OS-E: 0910 Shell Cantilever

Demonstrates how size optimization can be used.

Figure 1. Structural Model


Model Files

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

Model Description

For the cantilever beam, a thickness distribution is sought that minimizes the structural mass and allows a limited vertical deflection of the loading end. The displacement is limited to 2.0mm.

The thickness for each element is varied. Therefore, five variables are defined in the analysis deck. The initial thickness of all elements is 2mm. All thickness variables have a lower bound of 1mm and an upper bound of 3mm.

The optimization problem, objective and constraint functions, is defined in the same manner as for the other types of structural optimization. OptiStruct then goes through an iteration process to solve the optimization problem. OptiStruct converged after 3 iterations.


Table 1 shows the optimization results of the cantilever beam, which met the constraints and minimizes the mass (decrease of 6.6%).
Table 1. Optimization Result of Cantilever Beam
Element 1 Element 2 Element 3 Element 4 Element 5 Disp Volume
Initial 2.0mm 2.0mm 2.0mm 2.0mm 2.0mm 2.5mm 400.00mm3
Final 2.6mm 2.3mm 1.9mm 1.5mm 1.0mm 2.0mm 373.204mm3