Joining of components of complex structures for improved dynamic response

The goal of this work is to provide a method for choosing joining (e.g., bolt) locations for attaching structural reinforcements onto complex structures. The joining locations affect structural performance criteria such as the frequency response and the static compliance of the modified structure. One approach to finding improved/optimal joining locations is to place the joints such that the total amount of energy input into the structure (from external forces) is lowered/minimized, thus ensuring that the performance of the structure is least affected by the structural modifications. However, such an approach does not account for the stresses in the joints. Therefore, in this work, the amount of strain energy concentrated in the joints is also considered. The cost function for this optimization problem is then composed of two energies. These energies are different for the undamped and damped cases. Herein, the focus is on the (more realistic) damped case. The cost function is minimized by a modified optimality criteria method. This process is time consuming because it requires the calculation of sensitivities of the joint strain energy, which in turn requires the calculation of the displacements of all candidate joint locations by using the system-level mass and stiffness matrices and force vector (at each frequency in the range of interest). To address this issue, a series of complex algebraic manipulations and approximations are used to significantly reduce the computational cost. In addition, for the case where structural and geometrical variations are necessary, parametric reduced-order models are used to compute the cost function with further significant gains in computational speed. Numerical results for improved/optimal joining are presented for representative complex structures with structural variabilities.