Straight Cantilever Beam

MacNeal-Harder Test Problem

Length = 6.0; Height = 0.2; Depth = 0.1; E = 1.0E7: Poisson's ratio = 0.3.

Summary

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.

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 are used for each model; extension, in-plane bending, transverse bending, and twist. 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 as follows.

Linear Static Analysis Results

All results are normalized with the target value.

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.