Bending a Cantilevered Beam under a Concentrated Load (surface)

Bending a Cantilever Beam under a Concentrated Load

Let us consider a cantilevered beam of length L, loaded with the force P at the right-hand end. The beam cross-section is a rectangle of width b and height h.

Sought is the maximum beam deflection.
Material characteristics and other input data can be viewed here.

Bending of a Cantilever Beam under a Concentrated Load, the finite element model with applied loads and restraints

The finite element model with applied loads and restraints

The analytical solution can be viewed here.

After carrying out calculation with the help of AutoFEM, the following results are obtained:

Table 1.Parameters of the finite element mesh

Finite Element Type	Number of Nodes	Number of Finite Elements
linear triangle	104	150

Table 2. Result "Displacement, magnitude"*

Numerical Solution Displacement w*, m	Analytical Solution Displacement w, m	Error δ =100%* \|w* - w\| / \|w\|
4.8610E-003	4.9107E-003	1.01

Bending of a Cantilever Beam under a Concentrated Load, Result "Displacement, magnitude" of finite element analysis

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.