The Pipe Mechanics Interface

The interface (

), found under the branch (

) when adding a physics interface, is used for analysis of stresses and deformation in pipes. It can be modeled on 2D boundaries and 3D edges.

Two-noded straight elements with a Hermitian formulation are used. Two different assumptions about the physics can be used:

•

Euler (or Euler-Bernoulli) theory. This formulation is intended for slender pipes, and do not take shear deformations into account.

•

Timoshenko theory. In this formulation that extends the beam theory to ‘thick’ beams, shear deformations are taken into account. In a dynamic analysis, inertial effects from rotation are also included.


	The formulation in this physics interface is valid only for straight pipes. In pipe bends, the ovalization of the cross section will cause a reduction in stiffness and increase in stresses. These effects are not accounted for.

Among the computed results are displacements, rotations, stresses, strains, and section forces. In addition to giving the pipe properties explicitly in terms of area, moment of inertia, and so on, predefined common cross-section types are available. Cross section data to be used in Pipe Cross Section settings can be computed using The Beam Cross Section Interface.

The material in the pipe is assumed to be linear elastic.

When this physics interface is added, these default nodes are also added to the Model Builder: Fluid and Pipe Materials, Pipe Cross Section, Fluid Load, Free (a condition where points are free, with no loads or constraints), and Initial Values. Then, from the toolbar, add other nodes that implement, for example, loads and constraints. You can also right-click to select physics features from the context menu.

Settings

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is pipem.

Beam Formulation

Select or to use the appropriate beam theory. Timoshenko theory, which is the default, includes the effects of shear flexibility and rotary inertia. Euler-Bernoulli theory is appropriate for pipes with cross section dimensions which are small relative to the length of the pipe, whereas Timoshenko theory can be used both for thick and slender pipes.

Structural Transient Behavior

From the list, select (the default) or . Use to treat the dynamic behavior as quasi static (with no mass effects; that is, no second-order time derivatives). Selecting this option gives a more efficient solution for problems where the variation in time is slow when compared to the natural frequencies of the system. The default solver for the time stepping is changed from Generalized alpha to BDF when is selected.

This is often the case when the time dependence exists only in some other physics, like a transient heat transfer problem causing thermal strains.

Advanced Settings

To display this section, click the button (

) and select in the dialog box. Normally these settings do not need to be changed.

You can chose how to group in the solver nodes the extra ODE variables added by some features.

Select the check box to group in the solver node the variables added by the Rigid Connector feature.

The selection made in the section can be overridden by the settings in the section of the Rigid Connector feature.

Discretization

The discretization cannot be changed. The element has different shape functions for the axial and transversal degrees of freedom. The axial displacement and twist are represented by linear shape functions, while the bending is represented by a cubic shape function (“Hermitian element”).

Dependent Variables

The Pipe Mechanics interface has these dependent variables (fields):

•

The displacement field u, which has two components (u, v) in 2D and three components (u, v, and w) in 3D.

•

The rotation angle θ, which has one component in 2D (th) and three components in 3D (thx, thy, and thz).

The names can be changed but the names of fields and dependent variables must be unique within a model.


	The dependent variable names remain same in both a geometrically linear and a geometrically nonlinear analysis. Under geometric nonlinearity, the dependent variables are however not defined though shape functions. The equivalent shape function variables are (pipem.uLinx, pipem.uLiny, pipem.uLinz) and (pipem.thLinx, pipem.thLiny, pipem.thLinz). In this case, you will see the latter names under Dependent Variables in the Solver Configurations tree. If needed, these shape variables can be used to write any extra contributions in the Pipe Mechanics interface. If a physics interface that separates the material and spatial frame (Solid Mechanics is one such example) is added to the model, the coordinate indices change from (x, y, z) to (X, Y, Z) in the names of these variables.

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Boundary, Edge, Point, and Pair Nodes for the Pipe Mechanics Interface

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Theory for the Pipe Mechanics Interface

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Coupled Analysis of Flow and Stress in a Pipe: Application Library path