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Non linearities list

• nl_inout
• nl_contact
• nl_modaldmp

Purpose

List of supported non linearities. It is possible to create new ones (sdtweb nl_fun)

nl_inout

nl_inout is the more general non linearity, using observation and command matrix associated with elements supporting the kinematics (cbush for point connections, see section ??, zero thickness volumes for surface connections (where two layers of coincident nodes are considered for a hexa8 or penta6 element, see section ??), volume elements for 3D applications (see section ??) or the deprecated observation/sensor command/loads as detailed in  section ??.

The general form of the non-linearity f_NL=b × f(C.u,C.v) is detailed in section ??.
For a list of implemented non-linear constitutive laws xxx

The pro.NLdata structure has fields described in section ?? (with the need to distinguish the form for model declaration and during time integration).

By default, no Jacobian is computed for this non-linearity. Experimental Jacobian are computed according 3 methods according to the NL.Jacobian value:

• 0 : no Jacobian. (default).
• 1 : tangent matrices.
• 2 : fixed Jacobian (can be max stiffness / damping or mean, ...).

Then computed matrices are then multiplied by NL.alphaJK factor for Jacobian stiffness, and NL.alphaJD factor for Jacobian damping.

nl_contact

Supports non conform fixed matching contact (squeal applications for example) and (surface contact large displacement, as in rail/wheel interaction for example). For conform meshes, zero thickness elements associated with p_zt can be used.

See p_contact, ctc_utils.

nl_modaldmp

Implementation of modal damping. Although modal damping is not a non-linear feature in itself, its implementation requires it to be declared as a non-linearity.

The concept is to provide shapes defined on a part of a model with associated damping ratios. nl_modaldmp handles the kinematic projection on the model which can contain superelements. In the case where superelements are used and concerned with modal damping, the shapes provided must be written on the physical DOF of the superelements.

The set of shapes must be stacked in model with a valid ID field. It is a common deformation SDT data structure (see sdtweb def), with an additional .ID field. The .data field is equivalent to the ones of complex modes (see fe_ceig). It is a matrix of two columns respectively giving the frequency and the target damping ratio for each mode.

Since modal damping implies a modal sensor, the features performs both by default. It is however possible to simplify it as a pure modal sensor. The theory around modal sensing/damping can be found in [12].

The pro.NLdata structure has fields

• type: string 'nl_modaldmp'.
• CurveId: the curve ID stacked in model which provides the shapes and their damping ratios.
• SensorOnly: to use the feature only as a modal sensor in a def data structure.

The NLdata structure generation can be integrated using an nl_modaldmp('db') call. See sdtweb nl_spring#setpro for this integration. This is used in transient simulations, and in complex mode computations, see nl_solve.