Shape optimization of plate with static and dynamic constraints via virtual laminated element

Area of Science:

• Structural Engineering
• Computational Mechanics
• Optimization Methods

Background:

• Traditional structural shape optimization methods often struggle with mesh distortion and limited design variable definitions.
• Existing thin plate optimization techniques typically result in stepped thickness distributions, which are less practical.

Purpose of the Study:

• To introduce a new method, the virtual laminated element method (VLEM), for structural shape optimization.
• To demonstrate VLEM's capability in achieving continuous thickness distributions and avoiding mesh distortion problems.

Main Methods:

• Utilizing the virtual laminated element method (VLEM) with layer thickness values as design variables.
• Implementing a 'behavior model technique' for approximate reanalysis to reduce computational cost.
• Avoiding the need to regenerate finite element (FE) grids during the optimization process.

Main Results:

• VLEM successfully resolves structural shape optimization problems.
• The method allows for continuous thickness distributions in thin plate optimization, offering more realistic results compared to stepped designs.
• Optimization failures due to distorted FE grids are circumvented.

Conclusions:

• The virtual laminated element method (VLEM) is an effective and practical approach for structural shape optimization.
• VLEM offers advantages over traditional methods by simplifying design variables and improving the quality of optimized shapes.
• The integration of the behavior model technique enhances the efficiency of the VLEM optimization process.