Analytical Sensitivity Analysis of Flexible Multibody Systems Composed by Rigid Bodies and Beams

EasyChair Preprint 13503

Abstract

Gradient methods are very versatile and popular in optimizing the dynamics of multibody problems; and one of its main ingredients is the computation of sensitivities. This requires the computation of the gradient of the funcional to be optimized respect the parameters and to apply the chain rule.  Sensitivity analysis of mechanisms exclusively composed by rigid bodies has been studied in many works of the literature. However, analysis dealing with flexible mechanisms are rarer. In this work we show the results of a sensitivity analysis of special systems, where the flexible parts are slender beams, that could be represented either by a nonlinear beam model or with solid elements.  The specific nonlinear beam model considered in this work is defined as a collection of n identical deformable 1D segments (only withstand tensile or compressive forces) with regular section moving in a three-dimensional Euclidean space.The axial response of the beam is represented by the deformation of the segments and is governed by an hyperelastic potential. The bending response is represented by the misalignment of consecutive trusses and is governed by another potential. The sum of both potentials is an approximation of the strain energy of the beam.The approach with solid elements will explore the possibilities of performing the analytical derivatives in the isoparametric formulation of linear tetrahedra and/or bilinear hexahedra defining a beam. In both cases (beam or solid elements), the relevant proposal of this work is the analytical deduction of the sen- sitivities associated with the deformable parts, that are expected to improve the efficiency and accuracy of the computations.   A simple and physically intuitive approach based on a finite-difference method is used for validating the preliminary sensitivity results Some simple numerical examples are presented showing the performance of the proposed formulation.

Keyphrases: beam, flexible multibody, sensitivity

@booklet{EasyChair:13503,
  author    = {Juan C. García Orden and Juan J. Arribas Montejo and Daniel Dopico Dopico and Felipe Gabaldón Castillo},
  title     = {Analytical Sensitivity Analysis of Flexible Multibody Systems Composed by Rigid Bodies and Beams},
  howpublished = {EasyChair Preprint 13503},
  year      = {EasyChair, 2024}}