Analytical sensitivity analysis of dynamic problems with direct differentiation of generalized-α time integration

Wehrle, Erich; Gufler, Veit

doi:10.31224/osf.io/2mb6y

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…In addition to the sensitivity analysis of the equations of motion, the sensitivity analysis must be performed for the time integration method and the nonlinear solver [29]. A solution routine for flexible multibody dynamics, including the sensitivity analysis with generalized-α time integration and Baumgarte stabilization with a numerical computation of the partial derivatives, is shown in [9,11,30].…”

Section: Derivatives Of the Equations Of Motion Wrt The Design Variablesmentioning

confidence: 99%

“…The nonlinear solver for time integration methods that solve for accelerations as shown in [11,29,30] requires the acceleration Jacobian given by the total derivative of the equations of motion w.r.t. the generalized accelerations.…”

Section: Derivatives Of the Equations Of Motion Wrt Accelerationmentioning

confidence: 99%

“…The derivatives of the equations of motion have been performed in § 3 where the derivatives of the system parameters appear. In previous works [9,10,29,30], the derivatives of the system parameters have been computed numerically for a semi-analytical approach. To further increase the efficiency of the method and the precision of the results, the analytical derivatives of the system parameters will be introduced in the following.…”

Section: Partial Derivatives Of the System Parametersmentioning

confidence: 99%

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Analytical derivatives of flexible multibody dynamics with the floating frame of reference formulation

2022

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In this paper, the analytical derivatives of flexible multibody dynamics with the floating frame of reference formulation are derived in a new way using the invariants and their sensitivities. This enables the decoupling of the sensitivity analysis of flexible multibody dynamics from the finite-element solver and guarantees high accuracy and efficiency of the sensitivity computations. The invariants are shown with both consistent and lumped mass approaches. The latter allows generality towards the formulation of a finite-element type, including beams, shells, and solids. The expressions are fully derived with lumped masses, showing for the first time the compensation term of inertia due to the non-consideration of the mass distribution with this approach. It is then shown that the expressions of the system parameters in the lumped case with the newly introduced inertia compensation term correspond to the general case, and, therefore, the derived approach and equations are of general nature. Crucial for the decoupling of the sensitivity analysis are the analytical derivatives of the system parameters that contain the derivatives of the invariants and whose analytical expressions are derived and provided here for the first time. The partial derivatives arise in the sensitivity analysis with both the direct differentiation method and the adjoint variable method, and the former is shown here. In addition, the partial derivatives arise in the Jacobian matrix of the nonlinear solver for the transient solution of flexible multibody systems.

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