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Algebraic Formulation of Elastodynamics: the Cell Method

E. Tonti, F. Zarantonello1

1 University of Trieste, Italy. E-mail: tonti@units.it; f_zarantonello@libero.it

Computer Modeling in Engineering & Sciences 2010, 64(1), 37-70. https://doi.org/10.3970/cmes.2010.064.037

Abstract

This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual subdivision of the time axis, as we did for a space cell complex. The mass matrix obtained with the direct algebraic formulation is diagonal.

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Tonti,, E. (2010). Algebraic Formulation of Elastodynamics: the Cell Method. CMES-Computer Modeling in Engineering & Sciences, 64(1), 37–70.



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