Effects of Geometric Nonlinearities

Nonlinear Geometry with a Bending Plate

A horizontal plate has one edge encastered and the opposite edge subjected to a force ${\mathrm{F}}_z$ in negative Z-direction as well as a force ${\mathrm{F}}_x$ in positive X-direction where ${\mathrm{F}}_Z$ >> ${\mathrm{F}}_x$ . When taking only linear kinematics into account, the displacement of the loaded edge is only in the negative Z-direction because of the load in Z and superposed with the displacement in X causes by the X-load. Thus, the membrane load in X only contributes to the total displacement ${\mathrm{u}}_x$ in X: ${\mathrm{u}}_x$ = ${\mathrm{u}}_{\mathrm{xM}}$ . The plate elongates, which the graphic below shows (right side):

. By taking geometric nonlinearities into account (NLGEOM=YES), there is an additional displacement ${\mathrm{u}}_{\mathrm{xB}}$ in the negative X-direction due to the bending movement of the plate. Thus, the total displacement of the right edge is the sum of displacement because of the loads in X and Z, respectively. In this example, the bending load in Z is larger than the tensile force in X. This leads to a high bending displacement and the total displacement ${\mathrm{u}}_x$ = ${\mathrm{u}}_{\mathrm{xB}}$ + ${\mathrm{u}}_{\mathrm{xM}}$ is negative, which can be seen in the graphic above (left side).

See Also

The optimization for this example and further explanations can be found in the Tosca Structure Examples Guide (see Examples with Geometric Nonlinearities).