C^1自然邻近迦辽金法在偶应力理论中的应用

The application of the C^1 natural neighbor Galerkin method in the couple-stress elasticity theory

以non-Sibsonian插值函数作为三次单纯形Bernstein-Bézier的基坐标,构建了C1自然邻近插值函数,该函数具有二次完备性以及对结点函数值和梯度值的插值特性等性质.将C1插值函数应用于Toupin-Mindlin偶应力弹性理论,由于C1形函数的插值特性,偶应力理论迦辽金法可以直接施加本质边界条件,克服了其它无网格法施加本质边界条件的困难.具体算例包括单剪问题和中心圆孔无限大板单轴拉伸问题,数值解与理论解吻合得较好,表明C1自然邻近迦辽金法能够用来分析偶应力理论问题.

The C1 interpolant was realized when embedding the nonSibsonian natural neighbor coordinate in the Bernstein-Bézier surface representation of a cubic simplex.It had quadratic completeness,interpolation to nodal function and nodal gradient values,and can be reduced to a cubic polynomial on the boundary of domain.The essential boundary conditions were directly imposed in a Galerkin scheme for the Toupin-Mindlin couple-stress theory because the C1 interpolant had the interpolation property for nodal functions and nodal gradient values.The simple shear problem and infinite plate with circular hole under uniaxial tension were analyzed.The numerical solutions agree well with the analytical solutions,which show that the C1 natural neighbor Galerkin method can analyze the couple-stress elasticity theory.