Transcription of Lumped and Consistent Mass Matrices - Quickfem
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Lumped and Consistent Mass Matrices - Quickfem
31 LumpedandConsistentMassMatrices31 1 chapter 31: Lumped AND Consistent MASS MATRICES31 2 TABLE OF CONTENTSPage 3 Matrix Construction31 3 Direct Mass 3 Variational Mass 4 Template Mass 4 Mass Matrix 5 Ran kand Numerical 6 6 Matrix Examples: Bars and Beams31 8 The 3-Node 8 The Bernoulli-Euler Plane 8 The Plane 10 *The Timoshenko Plane 11 Spar and Shaft 12 Matrix Examples: Plane Stress31 12 The Plane Stress Linear 12 Four-Node Bilinear 14 Diagonalization Methods31 15 HRZ 15 Lobatto 15 and 16 18 1931 231 3 MASS MATRIX CONSTRUCTION IntroductionTo do dynamic and vibration finite element analysis, you need at least a mass matrix to pair withthe stiffness matrix. This chapter provides a quic kintroduction to standard methods for computingthis a general rule, the construction of the master mass matrixMlargely parallels of the masterstiffness matrixK. Mass Matrices for individual elements are formed in local coordinates, trans-formed to global, and merged into the master mass matrix following exactly the same techniquesused forK.
This is proven in the next Chapter. The most general method of this class uses finite element templates to fully parametrize the element mass matrix. For the prismatic 2-node bar element one would start with the 3-parameter template Me = ρA µ11 µ12 µ12 µ22,(31.9) which includes the symmetry constraint from the start.
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