- 著者
- 藤川 正毅 田中 真人 井元 佑介 三目 直登 浦本 武雄 山中 脩也
- 出版者
- 一般社団法人 日本機械学会
- 雑誌
- 日本機械学会論文集 (ISSN:21879761)
- 巻号頁・発行日
- vol.86, no.881, pp.19-00256, 2020 (Released:2020-01-25)
- 参考文献数
- 20
- 被引用文献数
- 1
A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.
1 0 0 0 OA 正規言語の所属問題への副有限モノイドと擬ガロア圏の構造論の応用
正規言語の分類理論であるEilenberg理論を公理化し、その整数論への応用例を見つけた。特にBorgerが定義した意味でのWitt vectorに対するChristolの定理の類似を証明した。その後、この定理の続編としてBostとConnesによって導入されたBost-Connes系というC*力学系の数論的部分代数とWitt vectorのなす代数が同型であることを観察している。このことから、Witt vectorをmodular関数の変形族の特殊値によって実現できるだろうことを示唆を得て、それに関する観察を得た。
- 著者
- 藤川 正毅 田中 真人 井元 佑介 三目 直登 浦本 武雄 山中 脩也
- 出版者
- 一般社団法人 日本機械学会
- 雑誌
- 日本機械学会論文集
- 巻号頁・発行日
- vol.86, no.881, pp.19-00256-19-00256, 2020
- 被引用文献数
- 1
<p>A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.</p>
<p>A numerical calculation scheme for stress and its consistent tangent moduli with hyper-dual numbers(HDN) for Ogden-type hyperelastic material model was proposed. The main advantage of this scheme is that once the framework is coded, any Ogden-type hyperelastic material model can be implemented by only re-coding the strain energy density function. In this scheme, the new differentiation method for eigenvalue and eigenvector of the symmetric matrices with HDN were proposed. The proposed method can calculate the eigenvalue and eigenvector in non-real part analytically by using the eigenvalue and eigenvector in real part, in case that all eigenvalues in real part are not multiple root. We implemented the Neo-Hookean model and the Ogden model with the proposed scheme, to confirm the effectiveness and robustness of this method, and applied it to some examples. As the results, it was confirmed that the numerical results of the proposed method showed good agreement with analytical ones.</p>