A comparison between different finite elements for elastic and aero-elastic analyses

Area of Science:

• Computational Mechanics
• Structural Analysis
• Finite Element Analysis

Background:

• Finite element methods are crucial for analyzing complex structures.
• Selecting appropriate shell finite elements impacts analysis accuracy and efficiency.
• Various elements exist, each with distinct mathematical formulations and performance characteristics.

Purpose of the Study:

• To compare the performance of five distinct shell finite elements.
• To evaluate elements based on mathematical formulation, accuracy, and computational cost.
• To identify optimal elements for specific engineering applications like vibration, stress, and aero-elastic analysis.

Main Methods:

• Detailed mathematical formulation of shape functions and element equations for each element.
• Derivation of strain-displacement matrices using a simplified Jacobian matrix for bending.
• Benchmarking elements against elastic and aero-elastic problems to assess convergence, accuracy, and computation time.

Main Results:

• The deformation-based linear quadrilateral element is optimal for elastic free vibration analysis.
• The 8-node quadrilateral element demonstrates superior performance in stress analysis.
• The 9-node quadrilateral element is the most suitable for aero-elastic analysis and laminated composite plates.
• The linear triangular element, while less effective for modal and stress analysis, provides accurate aero-elastic results at a higher computational cost.

Conclusions:

• Element selection is application-dependent, with no single element being universally superior.
• The 9-node quadrilateral element shows versatility, excelling in both aero-elasticity and composite plate analysis.
• The study provides valuable guidance for engineers in choosing the most efficient and accurate shell finite element for their specific structural analysis needs.