1996 Fiscal Year Final Research Report Summary
Variational Approach for Nonlinear Structural Optimization
| Project/Area Number |
07045029
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | University-to-University Cooperative Research |
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| Research Institution | Faculty of Engineering, Ehime University |
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Principal Investigator |
OHKUBO Sadaji Faculty of Engineering, Ehime University, 工学部, 教授 (80036235)
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| Co-Investigator(Kenkyū-buntansha) |
TANIWAKI Kazuhiro Faculty of Engineering, Ehime University, 工学部, 助手 (60207199)
卜 小明 愛媛大学, 工学部, 教授
BU Xiaoming Faculty of Engineering, Ehime University
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| Project Period (FY) |
1995 – 1996
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| Keywords | energy principle / rigid plane frams / material nonlinearity / optimum design method / without sensitivities / gradient projection method |
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| Research Abstract |
In this research project a new, efficient and unified optimum design method for rigid plane frame structures with either linear or arbitrary nonlinear stress-strain relationship materials is developed based on the energy principle. Different from the common optimum design method the calculation of behavior sensitivities of structure is not necessary in the proposed optimization process.
By using the principle of minimum complementary energy and the Lagrangian interpretation, necessary conditions for linear-nonlinear structural analysis problem are derived, then the primary optimum design problem is reformulated considering both the primary design constraints on stresses of member elements and nodal displacements and the necessary conditions for analysis problem derived above. In the reformulation of optimum design problem, structural behaviors, member-end forces and nodal displacements, are also considered as the independent design variables in addition to the primary design variables,
… More
namely widths of cross sections of all member elements. This reformulated optimum design problem is solved by using a linear approximation concept and a gradient projection method without behavior sensitivities.
For the confirmation of rigorousness, efficiency and reliability of the proposed method, a comparison is made with another optimum design method in which the sensitivities of stress and displacement constraints are calculated and the optimum solution is determined by using linear approximation concept and a dual algorithm.
The numerical comparisons of design examples shows that the same optimal solutions are obtained by both methods, however CPU times to obtain the optimum solutions by the proposed method are less than 1/10 of ones by the method with behavior sensitivities and furthermore the reliability to obtain the optimum solutions at any design conditions is excellent in the proposed method. From these results, it can be concluded that the rigorousness, efficiency and reliability of the proposed method are very excellent compared with the common optimum design method with behavior sensitivities. Less
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