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Orthogonal base functions and consistent diagonal mass matrices for two‐dimensional elements
Author(s) -
Schreyer Howard L.,
Fedock Joseph J.
Publication year - 1979
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620140910
Subject(s) - diagonal , discretization , mathematics , centroid , mass matrix , orthogonal polynomials , mathematical analysis , matrix (chemical analysis) , rotation matrix , base (topology) , rigid body , diagonal matrix , rotation (mathematics) , geometry , field (mathematics) , classical mechanics , pure mathematics , physics , materials science , nuclear physics , neutrino , composite material
Abstract Orthogonal base functions that are complete first‐order polynomials but contain higher order terms are developed for normalized rectangular and triangular elements. To obtain exact expressions for kinetic energy under rigid body rotation, an internal node is introduced at the centroid of each element. Then the corresponding mass matrix is both diagonal and consistent. A mixed variational formulation is used in the derivation of spatially discretized field equations. Central Difference time integration is utilized to provide sample results which are compared with other numerical or analytical solutions.