Chapter 19 Using Abaqus with Python to Perform QSMA on the TMD Structure Brennan Bahr, Drithi Shetty, and Matthew S. Allen Abstrac t 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. Keyword s Friction · Geometric Nonlinearity · Reduced-order modeling · Contact · Hysteresis 19.1 Introduction Thin panels are commonly used in the design of lightweight, high-speed structures that are assembled together using mechanical fasteners. These panels exhibit nonlinear behavior due to bending-stretching coupling at large deformations [1, 2]. Additionally, friction at the interfaces that are fastened together results in energy dissipation which has a nonlinear effect on the system dynamics [3]. The industry standard is often to make linear approximations to create a computationally efficient finite element model. Such simplifications lead to conservative designs that need to be iterated on, resulting in greater cost of prototyping and dynamic testing. However, simulating the dynamic response of a high-fidelity nonlinear finite element model can be highly computationally expensive, with the cost increasing with complexity [4]. Therefore, reducedorder modeling approaches have been developed as a more efficient alternative [5, 6]. One such approach that has been gaining traction in the structural dynamics community is the method of quasi-static modal analysis [7, 8], or QSMA. In this method, the nonlinear FE model under consideration is statically excited in the shape of the mode of interest. The corresponding displacement can then be calculated using any finite element package. This is done over a range of load amplitudes to obtain the force-displacement backbone curve. The results can then be used to quantify the modal dynamic response of the structure over the amplitude range of interest, typically by estimating the B. Bahr ( ) . · M. S. Allen Department of Mechanical Engineering, Brigham Young University, Provo, UT, USA e-mail: matt.allen@byu.edu D. Shetty Department of Mechanical Engineering, UW-Madison, Madison, WI, USA e-mail: ddshetty@wisc.edu © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1 , Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_19 137
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