ABA理论手册JOINTC单元方程

1、Abaqus Theory Manual   3.9.6 Flexible joint elementProduct: Abaqus/Standard  The JOINTC elements in Abaqus/Standard provide for flexible joints between two nodes. This section defines the kinematic variables used in these elements.KinematicsA JOINTC element consists of two nodes,

2、 referred to here as nodes 1 and 2. Each node has six degrees of freedom: displacements and rotations . A local orientation is defined for the element by the user. In a large-displacement analysis that local system rotates with the first node of the element. Figure 3.9.61 JOINTC geometry.W

3、e define the local system by its unit, orthogonal base vectors, , for . Then at any time in the analysis where is the rotation matrix defined by the rotation at the first node of the element. The relative displacements in the element are then with first variations where is a linearized rotation fiel

4、d (see “Rotation variables,” Section 1.3.1), and second variations The relative rotation about the local 3-axis is defined as with and defined by cyclic permutation of the local direction indices. These rotation measures define only relative angular rotations for small relative rotations. They are s

5、imple to compute, increase monotonically for relative rotations up to 180°, and are taken as suitable for use in the elements for these reasons.The first variation of is and its second variation is The relative translational velocities in the element are taken as and the relative angular veloci

6、ty about the local 3-axis is taken as Virtual workThe virtual work contribution of the element is We assume that the behavior of the joint is defined by The contribution to the operator matrix for the Newton solution is where is defined by the dynamic time integration operator. Reference· “Flex

7、ible joint elements,” Section 31.3 of the Abaqus Analysis User's Manual  Abaqus Theory Manual   3.9.6 Flexible joint elementProduct: Abaqus/Standard  The JOINTC elements in Abaqus/Standard provide for flexible joints between two nodes. This section defines the kinematic

8、variables used in these elements.KinematicsA JOINTC element consists of two nodes, referred to here as nodes 1 and 2. Each node has six degrees of freedom: displacements and rotations . A local orientation is defined for the element by the user. In a large-displacement analysis that local

9、system rotates with the first node of the element. Figure 3.9.61 JOINTC geometry.We define the local system by its unit, orthogonal base vectors, , for . Then at any time in the analysis where is the rotation matrix defined by the rotation at the first node of the element. The relative displacements

10、 in the element are then with first variations where is a linearized rotation field (see “Rotation variables,” Section 1.3.1), and second variations The relative rotation about the local 3-axis is defined as with and defined by cyclic permutation of the local direction indices. These rotation measur

11、es define only relative angular rotations for small relative rotations. They are simple to compute, increase monotonically for relative rotations up to 180°, and are taken as suitable for use in the elements for these reasons.The first variation of is and its second variation is The relative translational velocities in the element are taken as and the relative angular velocity about the local 3-axis is taken as Virtual workThe virtual work contribution of the element is We assume that the behavior of the joint is defined by The contribution to the operator matrix