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Method and verification / 方法と検証

The benchmark minimizes compliance for a 2-D cantilever with a fixed left edge and a downward point load on the right edge, subject to a prescribed material volume.

Method

1. Assemble four-node plane-stress elements.
2. Interpolate stiffness with SIMP.
3. Solve K(x)u=f and calculate compliance sensitivities.
4. Apply a cone-weighted sensitivity filter.
5. Update density with a volume-constrained optimality criterion.

Checked run

On an 18 × 6 mesh, compliance decreased from 1802.5563 to 563.5914 while final mean density was 0.3999934. The run converged after 64 updates with a final maximum density change of 0.009516, below the 0.01 tolerance.

Tests

Three tests passed: element-matrix symmetry/semidefiniteness, density bounds and volume conservation with objective improvement, and creation of all expected artifacts.

Limitations

This is a compact educational benchmark using dense linear algebra, a structured mesh and simplified loading. It is not a production CAE validation.