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Using MPC type QUADRATIC
MPC type QUADRATIC is a standard method for mesh refinement of second-order elements. This MPC type is available only in Abaqus/Standard.
This MPC constrains each degree of freedom at node p (where p is either p _ { 1 } or ) to be interpolated quadratically from the corresponding degrees of freedom at nodes a, b, and c (Figure 35.2.2–2). For coupled temperature-displacement, coupled thermal-electrical-structural, or pore pressure elements, only the displacement degrees of freedom are constrained.
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a b c p₁ p₂ p₁ a b c p₂ p₁ a
Figure 35.2.2–2 QUADRATIC type MPC.
Input data
Give the nodes p, a, b, and c as shown in Figure 35.2.2–2, where p is either p _ { 1 } or .
Input File Usage: *MPC
QUADRATIC, p, a, b, c
Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE.
Using MPC type BILINEAR
MPC type BILINEAR is a standard method for mesh refinement of first-order solid elements in three dimensions. This MPC type is available only in Abaqus/Standard.
This MPC constrains each degree of freedom at node p to be interpolated bilinearly from the corresponding degrees of freedom at nodes a, b, c, and d (Figure 35.2.2–3).
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a b c p d
Figure 35.2.2–3 BILINEAR type MPC.
Input data
Give the nodes p, a, b, c, and d as shown in Figure 35.2.2–3.
Input File Usage: *MPC
BILINEAR, p, a, b, c, d
Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE.
Using MPC type C BIQUAD
MPC type C BIQUAD is a standard method for mesh refinement of second-order solid elements in three dimensions. This MPC type is available only in Abaqus/Standard.
This MPC constrains each degree of freedom at node p to be interpolated by a constrained biquadratic from the corresponding degrees of freedom at the eight nodes a, b, c, d, e, f, g, and h (Figure 35.2.2–4). For coupled temperature-displacement, coupled thermal-electrical-structural, or pore pressure elements, only the displacement degrees of freedom are constrained.
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a b e f p h c g d
Figure 35.2.2–4 C BIQUAD type MPC.
Input data
Give the nodes p, a, b, c, d, e, f, g, and h as shown in Figure 35.2.2–4.
Input File Usage: *MPC
C BIQUAD, p, a, b, c, d, e, f, g, h
Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE.
Using MPC types P LINEAR and T LINEAR
The P LINEAR MPC can be used in conjunction with the QUADRATIC MPC for mesh refinement of second-order, fully coupled pore fluid flow-displacement elements.
The T LINEAR MPC can be used in conjunction with the QUADRATIC MPC for mesh refinement of second-order, fully coupled temperature-displacement and fully coupled thermal-electrical-structural elements.
These MPC types are available only in Abaqus/Standard.
These MPCs constrain the pore pressure (P LINEAR) or temperature (T LINEAR) degree of freedom at node p to be interpolated linearly from the degrees of freedom at nodes a and b (Figure 35.2.2–5).
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a p b
Figure 35.2.2–5 P LINEAR and T LINEAR MPCs.
Input data
Give the nodes p, a, and b as shown in Figure 35.2.2–5.
Input File Usage: Use the following option to define a P LINEAR MPC:
*MPC
P LINEAR, p, a, b
Use the following option to define a T LINEAR MPC:
*MPC
T LINEAR, p, a, b
Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE.
Using MPC types P BILINEAR and T BILINEAR
The P BILINEAR MPC can be used in conjunction with the C BIQUAD MPC for mesh refinement of pore fluid flow-displacement elements in three dimensions.
The T BILINEAR MPC can be used in conjunction with the C BIQUAD MPC for mesh refinement of fully coupled temperature-displacement and fully coupled thermal-electrical-structural elements in three dimensions.
These MPC types are available only in Abaqus/Standard.
These MPCs constrain the pore pressure (P LINEAR) or temperature (T LINEAR) at node p to be interpolated bilinearly from the pore pressure or temperature at nodes a, b, c, and d (Figure 35.2.2–6).
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a b p c d
Figure 35.2.2–6 P BILINEAR and T BILINEAR MPCs.
Input data
Give the nodes p, a, b, c, and d as shown in Figure 35.2.2–6.
Input File Usage: Use the following option to define a P BILINEAR MPC:
*MPC
P BILINEAR, p, a, b, c, d
Use the following option to define a T BILINEAR MPC:
*MPC
T BILINEAR, p, a, b, c, d
Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE.
