Hello,
I have modeled a simply supported beam in Plaxis-2D and 3D, and by using a Poisson's ratio of zero the deflections are similar to theoretical values (and checked it vs. Abaqus). However, by considering a Poisson's ratio of 0.3 the displacements are reduced which is not consistent with expected behavior (by increasing the Poisson's ratio we expect shear modulus to be decreased, therefore resulting in increase of shear deformations). Also, by considering P-delta effects (updated mesh) in Plaxis the displacements decrease which is opposite of the expected behavior.
.Model_SimpleBeam_Poissonp3_FromScratch .p2dx.7z
Thank you for your support,
Shokoufeh
Dear Shokoufeh,You mention that you've modelled a simply supported beam in PLAXIS 2D and 3D with different Poisson's ratios. I'm not entirely sure how you did that, because in PLAXIS 2D there is no beam element - only plates, geogrids, embedded beams and anchors and in PLAXIS 3D there are beams, but they don't have a Poisson's ratio as they're considered very slender.
But assuming that in 2D you have used a Plate element, the explanation is quite simple: when introducing a Poisson's ratio the plate wants to reduce size in the out-of-plane direction due to the presence of out-of-plane stresses sigma_zz. However, in a plane strain model there cannot be a strain in out-of-plane direction and this limitation of not being able to deform in that direction though due to the Poisson's ratio it should deform in that direction has a stiffening effect on the Plate such that the apparent EI = EI_input / (1 - nu^2). So with a Poisson's ratio of 0.3 the apperent EI is about 10% higher then the input value, hence the deformation reduces.If for 3D you have also used a plate and the edges of that plate were on the boundaries of your model, the edges of the plate had boundary conditions applied which would then again prevent them from deforming in that direction like in the 2D case.In case of the P-delta effect I would actually expect the deformation to decrease. With the P-delta effect the beam/plate is loaded only under shear causing shear forces and bending moments in the beam/plate. However, taking into account the deformation of the plate the plate start developing axial forces as well, and those axial forces increase with deformation. So the axial stiffness plays here a role as well, not just the shear stiffness. Hence, the beam/plate behaves stiffer as a combination of axial and shear stiffness and thus deforms less.
With kind regards,
Dennis Waterman