MPCs for transitions

SS LINEAR	Constrain a shell node to a solid node line for linear elements (S4, S4R, S4R5, C3D8, C3D8R, SAX1, CAX4, etc.).
SS BILINEAR(S)	Constrain a shell node to a solid node line for edge lines on quadratic elements (S8R, S8R5, C3D20, C3D20R, SAX2, CAX8, etc.).
SSF BILINEAR(S)	Constrain a midside node of a quadratic shell element (S8R, S8R5) to midface lines on 20-node bricks (C3D20, C3D20R, etc.).

# Modeling a shell-to-solid element transition The SLIDER, SS LINEAR, SS BILINEAR, and SSF BILINEAR MPCs allow for a transition from shell element modeling to solid element modeling on a shell surface. This modeling technique can be used to obtain solutions at shell-solid intersections or other discontinuities, where the local modeling should use full three-dimensional theory but the other parts of the structure can be modeled as shells. The shellto-solid submodeling capability (“Submodeling: overview,” Section 10.2.1) and the surface-based shellto-solid coupling constraint (“Shell-to-solid coupling,” Section 35.3.3) can also be used to obtain more accurate solutions in such cases, with considerably less modeling effort. In Abaqus/Standard the MPC usage assumes that the interface between the shell and solid elements is a surface containing the normals to the shell along the line of intersection of the meshes, so that the lines of nodes on the solid mesh side of the interface in the normal direction to the surface are straight lines. (Line $a , p ^ { 1 } , p ^ { 2 } , . . . , b$ in Figure 35.2.2–14 and lines $p ^ { 1 } , p ^ { 2 } , . . . , p ^ { n }$ in Figure 35.2.2–19 to Figure 35.2.2–20 should be straight lines.) It also assumes that the nodes of the solid elements are spaced uniformly on the interface surface as indicated in Figure 35.2.2–14 and Figure 35.2.2–19 to Figure 35.2.2–20. For each shell node on the edge use MPC type SS LINEAR, SS BILINEAR, or SSF BILINEAR, as appropriate, to constrain the shell node to the corresponding line or face of solid element nodes through the thickness. Then, use a SLIDER MPC to constrain each interior node on the line through the thickness to remain on the straight line defined by the bottom and top nodes of that line. For an example, see “Multi-point constraints,” Section 5.1.17 of the Abaqus Verification Guide. The SS BILINEAR and SSF BILINEAR MPCs are not intended for use with the variable node solid elements (C3D27, C3D27H, C3D27R, and C3D27RH). In Abaqus/Standard MPCs SS LINEAR, SS BILINEAR, and SSF BILINEAR eliminate all displacement components and two of the rotation components at the shell node, and the SLIDER MPC eliminates two displacement components at each interior solid element node in the interface. Therefore, any boundary conditions needed at the interface (such as those required when the shell/solid interface intersects a symmetry plane) should be applied only to the top and bottom nodes on the solid element side of the interface. # Using MPC type SS LINEAR MPC type SS LINEAR constrains a shell corner node to a line of edge nodes on solid elements for linear elements (S4, S4R, or S4R5; C3D8, C3D8R; SAX1; CAX4; etc.). The constrained nodes need not lie exactly on these lines, but it is suggested that they be in close proximity to the lines for meaningful results. 

text_image

p^n p^2 p^1 s

Figure 35.2.2–19 SS LINEAR type MPC. 4-node shells to 8-node bricks. # Input data Give the shell node, S, then the list of nodes along the corresponding line through the thickness in the solid element mesh. In Abaqus/Explicit only two solid nodes can be given. Referring to Figure 35.2.2–19, in Abaqus/Standard give $S , p ^ { 1 } , p ^ { 2 } , . . . , p ^ { n }$ , and in Abaqus/Explicit give $S , p ^ { 1 } , p ^ { n }$ , where $n \geq 2$ . The shell node number must be different from the solid mesh node numbers. Input File Usage: In Abaqus/Standard use the following option: \*MPC SS LINEAR, S, , , …, In Abaqus/Explicit use the following option: \*MPC SS LINEAR, S, , Abaqus/CAE Usage: Multi-point constraints for transitions are not supported in Abaqus/CAE. # Using MPC type SS BILINEAR MPC type SS BILINEAR constrains a corner node of a quadratic shell element (S8R, S8R5) to a line of edge nodes on 20-node bricks. This MPC type is available only in Abaqus/Standard. The constrained node need not lie exactly on the line, but it is suggested that it be in close proximity to the line for meaningful results. 

