The gap between finite element analysis and computer-aided design derives the development of isogeometric analysis(IGA),which uses the same representation in the geometry and the analysis.However,the parameterization ...The gap between finite element analysis and computer-aided design derives the development of isogeometric analysis(IGA),which uses the same representation in the geometry and the analysis.However,the parameterization in IGA is non-trivial.Weighted extended B-splines(WEB)method replaces grid generation and parameterization with weight function construction(R-function or distance function).By using implicit spline representation,isogeometric analysis on implicit domains(IGAID)adopts the merits of the“isoparametric”in IGA and“weight function generation”in WEB.But the theoretical properties have not been fully studied yet.In this paper,we study the theoretical aspects of IGAID using tensor-product B-splines.Both the approximation and stability properties of IGAID are considered.By setting appropriate constraints on the weight function,we can derive the optimal approximation order and stability.Numerical examples show the effectiveness of the approach and validate the theoretical results.展开更多
基金Project supported by National Natural Science Fund Project(51205432)National Science and Technology Suppor tPlan(2012BAH32F01)Chongqing Science and Technology Research Projects(cstc2012gg-yyjsB0216)
文摘The gap between finite element analysis and computer-aided design derives the development of isogeometric analysis(IGA),which uses the same representation in the geometry and the analysis.However,the parameterization in IGA is non-trivial.Weighted extended B-splines(WEB)method replaces grid generation and parameterization with weight function construction(R-function or distance function).By using implicit spline representation,isogeometric analysis on implicit domains(IGAID)adopts the merits of the“isoparametric”in IGA and“weight function generation”in WEB.But the theoretical properties have not been fully studied yet.In this paper,we study the theoretical aspects of IGAID using tensor-product B-splines.Both the approximation and stability properties of IGAID are considered.By setting appropriate constraints on the weight function,we can derive the optimal approximation order and stability.Numerical examples show the effectiveness of the approach and validate the theoretical results.
