Isogeometric analysis for compound B-spline surfaces

• Directly utilizes compound surface models for isogeometric analysis.
• An integration scheme which avoids unnecessary local refinements.
• Exact displacement continuity along entire intersection curves.

In this work, an isogeometric analysis method for compound B-spline surfaces is proposed. The main advantage of the proposed method is that it directly utilizes the compound CAD surface model generated with surface Boolean operations in CAD systems, to achieve the analysis without additional efforts such as representing the CAD model with multiple tensor-product patches. For this, an integration scheme for trimmed elements is presented first, which can well handle the geometric complexities of cells within a trimmed element. Then, based on B-spline representations of the curves on surfaces, the displacement continuity requirement along an intersection curve is realized by the degree-of-freedom (DOF) coupling of the intersected surfaces, in which the DOF coupling constraint is enforced by minimizing the augmented potential energy with Lagrange multiplier. The stationarity of the augmented potential energy yields the equilibrium equations for the displacements of the compound surfaces. The validity of the proposed integration scheme is demonstrated with the convergence study on the problem of a hole within an infinite plate, and the effectiveness of the proposed isogeometric analysis method is illustrated with an elaborated 3D compound surface shell structure constructed by Boolean combination of several surfaces.