text_image

p^n p^4 p^3 p^2 p^1 s

Figure 35.2.2–20 SS BILINEAR type MPC. Corner of 8-node shell to edge of 20-node bricks. # Input data Give the shell node, S, then the list of nodes along the corresponding line through the thickness in the solid element mesh. Referring to Figure 35.2.2–20, give $S , p ^ { 1 } , p ^ { 2 } , . . . , p ^ { n }$ . The shell node number must be different from the solid mesh node numbers. Input File Usage: \*MPC $\mathrm { S S ~ B I L I N E A R } , S , p ^ { 1 } , p ^ { 2 } , . . . , p ^ { n }$ Abaqus/CAE Usage: Multi-point constraints for transitions are not supported in Abaqus/CAE. # Using MPC type SSF BILINEAR MPC type SSF BILINEAR constrains a midside node on a quadratic shell element (S8R, S8R5) to a line of midface nodes on solid 20-node bricks. This MPC type is available only in Abaqus/Standard. The constrained node need not lie exactly on the line, but it is suggested that it be in close proximity to the line for meaningful results. 

text_image

p^{n-2} p^{n-1} p^n p^6 p^7 p^8 p^4 p^2 p^5 p^1 p^3 s

Figure 35.2.2–21 SSF BILINEAR type MPC. Midside of 8-node shell to surface of 20-node bricks. # Input data Give the shell node, S, then the list of nodes on the solid face, in the order $p ^ { 1 } , p ^ { 2 } , . . . , p ^ { n }$ as shown in Figure 35.2.2–21. Input File Usage: \*MPC SSF BILINEAR, S, , , …, Abaqus/CAE Usage: Multi-point constraints for transitions are not supported in Abaqus/CAE. # 35.2.3 KINEMATIC COUPLING CONSTRAINTS Product: Abaqus/Standard # References • “Kinematic constraints: overview,” Section 35.1.1 • \*KINEMATIC COUPLING # Overview Kinematic coupling constraints: • limit the motion of a group of nodes to the rigid body motion defined by a reference node; • can be applied only to specific user-specified degrees of freedom at the constrained nodes; • can be specified with respect to local coordinate systems at the constrained nodes; and • can be used in geometrically linear or nonlinear analysis. The preferred method of providing a kinematic constraint of this type is described in “Coupling constraints,” Section 35.3.2. # Typical applications The kinematic coupling constraints are useful in cases where a large number of nodes (the “coupling” nodes) are constrained to the rigid body motion of a single node and the degrees of freedom that participate in the constraint are selected individually in a local coordinate system. In many such cases MPCs either are not available or would have to be prescribed individually for each constrained node. A typical example is shown in Figure 35.2.3–1, where a kinematic coupling constraint is used to prescribe a twisting motion to a model without constraining radial motions. In other applications the kinematic coupling constraint can be used to provide coupling between continuum and structural elements. # Defining the constraint A kinematic coupling constraint requires the specification of a reference node, coupling nodes, and the constrained degrees of freedom at these nodes. The reference node has both translational and rotational degrees of freedom. Kinematic constraints are imposed by eliminating degrees of freedom at the coupling nodes. Once any combination of displacement degrees of freedom at a coupling node is constrained, additional displacement constraints—such as MPCs, boundary conditions, or other kinematic coupling definitions—cannot be applied to any coupling node involved in a kinematic coupling constraint. The same limitation applies for rotational degrees of freedom. Input File Usage: To constrain all available degrees of freedom: \*KINEMATIC COUPLING, REF NODE=node coupling node number or node set 

text_image

z y x R θ R z b constrained nodes that are free to translate radially (COUPLESET) θ a reference node (node 500) axis of cylindrical coordinate system (COUPLEAXIS)

