed by heuristics, and the mathematical model was established.
2)Cellular automata for structural morphogenesis
An efficient technique of solving morphogenesis problems was developed using the characteristic of cellular automata.
3)Application to morphogenesis under dynamic external forces
The developed local rule was applied to the optimization problem under dynamic external force, and the applicability and validity were shown.
4)Application to morphogenesis under dynamic boundary conditions
The developed local rule was applied to the optimization problem under dynamic boundary conditions, and the applicability and validity were shown.
5)Application to morphogenesis considering inertia
The possibility of application on the optimization problem of the structure moving with acceleration was obtained.
6)Application to frequency optimization problems
The possibility of application on frequency optimization problems was obtained by extension of the local rule.
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