Model: Large Deformation Beam

Introduction

• This example shows the deflection of a cantilever beam undergoing very large deflections.

• The model is called “Straight cantilever GNL Benchmark” and is described in detail in the NAFEMS report “Background to Finite Element Analysis of Geometric Non-linearity Benchmarks”.

Problem definition

• The beam is linear elastic, with E = 2.1.1011 and =0.• The left end is fixed.• The right end is subjected to distributed loads.

Fx = -3.844.106 and Fy=-3.844.103.

Fy

Fx

Results

• The final state (using 1:1 displacement scaling) is shown in the figure.• Due to the large compressive axial load, this is a buckling problem.

It is necessary to perturb the symmetry somewhat. The small transversal load (Fy) serves this cause.

Results

• The vertical (solid line) and horizontal (dashed line) displacements for varying load (Fx).

• The results are in excellent agreement with the NAFEMS report.