Abstract:

The C1 interpolant was realized when embedding the non-Sibsonian 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.

Key words: non-Sibsonian natural neighbor coordinates; Bernstein-Bézier polynomial; C1 interpolant; couple stress elasticity theory