MPCs for connections and joints
| BEAM | Provide a rigid beam between two nodes to constrain the displacement and rotation at the first node to the displacement and rotation at the second node, corresponding to the presence of a rigid beam between the two nodes. |
| CYCLSYM(S) | Constrain nodes to impose cyclic symmetry in a model. |
| ELBOW(S) | Constrain two nodes of ELBOW31 or ELBOW32 elements together, where the cross-sectional direction, a2, changes (see “Pipes and pipebends with deforming cross-sections: elbow elements,” Section 29.5.1). |
| LINK | Provide a pinned rigid link between two nodes to keep the distance between the two nodes constant. The displacements of the first node are modified to enforce this constraint. The rotations at the nodes, if they exist, are not involved in this constraint. |
| PIN | Provide a pinned joint between two nodes. This MPC makes the displacements equal but leaves the rotations, if they exist, independent of each other. |
| REVOLUTE(S) | Provide a revolute joint. |
| SLIDER | Keep a node on a straight line defined by two other nodes, but allow the possibility of moving along the line and allow the line to change length. |
| TIE | Make all active degrees of freedom equal at two nodes. |
| UNIVERSAL(S) | Provide a universal joint. |
| V LOCAL(S) | Allow the velocity at the constrained node to be expressed in terms of velocity components at the third node defined in a local, body axis system. These local velocity components can be constrained, thus providing prescribed velocity boundary conditions in a rotating, body axis system. |
See “Connectors: overview,” Section 31.1.1, for element-based versions of several of these MPCs for connections and joints.
Using MPC type BEAM
MPC type BEAM provides a rigid beam between two nodes to constrain the displacement and rotation at the first node to the displacement and rotation at the second node, corresponding to the presence of a rigid beam between the two nodes.
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beam node a' shell node beam node a' shell node
Figure 35.2.2–7 BEAM type MPC.
Input data
Give the nodes a and b as shown in Figure 35.2.2–7.
Input File Usage:
*MPC
BEAM, a, b
Abaqus/CAE Usage: Use one of the following options:
Interaction module: Create Connector Section: select MPC as the Connection Category and Beam as the MPC Type
Interaction module: Create Constraint: MPC Constraint; select Beam as the MPC Type
Constraining a beam stiffener to a shell
The general method of using a beam as a stiffener on a shell is to define the beam and shell elements with separate nodes. These nodes can then be constrained to each other using BEAM type MPCs.
A more economical way, when applicable, is to use the same node for the beam node and the shell node and then define the offset of the center of the cross-section of the beam in the beam section data. Figure 35.2.2–8 shows a T-shaped stiffener attached to a shell, using the I-beam cross-section. This is done by setting l (see “Beam cross-section library,” Section 29.3.9) equal to the distance between the node and the underside of the lower flange and setting the thickness of the top flange to zero. This approach can be used with all beam elements that use TRAPEZOID, I, or ARBITRARY beam sections.
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node t₃ t₁ l b₁ ≠ 0. t₂ = 0. b₁
Figure 35.2.2–8 Stiffened shell.
Using MPC type CYCLSYM
MPC type CYCLSYM is used to enforce proper constraints on the radial faces bounding a segment of a cyclic symmetric structure (see Figure 35.2.2–9). This MPC type is available only in Abaqus/Standard.
MPC type CYCLSYM imposes the cyclic symmetry by equating radial, circumferential, and axial displacement components (and rotations, if active) at the two nodes (a and b). The symmetry axis can be defined by the original coordinates of two additional nodes (c and d) that do not need to be connected to any element in the structure. Scalar degrees of freedom (such as temperature) are made equal.
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original part intended to be analyzed possessing cyclic symmetry axis of cyclic symmetry a b c section actually modeled z y x d
Figure 35.2.2–9 MPC type CYCLSYM.
Input data
Give the nodes a, b, and (optionally) node c and/or d that define the axis of symmetry as shown in Figure 35.2.2–9. Node set names can be used instead of the nodes a and b. If neither c nor d is given, the global z-axis is taken to be the axis of cyclic symmetry. If only node c is given, the symmetry axis passes through c and is parallel to the global z-axis. Thus, node d is not needed in two-dimensional cases.
Input File Usage: *MPC
CYCLSYM, a, b, c, d
Abaqus/CAE Usage: Cyclic symmetry multi-point constraints are not supported in Abaqus/CAE.
Using MPC type ELBOW
MPC type ELBOW constrains two nodes of ELBOW31 or ELBOW32 elements together, where the cross-sectional direction, , changes (see “Pipes and pipebends with deforming cross-sections: elbow elements,” Section 29.5.1). This MPC type is available only in Abaqus/Standard.
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y a₂(0,1,0) a b x z a₂(0,0,1)
Figure 35.2.2–10 ELBOW type MPC.
Input data
Give the nodes a and b as shown in Figure 35.2.2–10.
Input File Usage: *MPC
ELBOW, a, b
Abaqus/CAE Usage: Use one of the following options:
Interaction module: Create Connector Section: select MPC as the Connection Category and Elbow as the MPC Type
Interaction module: Create Constraint: MPC Constraint; select Elbow as the MPC Type