ADMOS 2023

On a direct procedure to construct a basis for the divergence free polynomial stress field space in 3D.

  • Maunder, Edward (Ramsay Maunder Associates)

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It appears to be common practice to form a divergence free (hyperstatic) basis for polynomial stress fields in a 3D continuum by exploiting Maxwell or Morera stress functions, or forming a basis for the complete space of stress fields and then applying a reduction process. An alternative simpler procedure is proposed which directly constructs a hyperstatic basis by considering a pair of complementary subspaces. This basis can be used in the formation of hybrid equilibrium elements or wherever equilibrated stress fields are required.