IGAODG-the IGA Discontinuous Galerkin Method On Overlapped Domains

By applying NURBS to describe both the geometric models and the discrete solutions,the Iso Geometric analysis(IGA)method eliminates the errors caused by the boundary approximation in the FEA processes,and reduces the time costs of the mesh generation and refinement in the CAD-FEA iteration process.Nowadays,IGA are widely researched.In order to carry out integrations on trimmed domains to support the Boolean operations,traditional IGA methods need to reparameterize the trimmed domains or to apply the iterative integration algorithms.These two methods will affect the integration precision and the computation efficiency,so that the theoretical barriers and the implementation complexities are introduced to the seamless CAD-FEA integration process,and further,the efficiency of designing complex products is affected.Focusing on the above-mentioned problems and starting with the Boolean union operation,this dissertation firstly presents an IGA method for Overlapped domains by applying the Discontinuous Galerkin concept(IGAODG).Its convergence properties are also worked out theoretically.Secondly,the IGAODG is researched in the following three aspects:1)the numerical extendibility of IGAODG,2)its application on trimmed patches,3)its enhancement to the IGA computation efficiency.Finally,the architecture of an IGAODG framework is investigated.The detailed contents and results are summarized as below.(1)The IGAODG method is presented.By comparing two possible schemes,The IGAODG method is created.This method is the superset of the traditional IGA discontinuous Galerkin method.When creating the matrix equations,the integrations are carried out on the non-trimmed patches,and no trimmed patches are involved in the integration process.(2)The convergence properties of the IGAODG are manifested.The concept and definition of the broken function space on overlapped domains are presented.With definition of this function space,the following spaces can be described uniformly: 1)the discontinuous spaces with different continuities between elements on a single-patched domain,2)the discontinuous spaces on matching or mismatching meshes for non-overlapped domains,and 3)the discontinuous function space on overlapped or nonoverlapped domains.Based on these works,the optimal convergence properties of IGAODG are manifested.This overlapped discrete function space extends the traditional function spaces of IGA,and it is possible to present new theoretic foundations to IGA.(3)The extension of IGAODG and the enhancement to the CAD-FEA iteration process are researched.This research includes three sub-issues.Firstly,the original IGAODG is extended with incomplete interior penalty Galerkin method(IIPG)and the convergence properties of this extension are investigated with multiple kinds of problems.Secondly,in the condition of avoiding integrations on trimmed patches,a numeric method to apply IGAODG on trimmed patches is presented.Thirdly,by reducing the Jacobian matrix related computations,an analysis scheme to enhance the IGA efficiency is researched.On the one hand,this research shows the extendibility of IGAODG from the view point of FEA,and on the other hand this research shows its ability of designing complex products from the view point of the CADFEA iteration process.(4)An IGAODG framework is implemented.The software architecture of an IGAODG framework is researched and discussed.Two characteristics are simultaneously supported by this architecture: 1)the CAD process and the FEA process are highly integrated,and 2)one framework can be used to solve multiple kinds of engineering problems.This dissertation systematically discussed the main issues of IGAODG,including the background,theories,discrete forms,convergence properties,applications and implementation technologies.The presented theories and technologies can be used to remove the integrations on trimmed domains,and to exert the seamless CAD-FEA integration of IGA to enhance the design efficiency and quality for complex products.