Finite Element Analysis of Cantilever Beam(II)

Maximum displacement in y direction is -0.3752×10e-4m and in x direction is 0.102×10e-4m.

 

 

Matlab Result (16 element)

 

Gauss Point maximum stress in X direction is 288.83Pa

Gauss Point minimum stress in X direction is -259.6Pa

Maximum stress in X direction is 335.77 Pa

Minimum stress in X direction is –245.89 Pa

 

 

Matlab Result (64 elements)

 

Maximum displacement in y direction is -0.4124×10-4m and in x direction is 0.1117×10-4m.

 

 

Matlab Result (64 elements)

 

Gauss Point maximum stress in X direction is 387.23Pa

Gauss Point minimum stress in X direction is -294.74Pa

Maximum stress in X direction is 430.85 Pa

Minimum stress in X direction is –298.61 Pa

ABAQUS RESULT (16 ELEMENTS)

Finite Element Analysis of Cantilever Beam(I)

Problem Statement

A cantilever beam is subjected to a uniform distributed load with value 30 N/m. The trapezoid beam has right vertical length 0.5m and left vertical length 1m. And top length is 2m.as shown in the graph.

B.C.: The vertical left side is fixed; the bottom and the vertical right side are free.

Material properties: isotropic material   E=3×10⁷Pa Poisson’s ratio ν=0.3

Regard this problem as a plane stress one. (beam width is 0.1m)

Math expression of the problem

PDE:

Boundary Conditions：

where