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Index reduction for operator differential-algebraic equations in elastodynamics. (English) Zbl 1321.74007
Summary: In space semi-discretized equations of elastodynamics with weakly enforced Dirichlet boundary conditions lead to differential algebraic equations (DAE) of index 3. We rewrite the continuous model as operator DAE and present an index reduction technique on operator level. This means that a semi-discretization leads directly to an index-1 system.
We present existence results for the operator DAE with nonlinear damping term and show that the reformulated operator DAE is equivalent to the original equations of elastodynamics. Furthermore, we show that index reduction and semi-discretization in space commute if the discretization schemes are chosen in an appropriate way.

MSC:
74B05 Classical linear elasticity
34A09 Implicit ordinary differential equations, differential-algebraic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q74 PDEs in connection with mechanics of deformable solids
70J50 Systems arising from the discretization of structural vibration problems
74S05 Finite element methods applied to problems in solid mechanics
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