Isogeometric analysis for solving discontinuous two-phase engineering problems with precise and explicit interface representation

Abstract

This paper presents a new computational method for solving two-phase engineering problems. The novelty of this approach lies in its ability to perform the analysis over the exact two-phase geometry. The geometry is defined by a spline-based representation and constructed based on the level-set method. The level-set-based geometry is mapped into a spline-based geometry using an untrimming technique that is newly developed in this paper. The spline-based representation is defined over unstructured meshes enabling precise representations of geometrically complex domains. An analysis-suitable mechanical model that accurately replicates the geometry is constructed and the governing equations are solved using the isogeometric analysis method. The interface between phases is explicitly represented by cubic B-spline curves, allowing for the evaluation of the solution field and various physical measures over its exact geometry. Additionally, algorithms that allow for changing the continuity of the solution field between the phases while precisely preserving the discontinuous two-phase domain are developed. Consistent analytical sensitivity analysis is formulated for generating the geometrical and mechanical models to allow for solving engineering problems with moving boundaries following the gradient-based approach. The proposed approach is tested for solving Poisson’s equation, linear elasticity, topology optimization, and two-phase flow problems. The results expose the capability of the proposed approach to solve two-phase engineering problems while accurately representing the interface.