Proportional Topology Optimization: A New Non-Sensitivity Method for Solving Stress Constrained and Minimum...

Area of Science:

• Mechanical Engineering
• Computational Science

Background:

• Topology optimization is crucial for designing efficient structures.
• Existing methods often rely on sensitivity analysis, which can be complex.
• There is a need for simpler, yet accurate, topology optimization techniques.

Purpose of the Study:

• Introduce and detail the Proportional Topology Optimization (PTO) method.
• Implement PTO in MATLAB for stress-constrained and minimum compliance problems.
• Evaluate the efficiency and accuracy of PTO.

Main Methods:

• Developed a non-sensitivity based topology optimization algorithm (PTO).
• Created two MATLAB programs for stress-constrained and minimum compliance optimization.
• Applied PTO to three numerical examples for validation.

Main Results:

• PTO demonstrated comparable efficiency and accuracy to sensitivity-based methods.
• The PTO stress-constrained algorithm achieved lower maximum stress and volume fraction.
• The PTO minimum compliance algorithm showed higher compliance.
• PTO is simple to understand and implement.

Conclusions:

• Proportional Topology Optimization (PTO) is a viable alternative to sensitivity-based methods.
• PTO offers a balance of simplicity, efficiency, and accuracy.
• Publicly available MATLAB programs facilitate the adoption of PTO.