0102 - Cantilever with transverse loading (Postbuckling)

In this case the cantilever beam is subjected only to a transverse force of $\boldsymbol{F} = 10 \, \mathbf{E}_2$ in a single step.

Delta Geometry  

Exact Geometry  

In this case the cantilever beam is subjected only to a transverse force of $\boldsymbol{F} = 10 \, \mathbf{E}_2$ in a single step. The simulation uses the following geometric and material properties from the literature:

Two values for the shear modulus $G$ are used with a shear stiffness $GA$ of $500$ and $10$ , respectively, the latter representing the case with significant shear deformations. Table (#tab:transv) presents the numerical tip displacements and the analytic solution from using Jacobi elliptic functions and accounting for flexural and shear deformations. The analysis uses both 2-node and 4-node elements. For the sake of brevity, the results are reported only for the variants using the same parameterization as the wrapped element’s interpolation.

References