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# Tied Joints

# 20. Tied Joints

The `Tied Joint` provides an interface to the whole joint models. Multiple connection methods are supported, including weighted constraint equations.

Separate shear and normal forces are supported. The separation also reduces requirements on the constraints. The whole surface is no longer required to have \(6\) rigid body modes. The normal tied interface keeps surfaces together. This relaxes the requirements for shear constraints. The Tied Joint permits constraints that look more like a collection of trusses, not a collection of beams.

Rotational DOFs are necessary for the structure to move as a rigid body. However, the adjacent elements may have no rotational stiffness. This introduces singularities. Avoiding the rotational DOFs is important.

Normal direction constraints are tied surfaces. Shear direction constraints are a truss network. For curved surfaces, constraints may be inconsistent.

## 20.1. Lap joint

A lap joint contains regions of “welded” contact, microslip, and macroslip as shown in Figure 20.1. An elastic spring approximates normal forces. Tied surfaces approximate shear behavior of the “welded” region. The macroslip region is free. The region of microslip depends on the loading. Microslip introduces loss into the structure. This region is well approximated by an Iwan element.

Figure 20.1 Lap Joint with Contact Regions. The physics of bolted lap joints is complex. Tied Joints use a combination of constraints, springs and optionally Iwan elements to generate a reduced order model of the structure.

Without a Tied Joint, this lap joint can be modeled using a whole joint model. Each of the contact surfaces is rigidized (using a rigid set). A Joint2G connects the surfaces. The mesh is represented in Figure 20.2. Listing 20.1 illustrates the conventional means of connecting this structure. This method reduces all the behavior of the joint to a single Joint2G element. That element must be included as part of the mesh. Because the surfaces are allowed to translate and rotate independently, interpenetration can occur. Nevertheless, the method is effective in representing the energy loss that occurs in this structure.

Figure 20.2 Lap Joint Finite Element Mesh. The physical lap joint is represented by a reduced order model which uses disconnected meshes of the top and bottom material. These are shown separated in the cartoon but may have overlapping nodes. In a conventional connection the Joint2G which represents the bolt must be explicitly meshed. The Tied Joint approach generates that element internally.

Listing 20.1 Conventional Input for Whole Lap Model.

    Rigidset
      sideset 1
    end
    Rigidset
      sideset 2
    end

    Block 3
      Joint2G
        Kz = Elastic 1e6
        Kx = Iwan 1
        Ky = Iwan 1
        Krx = Elastic 1e9
        Kry = Elastic 1e9
        Krz = Elastic 1e9
    end

The input included in Listing 20.2 represents the same physics. The normal definition is `none` because the normal stiffness is part of the Joint2G structure. The shear side definition is `rigid` corresponding to a rigid set definition on each of the surfaces. No mesh of block 3 is required.

Listing 20.2 Tied Joint Input for Whole Lap Model.

    Tied Joint
       Normal Definition = none
         surface 1,2
       Shear Definition
         side = rigid
         connect to Block 3
    end
    Block 3
       Joint2G
        Kz = Elastic 1e6
        Kx = Iwan 1
        Ky = Iwan 1
        Krx = Elastic 1e9
        Kry = Elastic 1e9
        Krz = Elastic 1e9
    end

## 20.2. Joint with Slip

The whole joint model of Section 20.1 can be modified to prevent penetration of the two surfaces. The models are shown in Listing 20.3 and Listing 20.4 for the conventional and Tied Joints.

Sliding contact or slip keeps two surfaces in contact with no resistance to transverse motion. Because the sliding contact constrains the normal behavior, the Joint2G parameters for that direction are irrelevant. Because the surfaces are flexible, properly constraining the transverse motion of the connection nodes is challenging. The constraint method is specified using the `side`. The `Rrod` and `average` methods are available. Listing 20.3 uses the `Rrod` approach.

Listing 20.3 Conventional Input for Whole Lap Model with Sliding Contact.

    Rigidrod
       sideset 1
    end
    Rigidrod
       sideset 2
    end
    Block 3
       Joint2G
        Kx = Iwan 1
        Ky = Iwan 1
        Krz = Elastic 1e9
    END

    Tied Data
         name = 'block_3_tj'
         surface 1,2
         transverse slip
    end

Listing 20.4 Tied Joint Input for Whole Lap Model with Sliding Contact.

    Tied Joint
       Normal Definition = slip
         surface 1,2
       Shear Definition
         side = Rrod
         connect to Block 3
    end

    Block 3
       Joint2G
        Kx = Iwan 1
        Ky = Iwan 1
        Krz = Elastic 1e9
    end