ANSYS多点约束MPC个人总结

1、什么是MPC

    MPC定义的是一种节点自由度的耦合关系，即以一个节点的某几个自由度为标准值，然后另其他指定的节点的某几个自由度与这个标准值建立某种关系。多点约束常用于表征一些特定的物理现象，比如刚性连接、铰接、滑动等，多点约束也可以用于不相容单元之间的载荷传递。

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2、使用范围

MPC建立的是多点约束关系，包括刚性约束与柔性约束两种。从某种意义上说，建立约束即建立两个或多个节点之间的联系，因而也可以将MPC约束说成MPC单元。如RBAR、REB1、REB2建立的是刚性单元，这些单元局部刚度是无限大的；而RBE3、RSPLIBE单元则是柔性单元，其只是建立了不同节点的力与力矩的分配关系，也称之为插值单元。其局部刚度为零。不会对系统刚度产生影响。

1. 描述非常刚硬的结构单元。如果结构中存在两个或两个以上的刚度相差很大的部件时，刚硬结构在分析过程中，一方面起载荷传递作用，另一方面也发生部门变形。但其变形非常小，和柔软结构相比，它是‘刚性’的。这种情况下，对刚硬结构的描述尤为重要，如果用大刚度的弹性单元来模拟刚性结构，会造成病态解。原因是， 刚度矩阵中对角系数差别太大，引起矩阵病态。为解决本问题，应用适当的约束方程来替代刚硬的弹性单元，来创建更为合理的有限元模型。
2. 在不同类型的单元间传递载荷。如在有限元模型中，包含三维实体单元和壳单元，求解时会出现 “刚度矩阵奇异”的错误。原因是实体单元和壳体单元是不相容单元，自由度不匹配。若不采取特殊处理，则无法将壳单元上的力偶传递到实体单元上。为了消除这种奇异，必须建立一种连接，作用是在实体中建立一个耦合，以承受壳体力偶。
3. 任意方向的约束。当某节点可以沿着不平行于坐标轴的某个边界运动时，就需要定义一个约束方程，这个方程反映垂直于此边界的运动的约束。
4. 刚性连杆。

These surface-based constraints can be used in the following applications:

1. To apply loads and boundary conditions to the pilot node (such as torque load or drill rotation). Example: a bolt head submitted to a torque force using a force-distributed constraint.
2. To model rigid bodies. Example: rigid body definition in multi-body dynamics.
3. To model rigid end conditions. Example: using a rigid surface constraint to model a rigid end plate or rigid plane section of 3-D solid elements.
4. To model interactions with other joints. Example: two flexible parts linked by a hinge. This can be modeled by two force-distributed constraint definitions whose pilot nodes are connected by a revolute joint element.
5. To define transitions between solid and structure elements. Example: a beam element connected to a solid element face.

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3、数学基础

小位移理论

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4、力学原理

• 力分布（柔性约束）RBE3

（1）将参考节点载荷（力与力矩）等效移至节点围成面域的中心节点CG，生成新的力与力矩

Force-distributed constraint - In this type of constraint, forces or displacements applied on the pilot node are distributed to contact nodes (in an average sense) through shape functions (see Figure 10.6: Force-Distributed Constraint), similar to a constraint defined by the RBE3 command.       

    

（2）将CG节点的力与力矩按照响应的权值，分配到各主节点上

  

• 刚性绑定（CERIG） 所有节点自由度（6个）绑定

Rigid surface constraint - In this type of constraint, the contact nodes are constrained to the rigid body motion defined by the pilot node (see Figure 10.5: Rigid Surface Constraint), similar to a constraint defined by the CERIG command.

  

• 耦合约束（CP） 某几个节点自由度绑定

Coupling constraint - In this type of constraint, the degrees of freedom of contact nodes are constrained to have the same solution as the degrees of freedom of the pilot node (see Figure 10.7: Coupling Constraint), similar to a constraint defined by the CP command.

Coupling Constraint, the pilot node's x-direction has been rotated by 45 degrees. Only UX is included in the coupling constraint, so UY on the contact nodes are left free. The resulting deformation shows that UX (rotated 45 degrees from global x) is constant on the contact nodes, but UY is nonuniform.

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5、APDL设置

You can specify the surface-based constraint in a local coordinate system. For the rigid surface constraint, rotate the contact nodes into a local coordinate system. For the force-distributed constraint and the coupling constraint, rotate the pilot node into a local coordinate system.

Note:  If all degrees of freedom are included in the constraint equations, there will be no difference between the KEYOPT(12) = 5 and KEYOPT(12) = 6 settings.

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6、个人总结

力分布式约束：不对pilot节点和contact节点自由度进行约束，根据力的平衡条件，将施加在pilot节点的载荷传递到contact节点，重新分布。

刚性约束：pilot节点和contact节点所有自由度进行约束，所有节点位移相同，只发生刚性位移，contact各节点不发生位置的相对改变。

耦合约束：与刚性约束相比，没有对所有自由度进行约束，只约束某个或多个自由度。