A constitutive model based on energy density for power-law variable thickness plates and its application

Area of Science:

• Mechanical Engineering
• Computational Mechanics
• Structural Dynamics

Background:

• Variable thickness plates are crucial in large-scale transportation systems like aerospace and ships.
• High-frequency vibrations in these structures can cause significant damage, necessitating accurate predictive models.
• Current approximate methods (AEFEM) for high-frequency dynamic response are imprecise and time-consuming.

Purpose of the Study:

• To develop a precise new energy finite element method (NEFEM) for analyzing variable thickness plates.
• To establish a reliable and time-saving constitutive model for power-law variable thickness plates.
• To validate the accuracy and efficiency of NEFEM against traditional FEM and AEFEM.

Main Methods:

• Derivation of a new constitutive equation based on energy density for power-law variable thickness plates.
• Development of a finite element discrete scheme for the derived constitutive equation.
• Implementation of the new precise energy finite element method (NEFEM).

Main Results:

• The NEFEM provides accurate predictions for the dynamic response of variable thickness plates.
• The derived constitutive model is shown to be reliable and efficient.
• NEFEM achieves higher accuracy with fewer elements compared to the approximate method (AEFEM).

Conclusions:

• The developed NEFEM offers a precise and efficient approach for predicting high-frequency dynamic responses in power-law variable thickness plates.
• This new method enhances structural design by providing reliable vibration analysis.
• NEFEM represents a significant advancement over existing approximate methods for complex plate structures.