Shape optimization of a flexible beam with a local shape feature based on ANCF

Abstract

This paper proposes a shape optimization method of local shape features on a flexible beam modeled with the absolute nodal coordinate formulation (ANCF). A fully parameterized ANCF beam element is used to model the global geometry for flexible body dynamics analysis. The local shape feature of the ANCF element surfaces can be described by a nonuniform rational B-spline (NURBS) without the need for mesh refinement by changing the distribution of the integration points. A mapping between the ANCF element local coordinates and the NURBS localized geometric parameters is used for the consistent implementation of the overlapping methods. The selected shape parameters of the localized surface geometry are taken as the design variables for beam shape optimization, and the weighted summation of the compliance of the beam is taken as the objective to evaluate the influence of the dynamic response. Different weighting schemes are used to compare the effects of weighting. An example of an ANCF beam with a rib is given to validate our method. A two-stage shape optimization method based on SQP (Sequence quadratic program ) is run to reduce the compliance of the beam. Because few design variables are used to represent the local and global shapes of the beam geometry, our shape optimization method based on the localized surface geometry has a significantly reduced computational burden and improved optimization efficiency.

Keywords

• shape optimization
• local feature
• absolute nodal coordinate formulation(ancf)
• flexible beam
• two-stage optimization
• equivalent static load