The Beam Interface
The Beam (beam) interface (), found under the Structural Mechanics branch () when adding a physics interface, is used for modeling slender structural elements, having a significant bending stiffness. The formulation allows geometric nonlinearity, with large rotations and small strains, and beams can be modeled on 2D boundaries and 3D edges.
Two-noded straight elements with an Hermitian formulation are used. Two different assumptions about the physics can be used:
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Euler (or Euler-Bernoulli) theory. This formulation is intended for slender beams, and do not take shear deformations into account.
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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.
Among the computed results are displacements, rotations, stresses, strains, and section forces. In addition to giving the beam properties explicitly in terms of area, moment of inertia, and so on, several predefined common cross-section types are available. Cross section data to be used in Cross Section Data settings can be computed using Theory for the Beam Cross Section Interface.
The Linear Elastic Material node is the only available material model.
When this physics interface is added, these default nodes are also added to the Model Builder: Linear Elastic Material, Cross Section Data, Free (a condition where points are free, with no loads or constraints), and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, loads and constraints. You can also right-click Beam to select physics features from the context menu.
Settings
The Label is the default physics interface name.
The Name 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 Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is beam.
Beam Formulation
Select Euler-Bernoulli or Timoshenko to use the appropriate beam theory.
For COMSOL Multiphysics models created in versions 4.3b and earlier, the only option available is Euler-Bernoulli. See the Backward Compatibility section to make changes to such a model.
Backward Compatibility
The formulation of the beam element was significantly changed as of COMSOL Multiphysics version 4.4. For this reason, by default, models created in previous versions default to using the Euler-Bernoulli theory.
This section only displays if a model was created in an earlier version. You also need to click the Show button () and select Advanced Physics Options to edit the section and change the Beam Formulation to Timoshenko (if required).
Click to clear the Use pre 4.4 formulation check box to convert a model into the new formulation. For most models, the only difference is that it will then be possible to select Timoshenko theory in the Beam Formulation section.
There are, however, some situations where you need to make additional changes to your model when migrating to the new formulation:
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If you have made manual adjustments to the solver sequence, such as scaling the dependent variables or adjusting groups in a segregated solver. These settings might have to be redone.
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If you are using multiple physics interfaces and use the same degree of freedom names for the displacements in the Beam interface and other structural mechanics interfaces. In this case, you need to rename the degrees of freedom in the Beam interface and create a different type of connection between the beams and the other physics interface, for example using a Solid Connection or Shell Connection.
Reference Point for Moment Computation
Enter the default coordinates for the Reference point for moment computation xref. The resulting moments (applied or as reactions) are then computed relative to this reference point. During the results and analysis stage, the coordinates can be changed in the Parameters section in the result nodes.
Dependent Variables
The Beam interface has these dependent variables (fields):
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The displacement field u, which has two components (u, v) in 2D and three components (u, v, and w) in 3D.
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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 (beam.uLinx, beam.uLiny, beam.uLinz) and (beam.thLinx, beam.thLiny, beam.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 Beam 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 name of these variables.
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”).
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Boundary, Edge, Point, and Pair Nodes for the Beam Interface
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Theory for the Beam Interface
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Theory for the Beam Cross Section Interface
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Channel Beam: Application Library path Structural_Mechanics_Module/Verification_Examples/channel_beam
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Instability of a Space Arc Frame: Application Library path Structural_Mechanics_Module/Verification_Examples/space_frame_instability