A Dynamic Programming Setting for Functionally Graded Thick-Walled Cylinders

Area of Science:

• Solid Mechanics
• Materials Science
• Optimization Theory

Background:

• Thick-walled cylinders under internal pressure experience non-uniform stress distributions.
• Material property variation is crucial for optimizing structural performance.
• Functionally graded materials offer tailored mechanical responses.

Purpose of the Study:

• To investigate material property variation in internally pressurized thick-walled cylinders.
• To determine optimal material distribution for stress reduction.
• To apply dynamic programming and optimal control theory to material design.

Main Methods:

• Formulation of a state space model based on the plane stress hypothesis.
• Application of Pontryagin's Principle to solve the optimal control problem.
• Analysis of linear, elastic, isotropic, and radially graded materials.

Main Results:

• The optimal Young's modulus distribution is piecewise linear along the radial direction.
• Investigation into the potential existence of switching points in the optimal solution.
• Numerical examples demonstrate significant equivalent stress reduction.

Conclusions:

• Dynamic programming provides an effective framework for optimizing material properties in thick-walled cylinders.
• Piecewise linear material grading can lead to improved stress management.
• The proposed method shows promise for enhancing the performance of pressure vessels.