摘要：The ‘relaxed continuity’ hypothesis adopted on the self-regular traction-BIE is investigated for bidimensional problems. The self-regular traction-BIE, a fully regular equation, is derived from Somigliana stress identity, which contains hypersingular integrals. Due to the presence of hypersingular integrals the displacement field is required to achieve C1, Hölder continuity. This condition is not met by the use of standard conforming elements, based on C0 interpolation functions, which only provide a piecewise C1, continuity. Thus, a relaxed continuity hypothesis is adopted, allowing the displacement field to be C1, piecewise continuous at the vicinity of the source point. The self-regular traction-BIE makes use of the displacement tangential derivatives, which are not part of the original BIE. The tangential derivatives are obtained from the derivative of the element interpolation functions. Therefore, two possible sources of error, which are the discontinuity of the displacement gradients at inter-element nodes and the approximation of the displacement tangential derivatives, are introduced. In order to establish the dominant error, non-conforming elements are implemented since they satisfy the continuity requirement at each collocation point. Standard Gaussian integration scheme is applied in the evaluation of all integrals involved. Quadratic, cubic and quartic isoparametric boundary elements are employed. Some numerical results are presented comparing the accuracy of conforming and non-conforming elements on the self-regular traction-BIE and highlighting the dominant error.
其他摘要：The ‘relaxed continuity’ hypothesis adopted on the self-regular traction-BIE is investigated for bidimensional problems. The self-regular traction-BIE, a fully regular equation, is derived from Somigliana stress identity, which contains hypersingular integrals. Due to the presence of hypersingular integrals the displacement field is required to achieve C1, Hölder continuity. This condition is not met by the use of standard conforming elements, based on C0 interpolation functions, which only provide a piecewise C1, continuity. Thus, a relaxed continuity hypothesis is adopted, allowing the displacement field to be C1, piecewise continuous at the vicinity of the source point. The self-regular traction-BIE makes use of the displacement tangential derivatives, which are not part of the original BIE. The tangential derivatives are obtained from the derivative of the element interpolation functions. Therefore, two possible sources of error, which are the discontinuity of the displacement gradients at inter-element nodes and the approximation of the displacement tangential derivatives, are introduced. In order to establish the dominant error, non-conforming elements are implemented since they satisfy the continuity requirement at each collocation point. Standard Gaussian integration scheme is applied in the evaluation of all integrals involved. Quadratic, cubic and quartic isoparametric boundary elements are employed. Some numerical results are presented comparing the accuracy of conforming and non-conforming elements on the self-regular traction-BIE and highlighting the dominant error.
