2022-01-20T08:40:44Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000190912021-03-01T16:22:49ZRegular solution to topology optimization problems of continuaAzegami, Hideyuki55781Kaizu, Satoshi55782Takeuchi, Kenzen55783calculus of variationsboundary value problemtopology optimizationdensity methodH1 gradient methodThe present paper describes a numerical solution to topology optimization problems of domains in which boundary value problems of partial differential equations are defined. Density raised to a power is used instead of the characteristic function of the domain. A design variable is set by a function on a fixed domain which is converted to the density by a sigmoidal function. Evaluation of derivatives of cost functions with respect to the design variable appear as stationary conditions of the Lagrangians. A numerical solution is constructed by a gradient method in a design space for the design variable.journal article日本応用数理学会2011application/pdfJSIAM Letters314http://dx.doi.org/10.14495/jsiaml.3.1http://hdl.handle.net/2237/211961883-0609https://nagoya.repo.nii.ac.jp/record/19091/files/3_1.pdfeng