Polynomial stress functions of anisotropic plane problems and their applications in hybrid finite elements

@article{Zhao2012PolynomialSF,
  title={Polynomial stress functions of anisotropic plane problems and their applications in hybrid finite elements},
  author={Ying-tao Zhao and Min-zhong Wang and Yi Chen and Yu Su},
  journal={Acta Mechanica},
  year={2012},
  volume={223},
  pages={493-503}
}
In this paper, systematic approaches to determine the polynomial stress functions for anisotropic plane problems are presented based on the Lekhnitskii’s theory of anisotropic elasticity. It is demonstrated that, for plane problems, there are at most four independent polynomials for arbitrary n-th order homogeneous polynomial stress functions: three independent polynomials for n equal to two and four for n greater than or equal to three. General expressions for such polynomial stress functions… CONTINUE READING