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.

A contact description for continuum beams with deformable arbitrary cross-section

“…Remark 3. The normal projection (37) is performed to assure that the vector field , ( , ) represents the contact points candidate in terms of the deformation-dependent coordinate parameter ( ).…”

“…Within the finite element analysis with ANCF elements, there have been a few attempts made to go beyond the standard cross-sections, such as rectangular and circular forms. Nonetheless, they intend to capture only a local deviation from common cases [37,38] and therefore, they are not suitable for addressing a sophisticated cross-sectional areas.…”

Research status and prospect of plate elements in absolute nodal coordinate formulation

“…For the problem of variable thickness, firstly, Abbas and Rui et al proposed a variable-thickness quadrilateral plate element 48 based on the fully parameterized element, which is suitable for regions where the thickness does not vary greatly. Later, He et al 94 proposed a modeling method for the local features in elements, which can be used to study the mechanical effects of protruding features on large plates, 95 which has been applied to the study of the effect of tire treads. 96 In another research direction, when the sheet-like structure is continuously thinned in thickness, it can be converted to a membrane structure.…”

“…Later, He et al . 94 proposed a modeling method for the local features in elements, which can be used to study the mechanical effects of protruding features on large plates, 95 which has been applied to the study of the effect of tire treads. 96…”