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Finite element analysis of viscoelastic structures using Rosenbrock-type methods. (English) Zbl 1163.74044

Summary: The consistent application of space-time discretisation in the case of quasi-static structural problems based on constitutive equations of evolutionary type yields after the spatial discretisation by means of the finite element method a system of differential-algebraic equations. In this case the resulting system of differential-algebraic equations with the unknown nodal displacements and the evolution equations at all spatial quadrature points of the finite element discretisation are solved by means of a time-adaptive Rosenbrock-type methods leading to an iteration-less solution scheme in nonlinear finite element analysis. The applicability of the method is studied by means of a simple example of a viscoelastic structure.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory

Software:

ROS3P
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References:

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