1. Reference problem#

1.1. Geometry#

_images/100011E400002EB700001E480BBD016A6C22E4FD.svg

1.2. Material properties#

\(E=200000\mathrm{MPa}\)

\(\nu =0.3\)

\(\nu =0.0\) makes it possible to avoid the variation in orthogonal curvature induced by the Poisson effect in plates, which causes a discrepancy between the theories of beams and plates, outside the average fiber.

1.3. Boundary conditions and loads#

  • force \({F}_{y}=-1\) (load 1) or torque \({C}_{z}=1\) (load 2)

  • defined or applied to the neutral fiber

  • embedding section \(x=0\)

  • continuity of translational movements on \(\mathrm{AB}\)

  • continuity of translational movements in \(C\)

  • equal rotation movements around \(z\) on \(\mathrm{C1}-\mathrm{C2}\)

  • for points \(M\) of the section (\(\mathrm{M1}\) \(\mathrm{M2}\) \(\mathrm{M4}\)) the translational displacements \(u(M)\) depend linearly on the rotational displacement \({\varphi }_{z}\) of the points \(P\) of \(\mathrm{AB}\)

\(u(M)=–{\varphi }_{z}(P)\mathrm{.}y+\mathrm{dx}(P)\)