TR1: Co-rotated and reduced order time integrators

Technical Report 1 describes a linearly implicit time integration method combined with a family of finite element formulations: (…)

  • Total Lagrangian (TL)

  • body co–rotational full mesh (BC)

  • body co–rotational reduced order (BC–RO)

  • body co–rotational modal (BC–MODAL)

as they are implemented in SOLFEC-1.0. These formulations allow to vary the amount of deformation expressed by a finite element mesh and facilitate saving computational time and storage. They may be helpful in the context of multibody modeling.

The methods described in TR1 can be accessed by creating a BODY object as follows

bdTL = BODY (solfec, 'FINITE_ELEMENT', shape, material, form = 'TL')
bdTL.scheme = 'DEF_LIM'

bdBC = BODY (solfec, 'FINITE_ELEMENT', shape, material, form = 'BC')
bdBC.scheme = 'DEF_LIM'

bdRO = BODY (solfec, 'FINITE_ELEMENT', shape, material,
             form = 'BC-RO', base = pod_base)

dbMD = BODY (solfec, 'FINITE_ELEMENT', shape, material,
             form = 'BC-MODAL', base = modal_base)

In case of the ‘BC–RO’ and ‘BC–MODAL’ the linearly implicit integrator is default. For ‘TL’ and ‘BC’ the default time integration scheme is ‘DEF_EXP’ (Table 7); we change it to ‘DEF_LIM’ after body creation.

The base format is a tuple of two lists

base = ([eval1, eval2, ..., evaln],
        [evec11, evec12, ..., evec1m,
         evec21, evec22, ..., evec2m,
         ..., evecnm])

where we assumed n base vectors of size m. The first list stores eigenvalues and the second list stores eigenvectors. COROTATED_DISPLACEMENTS and RIGID_DISPLACEMENTS commands can be used together to sample displacements and generate a reduced base using Python’s modred package. MODAL_ANALYSIS command can be used to generate a modal base.

Input decks for the rotating bar, pipe impact, and array excitation examples from TR1 can be respectively found in

directories. See also the online version of these examples.


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