Proper Generalized Decomposition for Parametric Study and Material Distribution Design of Multi-Directional...

Area of Science:

• Computational mechanics
• Solid mechanics
• Materials science

Background:

• Mesh-based numerical methods for 3D elasticity problems are computationally intensive.
• High computational costs hinder parametric studies and material distribution design for thick plates.

Purpose of the Study:

• To adopt the Proper Generalized Decomposition (PGD) technique for solving 3D elasticity problems.
• To overcome computational limitations in high-dimensional parametric spaces for thick plate analysis.
• To enable efficient parametric solutions and material distribution design.

Main Methods:

• Proper Generalized Decomposition (PGD) as an a priori model order reduction technique.
• Reduction of 3D partial differential equations to a set of 1D ordinary differential equations.
• Application to multi-directional Functionally Graded Material (FGM) composite thick plates.

Main Results:

• PGD significantly reduces computational costs compared to traditional mesh-based methods.
• Unified and efficient parametric solutions are achieved in high-dimensional spaces.
• Validation case studies demonstrate the applicability of PGD for complex plate designs.

Conclusions:

• PGD is a powerful technique for efficient 3D elasticity solutions of thick plates.
• The method facilitates advanced parametric studies and material optimization.
• PGD offers a viable approach for designing multi-directional FGM composite thick plates.