OS-V: 0720 Straight Cantilever Beam

MacNeal-Harder Test This is a straight cantilever beam solved with solid and shell elements. Three models (rectangular, parallelogram, trapezoidal) are made with each element's type to investigate the effect of distorted elements with a high aspect ratio.


veri_straight
Figure 1. FE Model of the Beam with Boundary Conditions and Loadcases

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

Six types of elements are used for this problem. They are tria-shell, quad-shell, and hexa-solid elements, each with 1st and 2nd order. Four loading cases, extension, in-plane bending, transverse bending, and twist, are used for each model. For the extension and bending load cases, unit loads are applied in a consistent fashion over all of the nodes at the tip of the beam. For the twist load cases, a unit moment is applied at the tip.

Theoretical solutions for the deflections at the tip, computed by beam theory, are:
Load Type Component Value
Extension UX 0.00003
In-plane bending UZ 0.1081
Transverse bending UY 0.4321
Twist ROTX 0.03208

Linear Static Analysis Results

All results are normalized with the target value.
Table 1. (a) Rectangular
  In-plane Extension In-plane Bending Transverse Bending Twist
QUAD4 1.000 0.992 0.981 0.941
QUAD8 1.006 1.000 1.016 0.953
TRI3 1.000 0.032 0.973 1.072
TRI6 1.006 0.994 1.001 0.950
HEX8 0.988 0.978 0.973 0.892
HEX20 1.008 0.992 0.992 0.905
Table 2. (b) Parallelogram
  In-plane Extension In-plane Bending Transverse Bending Twist
QUAD4 1.000 0.712 0.981 0.905
QUAD8 1.008 0.999 1.015 0.937
TRI3 1.000 0.012 0.955 0.931
TRI6 1.005 0.962 0.995 0.982
HEX8 1.012 0.624 0.529 0.820
HEX20 1.008 0.976 0.977 0.905
Table 3. (c) Trapezoidal
  In-plane Extension In-plane Bending Transverse Bending Twist
QUAD4 1.000 0.173 0.964 0.869
QUAD8 1.005 0.981 1.015 0.950
TRI3 1.000 0.019 0.965 1.175
TRI6 1.006 0.972 0.999 0.947
HEX8 1.010 0.047 0.030 0.563
HEX20 1.008 0.902 0.950 0.905

Reference

MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1 (1985) 3-20.