Geometry and Mesh

Rectangular domain. 8 m long, 0.5 m tall. Q4 elements. A fine mesh density is applied to avoid shear locking. 200 elements along the length x 20 elements across the width.

Material properties

Parameter	Value
Young's Modulus	200 GPa
Poisson's ratio	0.3
Thickness	1 m

Plane stress conditions applied

Applied loads

A traction of -400 kPa is applied to the y- degrees of freedom along the left edge (x=L), and traction free conditions are applied elsewhere.

Boundary conditions

All the x- and y- degrees of freedom along the left edge (x = 0) are fixed.

Solution

The displacement of the cantilever beam is given by the analytical Bernoulli solution.

where u_y is the vertical displacement, P is the total applied force on the end of the beam, L is the beam length, E is the elastic modulus, I is the moment of inertia, t is the beam thickness, and w is the beam width.

Given the prescribed inputs, the displacement at the end of the bar is -16.4 mm.