Chapter 3 A Deformed Geometry Synthesis Technique for Determining Stacking and Cryogenically Induced Preloads for the Space Launch System Joel Sills, Arya Majed, and Edwin Henkel Abstract The Space Launch System (SLS) stacking and Core Stage (CS) fueling induce significant preloads that contribute to the liftoff pad separation “twang”. To accurately capture this, an approach is required that can replicate the physics of all SLS physical stacking steps, CS cryogenic shrinkage, associated geometric nonlinearities, and the transient behavior and decay of the preloads with changing boundary conditions as the vehicle separates from the pad. The Deformed Geometry Synthesis (DGS) approach presented here satisfies the above requirements. DGS determines induced preloads by modeling components in their deformed geometry states and then enforcing compatibility by closing the resulting “deadbands”. DGS seamlessly integrates into the multibody modal synthesis framework and does not require the use of artificial external loads to enforce preloads or post-processing steps to remove their influence. Since DGS iterates to solve for the deformed state inclusive of geometric nonlinearities, running linearized parametrics to exercise different potential orientations of ball jointed struts that connect the CS to Boosters for cryo-shrinkage analyses is entirely avoided. Relative to the transient behavior and decay of stacking and cryo-induced preloads with SLS liftoff pad separation, this is an area of considerable interest to the SLS program. To capture this in the most accurate way possible, DGS algorithms are designed to work with Henkel-Mar nonlinear pad separation algorithms which operate on the separating longitudinal and lateral degrees of freedom (DoFs) between the vehicle and the pad. As the separating DoFs release, in whatever manner as dictated by the interface geometries, interface loads and interface flexibilities as well as the external loading on the vehicle, the subject preloads generate a complex twang/decay time-trace as dictated by the physics of the problem. This paper presents DGS numerical verification against the closed-form solution for Timoshenko’s 3 ball-jointed strut preload problem. This problem is then extended by the authors to the geometric nonlinear case where DGS is compared to the Newton-Raphson solution of the nonlinear equations. Next, DGS is utilized to solve the SLS stacking and cryogenic shrinkage coupled loads analyses. Finally, Henkel-Mar pad separation simulations are executed that isolate the impact of the induced preloads’ twang and decay characteristics. Keywords Space launch system · Deformed geometry synthesis · Henkel-Mar pad separation · Geometric nonlinear 3.1 Introduction A new approach for coupling deformed geometries and determining vehicle load indicators inclusive of prelaunch stacking and cryogenic induced preloads has been developed. This Deformed Geometry Synthesis (DGS) technique [1] is a specialized procedure in modal synthesis where components are coupled in their deformed geometry states by enforcing compatibility at the interfaces via a process of statically closing the resulting deadbands to lock-in the preloads. The procedure evokes a static version of the nonlinear deadband methodology first developed for the Space Shuttle Program (SSP). It has the advantage of being NASA verified and validated against test and utilized in the SSP nonlinear coupled loads analyses (CLAs) from 2005 until final flight in 2011. To accurately capture the SLS stacking and cryo-induced preloads, DGS replicates the physics of all SLS physical stacking steps, Core Stage (CS) cryogenic shrinkage, associated geometric nonlinearities (e.g., aft strut rotations – a set of 3 ball J. Sills ( ) NASA Engineering and Safety Center (NESC), Houston, TX, USA e-mail: joel.w.sills@nasa.gov A. Majed · E. Henkel Applied Structural Dynamics (ASD), Inc., Houston, TX, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_3 17
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