System for analyzing fastener loads

A method of analyzing a fastener in a computer-based finite element model of a mechanically fastened multi-layer joint having a plurality of layers, each layer including a hole, and the plurality of layers being joined by the fastener extending through the holes, the joint finite element model including a nodal mesh which does not explicitly include the holes and further including a system stiffness matrix, the method allowing determination of stresses and strains existing in the fastener and in the plurality of layers at the joint, the method comprising the steps of:

• incorporating into the finite element model a line element representing the fastener, the line element having a plurality of nodes, with one node corresponding to each layer;
• calculating coefficients of a line element stiffness matrix for the model, the step of calculating the coefficients including the sub-steps of:
• calculating distributed forces and moments resulting from unit displacements imposed on each line element node while maintaining all other nodes of the line element fixed and applying boundary conditions;
• calculating concentrated unit forces and moments for each node, each concentrated unit force and moment having a value that corresponds to a work-averaged value of the calculated distributed force and moment for each node;
• and
• calculating the coefficients of the stiffness matrix by superimposing, on a node-by-node basis, the forces and moments required to produce the concentrated unit displacements and rotations and the reactions induced in the other nodes;
• incorporating the coefficients of the line element stiffness matrix into the system stiffness matrix;
• solving the joint finite element model for nodal displacements and forces at the fastener line element nodes, and
• calculating distributed through-the-thickness variation of bearing stresses and a stress field surrounding the hole of each layer based upon the nodal displacement and forces for each layer.

A storage medium encoded with machine-readable computer program code, the computer program code for directing a computer to perform the steps of:

• receiving a line element finite element model of a fastener for a multi-layer joint having a plurality of layers, each layer including a hole, and the plurality of layers being joined by the fastener extending through the holes, the finite element model including a node point for each layer of the multi-layer joint;
• and
• determining coefficients of a line element stiffness matrix for the model, the step of determining the coefficients including the sub-steps of:
• calculating distributed forces and moments resulting from unit displacements imposed on each line element node while maintaining remaining nodes of the line element fixed and applying boundary conditions;
• calculating concentrated unit forces and moments applied at each node, each unit force and moment having a value that corresponds to the calculated distributed force and moment at a particular node;
• and
• calculating the coefficients of the line element stiffness matrix based on ratios of the concentrated unit forces and moments and the unit displacements.