Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aid...Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aided Geom Design 29:63-76,2012;Scott et al.Comput Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending functions.We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.展开更多
Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric ana...Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.展开更多
The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-...The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-standard T-splines and give the proof for the semi-standard of bi-degree(1,d)and(d,1)T-splines.展开更多
基金This work was supported by the NSF of China(No.11031007,No.60903148)the Chinese Universities Scientific Fund,SRF for ROCS SE,the CAS Startup Scientific Research Foundation and NBRPC 2011CB302400.
文摘Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et al.Comput Aided Geom Design 29:63-76,2012;Scott et al.Comput Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending functions.We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.
文摘Analysis-suitable T-splines （AS T-splines） are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1-3]. The present paper provides some more iso-geometric analysis （IGA） oriented properties for AS T- splines and generalizes them to arbitrary topology AS T-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor- product domain. And then, we prove that the number of T-spline control points contribute each Bezier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with T-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable T-splines.
基金supported by the NSF of China(No.61872328)NKBR-PC(2011CB302400)+1 种基金SRF for ROCS SEthe Youth Innovation Promotion Association CAS.
文摘The present paper conjectures a topological condition which classifies a T-spline into standard,semi-standard and non-standard.We also provide the basic framework to prove the conjecture on the classification of semi-standard T-splines and give the proof for the semi-standard of bi-degree(1,d)and(d,1)T-splines.
