等几何分析直接采用非均匀有理B样条等计算机样条函数作为基函数，当基函数阶次大于等于2时，存在控制点与单元节点不重合且基函数支撑域跨过多个单元的情况，导致等几何分析中难以精确施加局部固定约束。针对这一问题，该文使用阶跃函数修正等几何分析的位移插值函数。该阶跃函数在局部位移固定约束区域的值为0，在其余区域的值为1，从而强制固定约束区域的位移值为0，其余区域位移插值函数还原为原形式。为减小阶跃函数对分析域的影响范围，将其阶跃区间设置成相对较小。同时，采用层次样条局部细分技术对阶跃区间内的单元进行局部细分，使细分后单元的高斯点落入阶跃函数的上升区间，进而对刚度矩阵产生作用。此外，单元局部细分后，局部约束区域周边通常会产生较大应变，从而有效提高了求解精确性。将上述方法与解析解、有限元分析结果进行对比，发现计算结果与解析解吻合。在不同的局部固定区域形状、面积及位置下，使用单元数较少的有限元粗网格及单元数较多的有限元细网格进行算例分析，发现该文方法得到的位移值、应力值更接近细网格有限元分析结果，说明该文方法能以较少的单元数达到有限元分析的求解精度，具有较好的精确性、灵活性与可靠性。

Isogeometric analysis uses computer splines such as non-uniform rational B-splines as the basis functions. When the order of the basis function is 2 or greater, the control points do not coincide with the element nodes and the support domain of the basis function spans multiple elements, which makes it difficult to impose local fixed constraints precisely in isogeometric analysis. To solve this problem, this paper uses a step function to modify the displacement interpolation function of isogeometric analysis. The step function takes a value of 0 in the locally fixed constraint region and 1 in the other region, so that the displacement value in the fixed constraint region is forced to be 0, and the displacement interpolation function in other region is revert to the original form. In order to minimize the influence of step function on the analysis domain, the rising interval of the step function is set to be small. Meanwhile, the hierarchical spline is used to subdivide the elements in the rising interval locally, therefore, the Gaussian points of the subdivided elements fall into the rising interval of the step function as well as the step function has an effect on the stiffness matrix. In addition, the element subdivision also effectively improves the solution accuracy in the local constraint region where large strains are present. Finally, the method mentioned above is compared with analytical solution and the finite element method to verify its accuracy, flexibility and reliability, finding that the results of calculation coincide with the analytical solution. Finally, by considering the situations with different fixed constrains that vary in shape, area and location., the finite element method with coarse mesh and fine mesh are used to calculate the examples, finding that the displacement and stress obtained by the proposed method are closer to those obtained by the fine mesh finite element method, which illustrates that the solution accuracy can be achieved with fewer elements; and that the proposed method is of good accuracy, flexibility and reliability.