Formulations of an extra-degree-of-freedom (DOF) free extended isogeometric analysis (IGA) are presented in this study. The idea is achieved by reconstruction of the coefficients through a mesh-free-based local approximation, based on the framework of a generalized finite-element method. The enrichment functions are embedded in the mesh-free basis implicitly, resulting in an identical number of DOFs. Moreover, the system condition number is of the same level between the enriched IGA and non-enriched version. The approach to handling the blending issues is discussed. Numerical examples with a solution containing sharp features/singularities are designed and studied in terms of accuracy and convergence.

本研究介绍了额外自由度 (DOF) 自由扩展等几何分析 (IGA) 的公式。该想法是通过基于广义有限元方法框架的基于无网格的局部近似重建系数来实现的。富集函数隐式地嵌入在无网格基础中，从而产生相同数量的自由度。此外，丰富的IGA和非丰富的版本之间的系统条件数处于同一级别。讨论了处理混合问题的方法。在准确性和收敛性方面设计和研究了具有包含尖锐特征/奇异点的解决方案的数值示例。