Robust multi-curve trimming IGA method for layerwise composite plates with arbitrary cutouts

Abstract

Isogeometric analysis (IGA) provides a promising method for analysis, design and optimization of constant or variable stiffness composite laminates with inevitable cutouts. In this paper, a robust multi-curve trimming IGA modelling framework for composite plates with arbitrary complex cutouts is developed. A novel searching algorithm is proposed and developed to address the core challenge of correctly and reliably determining whether a point is in the multi-curve trimmed region. This searching algorithm is based on the angle bisector vector of the tangent vectors of two trimming curves at their intersection point. Through a comprehensive analysis of different conditions, new trimming element decomposition rules are introduced to develop a precise numerical integration method for multi-curve trimmed elements. This proposed robust multi-curve trimming method overcomes some limitations of conventional trimming curves analysis, particularly in analyzing arbitrary complex cutouts. With this proposed robust multi-curve trimming algorithm, an IGA modelling framework based on the generalized layerwise plate theory for the free vibrational analysis of composite laminates with either straight or curvilinear fibers is presented. The novel, simple, and effective multi-curve trimming IGA approach, as demonstrated in numerical examples, allows for precise modeling of arbitrarily complex cutouts of constant or variable stiffness laminated composite plates, yielding accurate results with high efficiency.