Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

Area of Science:

• Computational Mechanics
• Materials Science
• Structural Engineering

Background:

• Analysis of thin structures, particularly those made of functionally graded materials (FGM), requires advanced computational methods.
• Existing finite element formulations may face challenges in accurately capturing the behavior of FGMs under nonlinear conditions.

Purpose of the Study:

• To develop and validate prismatic and hexahedral quadratic solid-shell (SHB) finite elements for the geometrically nonlinear analysis of thin FGM structures.
• To integrate these elements with a 3D framework and address potential locking phenomena in the simulation of FGM plates.

Main Methods:

• Development of SHB finite elements within a purely 3D framework using displacements as the sole degrees of freedom.
• Application of the in-plane reduced-integration technique combined with the assumed-strain method to mitigate locking.
• Implementation of an arbitrary number of integration points along the thickness direction for FGM property variation.
• Coupling of SHB elements with functionally graded material behavior, specifically varying Young's modulus along the thickness.
• Integration into ABAQUS/Standard for quasi-static analysis under large displacements and rotations.

Main Results:

• The proposed SHB finite elements demonstrated good performance and accuracy in simulating thin FGM plates.
• Validation against established nonlinear benchmark problems confirmed the effectiveness of the developed elements.
• Comparisons with literature solutions validated the capabilities of the SHB elements for 3D simulations of FGM plates.

Conclusions:

• The developed SHB finite elements are suitable for the geometrically nonlinear analysis of thin FGM plates.
• The purely 3D formulation and advanced techniques effectively handle material gradients and large deformations.
• The study provides a reliable computational tool for simulating complex FGM structures.