Optimal Lightweight Engineering Design via a Three-Block Solver Scheme for Mechanical Analysis

Wehrle, Erich

doi:10.1007/978-3-031-50000-8_2

Cited by 2 publications

(2 citation statements)

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“…Overviews of design sensitivity analysis are provided by [2][3][4][5][6]. In transient problems, sensitivity analysis must be extended to time integration [7,8], which is handled here by introducing and deriving the equations for the direct differentiation of the generalized-α family of time integration.…”

Section: Introductionmentioning

confidence: 99%

“…Due to its nature, the adjoint variable method must be performed after the time integration of the primal analysis and integrated backwards in time. Thus, the adjoint variable method, in contrast to direct differentiation, needs dedicated solver routines to integrate backwards in time and cannot reuse primal forward time integration [7,8]. Furthermore, for nonlinear analysis, the system matrices must be stored or recalculated when integrating backwards in time.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-α Time Integration

Wehrle,

Gufler

2024

Machines

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In this paper, the direct differentiation of generalized-α time integration is derived, equations are introduced and results are shown. Although generalized-α time integration has found usage, the derivation and the resulting equations for the analytical sensitivity analysis via direct differentiation are missing. Thus, here, the sensitivity equations of generalized-α time integration via direct differentiation are provided. Results with generalized-α are compared with Newmark-β time integration and their sensitivities with numerical sensitivities via forward finite differencing in terms of accuracy and performance. An example is shown for each linear structural dynamics and flexible multibody dynamics.

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