Using Abaqus with Python to Perform QSMA on the TMD Structure

Automotive and aerospace structures are increasingly making use of thin panels to reduce weight while seeking to maintain durability and minimize noise transmission. These panels can exhibit geometrically nonlinear behavior due to bending-stretching coupling. Additionally, the use of mechanical fasteners results in nonlinear hysteretic behavior due to friction between the contact surfaces. The Tribomechadynamics benchmark structure, consisting of a thin panel clamped at the ends using bolted joints, was developed as part of a research challenge to test the ability of the nonlinear dynamics community to predict the dynamic behavior of a structure with both friction and geometric nonlinearity. Simulating the dynamic response of a high-fidelity nonlinear FE model is highly computationally expensive, even for such a small-scale structure. Therefore, quasi-static methods have been gaining popularity. This paper builds on our previous efforts to predict the amplitude-dependent frequency and damping of the first bending mode of this structure using quasi-static modal analysis (QSMA). A 3D FE model of the TMD structure was analyzed. The paper shows how Python, an open-source programming language, can be integrated with a commercial finite element package to perform QSMA. This minimizes file input/output compared to our previous approach and speeds up the process. We also investigate using the pseudo-inverse of the mode shape matrix, rather than the mass matrix times the mode shape matrix, to further accelerate the computations. The QSMA results are used to fit a reduced-order model to the structure, which comprises a single DOF implicit condensation and expansion (or SICE) ROM for geometric nonlinearity and an Iwan model to characterize friction nonlinearity. This model is able to reproduce the nonlinear modal behavior with high fidelity while significantly reducing the computational cost.