Nodal Stresses

Nodal Stresses

When you issue the command STREss,NODE,n1,n2,n3 at the Macro prompt, FEAP will compute a nodal projection of the Gauss point values and print them for nodes n1 to n2 in increments of n3 (default 1). The values printed consist for mechanical elements of the three principal stresses $\sigma _{I},\sigma _{II},\sigma _{III}$, then the max shear $(\sigma _{I}-\sigma _{III})/2$, then the pressure $p={\frac {1}{3}}\mathrm {tr} [\sigma ]$, then "J2" printed as ${\sqrt {\frac {3}{2}}}\Vert \mathbf {s} \Vert$ (the equivalent tensile stress, also known as the equivalent Mises stress, note $\mathbf {s}$ is the deviatoric stress tensor), and finally "J3" printed as ${\sqrt[{3}]{{\frac {1}{3}}[(\sigma _{I}-p)^{3}+(\sigma _{II}-p)^{3}+(\sigma _{III}-p)^{3}]}}$.

This is then followed by the six components of the stress tensor $\sigma _{11},\sigma _{22},\sigma _{33},\sigma _{12},\sigma _{23},\sigma _{31}$ and the six components of the strain tensor $\varepsilon _{11},\varepsilon _{22},\varepsilon _{33},\varepsilon _{12},\varepsilon _{23},\varepsilon _{31}$.

If the user has mapped element history variables for plotting using the HIST PLOT hvar hpnum card in the material definition, then these values will be printed, the enumeration matching hpnum.