To improve the accuracy of displacement discontinuity method and enhance its adaptivity, a general-purpose 3D displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering problems where discontinuous surfaces such as cracks are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity values, respectively. Both of them belong to discontinuous elements, in which the geometry shape functions are different from the interpolation shape functions. The new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains hypersingular integrals which can be evaluated in the sense of Hadamard principal value. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Various numerical examples including stress intensity factor calculation are given to validate the accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the present isoparametric displacement discontinuity elements show better accuracy.

为了提高位移不连续性方法的精度并增强其适应性，开发了一种同时具有线性和二次等参数单元的通用3D位移不连续性方法，用于对涉及裂缝等不连续表面的工程问题进行建模。线性和二次等参数元素分别具有位移不连续值的线性和二次分布。两者都属于不连续单元，其几何形函数与插值形函数不同。针对任意边界形状的位移不连续问题，给出了基于边界积分函数的新通用公式。该公式包含超奇异积分，可以在哈达玛主值的意义上进行评估。应用径向积分技术以足够高的精度执行这些奇异积分。给出了包括应力强度因子计算在内的各种数值例子来验证所提出方法的准确性。与常位移间断元相比，等参位移间断元表现出更好的精度。