Two-dimensional radial integration displacement discontinuity method with high-order isoparametric elements

Abstract

To improve the accuracy of Displacement Discontinuity Method and enhance its adaptivity, a general-purpose two-dimensional displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering discontinuity problems where cracks or cavities are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity, respectively. Both of them belong to the discontinuous element type, in which the geometry shape functions are different from the interpolation shape functions. A new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains singular and strongly singular integrals which can be evaluated in the sense of Cauchy principal value and Hadamard principal value, respectively. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Five numerical examples, most of which have analytic solutions, are given to illustrate the improved accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the numerical results by using the present isoparametric displacement discontinuity elements show better accuracy.