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Structural Homology Design Using Equality Constraints

The concept of homology design has been devised for the application to large telescope structure by S.v.Hoerner. It is defined that the deformation of a structure shall be called homologous, if a given geometrical relation holds, for a given number of structural points, before, during, and after the deformation. Recently, the need of homology design in the structural design has been increase due to the required precision in the structure. Some researchers have utilized the theory on the structural design with finite element method in the late 1980s In the present investigation, a simple method using geometrical equality constraints is suggested to gain homologous deformation. The previous method is improved in that the decomposition of FEM eqation, which is very expensive, is not necessary. The basic formulations of the homology design with the optimization concept are described and several practical examples are solved to verify the usefulness and validity. Especially, a back-up structure of a satellite antenna is designed by the suggested method. The results are compared with those of existing researches.