Case study data of "Optimizing Fixture Layout for Compliant Part Assembly: A Kriging-based Metaheuristic"

The dataset consists of the following excel files:

1.==== Initial fixture layout.xlsx ====

The initial fixture layout has in total 80 fixtures ("N" locators) allocated on Part I, and 88 fixtures allocated on Part II. Column [Fixtures on Part I] indicates the node ID on Part I at which a fixture is allocated. Column [Fixture on Part II] is for the fixtures allocated on Part II. 

2.==== Part I, Coordinates of mesh nodes.xlsx ====

Column [Node ID] is the local ID of the nodes on Part I. 

Column [x][y][z] are the spatial coordinates of the nodes.

Part I has in total 1271 mesh nodes. Among them, 1131 are available for placing the "N" locators, while the rest of them are at the sharp edges where the "N" locators cannot be set. Column [Available for placing "N" locators?] indicates that whether the node is available for placing an "N" locator (1) or not (0).

Part I is fixed by two "2" locators at node 45 and node 67 to constrain the x-direction nodal displacement, and is fixed by one "1" locator at node 105 to constrain the y-direction nodal displacement. Column [x-direction nodal displacement is constrained?] and Column [y-direction nodal displacement is constrained?] indicate whether the x-direction and y-direction nodal displacement are constrained.

During the assembly, there are 31 nodes on Part I that are to be assembled with the nodes on Part II. The Column [Assembly Node on Part II ] indicates the node on Part II with which this node will be assembly, if a node is not at the assembly interface, then this value is 0.

3.==== Part I, Global Stiffness Matrix.xlsx ====

* Part I has in total 1271 mesh nodes, and each node has six degree of freedom (x,y,z,xy,xz,yz). Thus, the global stiffness matrix K of Part I is of size (1271×6)×(1271×6), i.e., 7626 by 7626.

The element K(i,j) represents the stiffness between the i-th DOF and the j-th DOF. For example, the element K(1,2) represents the stiffness between Node 1 DOF 1 (i.e., x-direction) and Node 1 DOF 2 (i.e., y-direction); the element K(7,2) is the stiffness between Node 2 DOF 1 (i.e., x-direction) to Node 1 DOF 2 (i.e., y-direction), and so on.  

The global stiffness matrix is sparse, so to save space, we store only the non-zero elements and their indices. Specifically, the "Row" and "Column" represent the indices, and the "Value" represents the non-zero element in the matrix. For example, "Row = 1, Column = 1, Value = 465225.65" indicates that K(1,1) = 465225.65; "Row = 835, Column = 1, Value = 223266.81" indicates that K(835,1) = 223266.81. All other elements not appearing in the table are zeros in the matrix.

4.==== Part I, Nodal force vector.xlsx ====

* Part I has in total 1271 mesh nodes, and each node has six degree of freedom (x,y,z,xy,xz,yz). Thus, the nodal force vector f of Part I is of size (1271×6)×1, i.e., 7626 by 1.

For example, the f(3) is the nodal force of Node 1 DOF 3 (i.e., z direction), and f(9) is the nodal force of Node 2 DOF 3 (i.e., z direction)

5.==== Part II, Coordinates of mesh nodes.xlsx ====

Column [Node ID] is the local ID of the nodes on Part II. 

Column [x][y][z] are the spatial coordinates of the nodes.

Part II has in total 1426 mesh nodes. Among them, 1276 are available for placing the "N" locators, while the rest of them are at the sharp edges where the "N" locators cannot be set. Column [Available for placing "N" locators?] indicates that whether the node is available for placing an "N" locator (1) or not (0).

Part I is fixed by two "2" locators at node 111 and node 146 to constrain the y-direction nodal displacement, and is fixed by one "1" locator at node 84 to constrain the x-direction nodal displacement. Column [x-direction nodal displacement is constrained?] and Column [y-direction nodal displacement is constrained?] indicate whether the x-direction and y-direction nodal displacement are constrained.

During the assembly, there are 31 nodes on Part II that are to be assembled with the nodes on Part I. The Column [Assembly Node on Part I ] indicates the nodes on Part I with which this node will be assembly, if a node is not at the assembly interface, then this value is 0.

6.==== Part II, Global Stiffness Matrix.xlsx ====

* Part II has in total 1426 mesh nodes, and each node has six degree of freedom (x,y,z,xy,xz,yz). Thus, the global stiffness matrix of Part II is of size (1426×6)×(1426×6), i.e., 8556 by 8556. 

The element K(i,j) represents the stiffness between the i-th DOF and the j-th DOF. For example, the element K(1,2) represents the stiffness between Node 1 DOF 1 (i.e., x-direction) and Node 1 DOF 2 (i.e., y-direction); the element K(7,2) is the stiffness between Node 2 DOF 1 (i.e., x-direction) to Node 1 DOF 2 (i.e., y-direction), and so on.  

The global stiffness matrix is sparse, so to save space, we store only the non-zero elements and their indices. Specifically, the "Row" and "Column" represent the indices, and the "Value" represents the non-zero element in the matrix. For example, "Row = 1, Column = 1, Value = 469839.49" indicates that K(1,1) = 469839.49; "Row = 895, Column = 1, Value = -224798.91" indicates that K(835,1) = -224798.91. All other elements not appearing in the table are zeros in the matrix.

7.==== Part II, Nodal force vector.xlsx ====

* Part II has in total 1426 mesh nodes, and each node has six degree of freedom (x,y,z,xy,xz,yz). Thus, the nodal force vector of Part II is of size (1426×6)×1, i.e., 8556 by 1. 

For example, the f(3) is the nodal force of Node 1 DOF 3 (i.e., z direction), and f(9) is the nodal force of Node 2 DOF 3 (i.e., z direction)