Multiple Point Constraints (MPC) serve to define relationships between degrees of freedom across one or more nodes. While MPCs find application in various contexts, our focus in this text centers on their role in bolted connections, typically implemented through the Beam MPC type.
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.
Examples of Usage
To grasp the functioning of the MPC Type Beam, let’s delve into the study of a model featuring four distinct configurations for the MPC setup. The objective is to present a clear and intuitive demonstration of how this particular constraint type operates.
First Example – Two distributing couplings connected through a single MPC Type Beam
The initial model under examination is depicted in the image below.
The illustrated model showcases the connection of two lugs through the implementation of the MPC Type Beam, serving as a simplified representation of a bolted connection. This method proves advantageous when the primary goal is to establish a connection between two components without delving into a detailed stress analysis of the adjoining region. For scenarios where stress analysis is a focal point, it is recommended to model individual components such as bolts, nuts, and washers, define contact interactions, and apply bolt pretension. Detailed insights into modeling bolted connections like this are available in our dedicated blog post; you can access it by clicking here.
The MPC Type Beam is specifically defined between the reference nodes of the couplings (for more information on coupling constraints, refer to our blog post here). The upper node serves as the MPC Control Point, while the lower node functions as the MPC Slave node. In this instance, there is a singular MPC Slave node, but multiple slave nodes can be incorporated.
The connecting lugs are represented by shell elements with a thickness of 3.2 mm (1/8″). One of the lugs is immobilized through a boundary condition, fixing all degrees of freedom on the left edge. Meanwhile, the other lug undergoes a displacement of 15 mm in the positive X-axis direction, as indicated by the applied boundary condition on the right edge (refer to the coordinate system in the bottom left corner).
The material employed is a standard linear steel with a Young’s modulus of 200 GPa and a Poisson’s ratio of 0.3. The von-Mises stress contour plot is provided below:
A substantial displacement was intentionally applied to induce significant deformation in the components, facilitating a visual understanding of the MPC Type Beam’s operation. Consequently, the von-Mises stress levels are exceptionally high, surpassing typical steel yield strengths. It’s crucial to note that the focus here is not on stress analysis but rather on elucidating the functionality of the MPC Type Beam.
It’s noteworthy that this type of constraint emulates a rigid, non-deforming beam element with infinite stiffness. As a result, it induces rotations in the connected nodes and subsequently influences the surfaces to which the distributing couplings are attached. Additionally, the surfaces themselves undergo deformation owing to the nature of this distributing coupling.
Second example – Two kinematic couplings linked through a single MPC Type Beam
The sole distinction between the first and second examples lies in the utilization of kinematic couplings instead of distributing couplings. It is imperative to recall that kinematic couplings are inherently rigid, in contrast to the deformable nature of distributing couplings.
Referencing the von-Mises stress contour plot provided below:
A notable disparity arises in the behavior of the surfaces to which the kinematic couplings are affixed. In this scenario, these surfaces undergo a rigid body rotation without any deformation. It’s noteworthy that the plane of the couplings maintains its orientation perpendicular to the direction of the MPC Type Beam. Essentially, both the MPC and the kinematic couplings rotate together as a rigid body, demonstrating the distinctive characteristic of kinematic constraints.
Third example – One Kinematic Coupling and an MPC Type Beam with Multiple Slave Nodes
In the third example, a modification was introduced by retaining only one of the kinematic couplings and removing the other. All nodes previously associated with the surface of the deleted coupling were redefined as MPC slave nodes. Simultaneously, the MPC control point was specified as the reference node of the retained kinematic coupling.
Referencing the von-Mises stress contour plot provided below:
It’s noteworthy that the maximum von-Mises stress mirrors the value observed in the second example. This similarity arises from the analogous functioning of MPC Type Beam and Kinematic Couplings, which operate in comparable manners.
This modeling approach proves more efficient by eliminating one coupling. However, it diverges aesthetically from the second example, lacking the visual resemblance to a bolted connection (as per personal opinion). Despite the visual variance, the efficacy of the model is maintained, demonstrating the flexibility and efficiency of the MPC Type Beam in managing complex connections.
Fourth example – No couplings and MPC type Beam with multiple slave nodes
In the fourth example, we explore a configuration devoid of couplings, focusing exclusively on utilizing the MPC Type Beam with multiple slave nodes. This approach is designed to underscore the MPC Type Beam’s versatility in establishing connections without relying on additional coupling elements.
This modeling strategy proves to be the most effective when the goal is to maintain an entirely rigid system, akin to the second and third examples. The von-Mises stress contour plot for this configuration is provided below:
It’s noteworthy that the maximum von-Mises stress mirrors the values observed in the second and third examples, affirming that these three methods of modeling a completely rigid bolted connection yield identical results. This consistency underlines the robustness and reliability of the MPC Type Beam in achieving rigid connections, regardless of the specific configuration chosen.
Real-world Application: Evaluating Structural Stiffness in a Rotary Kiln Alignment System
Now, let’s delve into a practical illustration of employing the MPC Type Beam constraint. The image below unveils the intricate structure of a rotary kiln alignment system recently subjected to our analysis.
The primary objective of this scrutiny was to assess the overall structural stiffness—expressed as a Force vs Displacement Curve. The force was applied within the region highlighted by the red arrow, aligning with the arrow’s direction. This specific area denotes the crucial contact zone between the rotary kiln and the alignment system. The applied force, oriented horizontally, serves the purpose of preventing axial movement in the rotary kiln.
Across the entire structure, numerous bolted connections are present. Given that these weren’t the focal points of interest, we opted for a pragmatic approach. Two distributing couplings and one MPC Type Beam were strategically employed to model each bolted connection, mirroring the methodology showcased in our initial example.
It’s important to note that this simplification, involving the use of distributing couplings and the MPC, does not compromise the integrity of the desired outcome—the Force vs Displacement Curve. The resultant plot remains unaffected by this modeling simplification. The accompanying image vividly illustrates these streamlined connections.
Alternate Approaches Achieving Results Similar to MPC Type Beam
In addition to the MPC Type Beam, two alternative techniques yield comparable results:
- Kinematic Couplings: In lieu of exclusively relying on the MPC Type Beam, as demonstrated in the fourth example, an alternative is to employ a singular kinematic coupling. Moreover, the MPCs used in the first and second examples can be effectively replaced by a kinematic coupling comprising only two nodes.
- Connector Type Beam: Abaqus offers a variety of connectors, among which the Beam type operates analogously to the MPC Type Beam. This alternative connector type provides similar functionality and is equally adept at achieving the desired results.
Conclusion
In our exploration, the MPC Type Beam has proven to be a valuable tool for establishing rigid connections, especially in bolted assemblies. We started by understanding its fundamentals, showcasing its application in various scenarios.
The real-world application in assessing the structural stiffness of a rotary kiln alignment system highlighted its adaptability. Incorporating MPC Type Beam efficiently represented bolted connections, ensuring accurate assessments.
The MPC Type Beam offers a flexible approach, allowing engineers to choose techniques based on specific needs. Whether using it exclusively or in tandem with couplings, the consistent results affirm its reliability.
We also explored alternatives like kinematic couplings and Connector Type Beam, providing diverse options for achieving similar outcomes.
In essence, this type of constraint emerges as a valuable asset in structural analysis, offering efficiency without compromising accuracy. Its adaptability and consistent results make it a reliable tool for engineers seeking precise and streamlined modeling.
Explore additional details on MPC constraints by referring to the Abaqus Analysis User’s Manual.
