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Kotobuki performed the opening and ending themes of the 2009 anime series K-On!, alongside Aki Toyosaki, Yōko Hikasa, Satomi Satō and Ayana Taketatsu. Kotobuki played Tsumugi Kotobuki in K-On!, Karina Lyle/Blue Rose in Tiger & Bunny, Rikka Hishikawa/Cure Diamond in DokiDoki! PreCure, Mitsuko Kongō in A Certain Magical Index and A Certain Scientific Railgun, Yūko Nishi in A Channel, Lana and Cia from Hyrule Warriors, and Natsumi Aizawa in Natsuiro Kiseki, Touko Nanami in Bloom Into You, Asuka Tanaka in Hibike! Euphonium, Yoriko Fukase in A Whisker Away. The show launched her music career as she performed the opening and ending themes, and joined three other voice actresses as the music group Sphere. ![]() She played Tsumugi Kotobuki in the anime series K-On! about a high school girl band. 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The force vector is assembled by including the applied forces on each degree of freedom on each node in the mesh: The applied force vector will be an n x 1 vector, where n is 3 times the number of nodes in the mesh. For any elements which share a node, the stiffness contributions of that node will be summed from each element. When assembling the global stiffness matrix, the stiffness terms for each node in the elemental stiffness matrix are positioned in the corresponding location in the global matrix. The global stiffness matrix will be a square n x n matrix, where n is 3 times the number of nodes in the mesh (since each node has 3 degrees of freedom). ![]() ![]() Where the matrix is the local stiffness matrix of the i th element. At a high level, the global stiffness matrix is created by summing the local stiffness matrices: The global stiffness matrix for the overall structure is assembled based on the combination of the local stiffness matrices. 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