A review on topology optimization approaches under different scenarios for 2D and 3D problems

This paper represents an anthology of optimization procedures on several 2D and 3D case studies, solved by several compact and efficient MATLAB implementations of topology optimization via running finite element analysis, density filters, sensitivity analysis, various topology optimizers, and displaying the results along with an optimization module in ABAQUS. Three scenarios have been designed for topology optimization: first, minimizing the compliance factor while preserving the volume fraction; second, minimizing the volume fraction while satisfying a specified stress limit; and third, minimizing compliance while satisfying stress and volume fraction constraints. The benchmarking data are obtained from three sources: literature-derived results for established MATLAB-based methods, author-generated code-based results for benchmark cases, not available in the original references, and author-generated ABAQUS simulations performed under matched geometry, loading, boundary conditions, material properties, and volume or stress constraints. The objective is to enable a consistent cross-algorithm comparison in terms of compliance, stress-limit satisfaction, volume-fraction control, convergence behavior, runtime, and 2D/3D scalability. The results demonstrate that MATLAB-based methods provide efficient and transparent reference solutions for compliance-dominated benchmarks, whereas ABAQUS offers a more robust validation platform for stress-constrained and three-dimensional cases.