ADAPTIVE ANALYSIS USING ISOPARAMETRIC AND ISOGEOMETRIC ELEMENTS: APPLICATION TOWARDS TOPOLOGY OPTIMIZATION, FRACTURE, AND MULTI-PHYSICS PROBLEMS

Abstract

Isogeometric analysis (IGA) is an extension of the finite element analysis (FEM), which was developed to use a single mesh for geometric design and analysis; this, in theory, would accelerate the design process as the iterative design loop would benefit from the unified geometric description. IGA is based on spline description of the mesh, and, from the initial days of Non-Uniform Rational B-Splines (NURBS), researchers have explored many different spline technologies, such as T-splines, HB-splines, R-splines, and PHT-Splines. In this thesis, the problem of topology optimization(TO) and phase field fracture(PFF) is solved adaptively with FEA and IGA. In the process, a new tool is developed to realize the aim of IGA to have a unified package for design and analysis. NURBS-based plane-stress, plane-strain, plate, and shell elements are designed. The capabilities of the package are further extended to multi-patch geometries with support for adaptive meshing based on PHT-spline technology. The practical application of the developed approach is first demonstrated with isogeometric shape optimization for maximizing solar gains from a shell roof. Aspects concerning computational expense and accuracy of the finite element methods are investigated, and adaptive algorithms are proposed to achieve the desired accuracy with a reduced size of the analysis model. The developed adaptive algorithms are tested with phase-field fracture models to present the applicability of the method in a wider variety of problems. Then the adaptive algorithms are ported to solve the problem of TO. A state-ofthe- art compact code is developed to carry out large-scale high-performance computations to solve the problem of TO with FEM. The developed algorithms are then ported to adaptive isogeometric topology optimization using PHT splines. In the context of industrial applications, the developed tools are utilized to solve largescale engineering problems with a high-performance computing infrastructure that supports parallelization of up to 1000’s of CPU cores.