Figure 35.2.3–1 A kinematic coupling constraint used to transmit rotation to a structure while permitting radial motion. To constrain a single degree of freedom: \*KINEMATIC COUPLING, REF NODE=node coupling node number or node set, dof To constrain a range of degrees of freedom: \*KINEMATIC COUPLING, REF NODE=node coupling node number or node set, first dof, last dof To specify non-contiguous lists of constrained degrees of freedom, repeat the node numbers or node sets on subsequent data lines. For example, the following input is used to constrain degrees of freedom 1, 2, 3, and 6 at node 10 to the motion of reference node 5: \*KINEMATIC COUPLING, REF NODE=5 10, 1, 3 10, 6 # Translational degrees of freedom Translational degrees of freedom are constrained by eliminating the specified degrees of freedom at the coupling nodes. When all translational degrees of freedom are specified, the coupling nodes follow the rigid body motion of the reference node. # Rotational degrees of freedom All combinations of selected rotational degrees of freedom result in rotational behavior that is identical to existing MPC types. Specifically: • Selection of three rotational degrees of freedom along with three displacement degrees of freedom is equivalent to MPC type BEAM. • Selection of two rotational degrees of freedom is equivalent to MPC type REVOLUTE. • Selection of one rotational degree of freedom is equivalent to MPC type UNIVERSAL. Internal nodes are created by the kinematic coupling to enforce the constraints that are equivalent to MPC types REVOLUTE and UNIVERSAL. These nodes have the same degrees of freedom as the additional nodes used in these MPC types and are included in the residual check for nonlinear analysis. # Specifying a local coordinate system The constrained degrees of freedom at the coupling nodes can be specified in a local coordinate system instead of the (default) global coordinate system (see “Orientations,” Section 2.2.5). Figure 35.2.3–1 illustrates the use of a local coordinate system definition with a kinematic coupling constraint to constrain all but the radial translation of a group of nodes to a reference node. In this example a local cylindrical coordinate system is defined that has its axis coincident with the structure’s axis. The coupling node constraints are then specified in this local coordinate system. In this example the constrained nodes are attached to continuum elements; thus, only translational degrees of freedom need to be specified. Input File Usage: \*KINEMATIC COUPLING, REF NODE=node, ORIENTATION=name For example, the following input is used to specify the kinematic coupling constraint shown in Figure 35.2.3–1: ```csv *ORIENTATION, SYSTEM=CYLINDRICAL, NAME=COUPLEAXIS 0.0, -1.0, 0.0, 0.0, 1.0, 0.0 *KINEMATIC COUPLING, REF NODE=500, ORIENTATION=COUPLEAXIS COUPLESET, 2, 3 ``` # Constraint directions and finite rotations In geometrically nonlinear analysis steps, the coordinate system in which the constrained degrees of freedom are specified will rotate with the reference node regardless of whether the constrained degrees of freedom are specified in the global coordinate system or in a local system. Thus, the constraint shown in Figure 35.2.3–1 will enable free radial motion throughout arbitrary rotations of the structure. Radial motion in this case is defined as motion normal to the structure’s axis (defined in the undeformed configuration by points a and b in the figure), with this axis rotating with the reference node. Therefore, the free radial expansion shown in Figure 35.2.3–1 will not refer to an axis parallel to the global y-axis for general rotations of the reference node but will refer to an axis that rotates with the structure. Rotation of the constraint directions is not affected by the selection of the constrained degrees of freedom. # 35.3 Surface-based constraints • “Mesh tie constraints,” Section 35.3.1 • “Coupling constraints,” Section 35.3.2 • “Shell-to-solid coupling,” Section 35.3.3 • “Mesh-independent fasteners,” Section 35.3.4