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The MAMBA model order reduction is capable of preserving the nonlinear behavior stemming from the contact interfaces of jointed structures.
While the contact interfaces introduce local nonlinearities into a jointed structure the components of the jointed structure can still be assumed as linear elastic. Therefore it is possible to utilize the superposition principle to describe the total deformation of the involved components.
A reduction basis constructed according to Craig and Bampton ensures very good result quality in case of linear elastic structures. This is achieved by the so called constrained modes, which represent static displacement shapes, and boundary fixed normal modes, which represent the internal dynamics of the linear elastic structure.
In case of jointed structures it is also essential that the reduction basis is capable to accurately capture the local displacements due to the occurring contact stresses. This is achieved by an additional set of trial vectors. These so called joint interface or contact modes are formulated to reproduce the local deformations due to the contact stresses. As the structure is capable to deform in a physical meaningful way the computed contact stresses are meaningful as well.
The total deformation is described as superposition of selected trial vectors.
Exemplary constraint modes accorting to Craig and Bampton.
Exemplary normal modes according to Craig and Bampton.
Exemplary contact modes computed during the MAMBA preprocessing step.
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In complex mechanic and mechatronic structures different types of contact interfaces can be identified.
First are contact interfaces where the contact stresses in surface normal direction are the dominating quantity. This is e.g. the case in many areas of spot welded structures. In MAMBA these contact interfaces are denoted as “Normal Contact”.
Second are contact interfaces where also shear stresses due to friction are occurring. This is e.g. the case for areas where the external loading would lead to tangential relative movement within the contact interface. In MAMBA these contact interfaces are denoted as “Frictional Contact” and comprise the “Normal Contact” as well.
Third are contact interfaces where high contact pressures values occur due to e.g. pretension of the structure. This is the case for bolted connections which are thoroughly tightened. In MAMBA these contact interfaces are denoted as “Pretensioned Contact” and comprise the “Frictional Contact” as well.
Contact stress component in normal direction within normal contact interfaces.
Additional shear stresses within frictional contact interfaces.
Hysteresis curve obtained from a pretensioned contact interface.