该文基于相场法和自适应PHT(Polynomial splines over Hierarchical T-meshes)等几何薄壳理论,建立了自适应PHT等几何薄壳结构断裂问题相场模型。从能量和断裂力学的角度出发,推导了Kirchhoff-Love薄壳自适应等几何断裂相场模型的微分方...该文基于相场法和自适应PHT(Polynomial splines over Hierarchical T-meshes)等几何薄壳理论,建立了自适应PHT等几何薄壳结构断裂问题相场模型。从能量和断裂力学的角度出发,推导了Kirchhoff-Love薄壳自适应等几何断裂相场模型的微分方程,并采用自适应PHT样条基函数作为插值函数,对位移场和相场进行离散。一方面,Kirchhoff-Love薄壳理论不需要转动自由度,大大减小了计算规模;另一方面,PHT样条几何精确且满足Kirchhoff-Love薄壳理论C1的连续性,同时PHT样条不仅继承了NURBS样条的优点,还具有局部细分。最后,编写了相应程序,对比分析经典数值算例,讨论了该断裂相场模型的正确性和收敛性。展开更多
In this paper, we present a new surface reconstruction algorithm for polynomial spline surfaces of S(3, 3, 1, 1, T) over arbitrary hierarchical T-mesh T. The surface is piecewisely constructed by Coons surface interpo...In this paper, we present a new surface reconstruction algorithm for polynomial spline surfaces of S(3, 3, 1, 1, T) over arbitrary hierarchical T-mesh T. The surface is piecewisely constructed by Coons surface interpolation of the 16 parameters at four vertices on each rectangular cell of hierarchical T-mesh. For a given hierarchical T-mesh T and geometric information(the function values, the two first order partial derivatives and the mixed partial derivatives) at corresponding basis vertices of the hierarchical T-mesh, the surface is the same as the polynomial spline surface of S(3, 3, 1, 1, T), but our algorithm avoids the complexity of PHT-spline basis functions. Moreover, we give an adaptively refined surface algorithm for fitting scattered data points based on piecewise Coons surface construction. The numerical results show that the proposed adaptive algorithm is efficient in fitting scattered data points.展开更多
文摘该文基于相场法和自适应PHT(Polynomial splines over Hierarchical T-meshes)等几何薄壳理论,建立了自适应PHT等几何薄壳结构断裂问题相场模型。从能量和断裂力学的角度出发,推导了Kirchhoff-Love薄壳自适应等几何断裂相场模型的微分方程,并采用自适应PHT样条基函数作为插值函数,对位移场和相场进行离散。一方面,Kirchhoff-Love薄壳理论不需要转动自由度,大大减小了计算规模;另一方面,PHT样条几何精确且满足Kirchhoff-Love薄壳理论C1的连续性,同时PHT样条不仅继承了NURBS样条的优点,还具有局部细分。最后,编写了相应程序,对比分析经典数值算例,讨论了该断裂相场模型的正确性和收敛性。
基金Supported by the National Natural Science Foundation of China(Grant Nos.11572081 11871137)the Program for Liaoning Innovation Talents in University(Grant No.LCR2018001)
文摘In this paper, we present a new surface reconstruction algorithm for polynomial spline surfaces of S(3, 3, 1, 1, T) over arbitrary hierarchical T-mesh T. The surface is piecewisely constructed by Coons surface interpolation of the 16 parameters at four vertices on each rectangular cell of hierarchical T-mesh. For a given hierarchical T-mesh T and geometric information(the function values, the two first order partial derivatives and the mixed partial derivatives) at corresponding basis vertices of the hierarchical T-mesh, the surface is the same as the polynomial spline surface of S(3, 3, 1, 1, T), but our algorithm avoids the complexity of PHT-spline basis functions. Moreover, we give an adaptively refined surface algorithm for fitting scattered data points based on piecewise Coons surface construction. The numerical results show that the proposed adaptive algorithm is efficient in fitting scattered data points.
