We present an adjoint sensitivity method for hybrid discrete—continuous systems, extending previously published forward sensitivity methods (FSA). We treat ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) of index up to two (Hessenberg) and provide sufficient solvability conditions for consistent initialization and state transfer at mode switching points, for both the sensitivity and adjoint systems. Furthermore, we extend the analysis to so-called hybrid systems with memory where the dynamics of any given mode depend explicitly on the states at the last mode transition point. We present and discuss several numerical examples, including a computational mechanics problem based on the so-called exponential model (EM) constitutive material law for steel reinforcement under cyclic loading.
Sensitivity Analysis for Hybrid Systems and Systems With Memory
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 17, 2019; final manuscript received May 30, 2019; published online July 15, 2019. Assoc. Editor: Zdravko Terze.
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Serban, R., and Recuero, A. (July 15, 2019). "Sensitivity Analysis for Hybrid Systems and Systems With Memory." ASME. J. Comput. Nonlinear Dynam. September 2019; 14(9): 091006. doi: https://doi.org/10.1115/1.4044028
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