Topology optimization based on structural flexibility in the periodic loading

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76428/1/AIAA-2000-4737-762.pd

Topology optimization for flextensional actuators

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76744/1/AIAA-1998-4951-939.pd

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. © 1998 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34532/1/372_ftp.pd

Topological design considering flexibility under periodic loads

Topology optimization has been extensively considered to design the structural configuration for the stiffness maximization and the eigenfrequency maximization. In this paper, we construct a topology optimization method implementing flexibility with the time-periodic loading condition. First, the flexibility in the dynamic periodic loading is formulated using the mutual energy concept. Second, the multi-optimization problem is formulated using a new multi-objective function in order to obtain an optimal solution incorporating both flexibility and stiffness. Next, the topology optimization procedure is developed using the homogenization design method. Finally, some examples are provided to confirm the optimal design method presented here.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41900/1/158-19-1-4_00190004.pd

Studies on heterocyclic analogs of azulenes. XI. Syntheses and cycloadditions of cyclohepta[4,5]pyrrolo[1,2-a]imidazoles and cyclohept[d]imidazo[1,2-a]imidazoles

Cyclohepta[4,5]pyrrolo[1,2-a]imidazoles (1,3a-diazacyclopent[a]azulenes) (2) and cyclohept[d]imidazo[1,2-a]imidazoles (1,3a,9-triazacyclopent[a]azulenes) (6) were synthesized from 2-aminocyclohepta[b]pyrroles and 2-aminocycloheptimidazole, respectively, in moderate to good yields. Reactions of 2 and 6 with reactive acetylenes gave 2-azacyclohepta[ef]cycl[3.2.2]azines together with bis(1,3a-diazacyclopent[a]azuleno)[1,7]diaza[12]annulenes (4) and 2,3-diazacyclohepta[ef]cycl[3.2.2]azines together with bis(1,3a,9-triazacyclopent[a]azuleno)[1,7]diaza[12]annulenes (8), respectively. Reactions of 2 and 6 with electron deficient olefins gave 4 and 8, respectively. These reactions proceeded regioselectively via 1,10-dipolar intermediates