Curved Cantilever Beam

MacNeal-Harder Test Problem

E = 1.0E7; Poisson's ratio = 0.25; Loading; unit force at tip.

Summary

This is a curved cantilever beam solved with solid and shell elements. A model is 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. Two loading cases are used for each model; in-plane bending, transverse bending. For both load cases, unit loads are applied in a consistent fashion over all of the nodes at the tip of the beam.

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.