Deriving analytical solutions using symbolic matrix structural analysis: Part 2 - Plane trusses

Area of Science:

• Structural Engineering
• Computational Mechanics
• Symbolic Computation

Background:

• Traditional matrix structural analysis often relies on numerical methods, limiting insight into parameter sensitivities.
• Previous symbolic computation applications were primarily focused on continuous beams, leaving gaps in analysis for other structures.
• Developing advanced computational tools is crucial for enhancing structural design and engineering education.

Purpose of the Study:

• To extend symbolic computation to the matrix structural analysis of 2D plane trusses.
• To develop and present a fully open-source MATLAB program for symbolic analysis of any 2D truss configuration.
• To provide closed-form analytical expressions for structural responses and enable efficient sensitivity analysis.

Main Methods:

• Utilized MATLAB's Symbolic Math Toolbox to derive symbolic expressions for displacements, support reactions, and axial forces.
• Developed a scalable framework capable of handling large-scale truss structures.
• Implemented sensitivity analysis through the computation of partial derivatives of structural responses.

Main Results:

• Generated closed-form analytical solutions for 2D truss analysis, offering deeper insights into structural behavior.
• Demonstrated the efficiency of symbolic computation for sensitivity analysis, aiding design exploration and optimization.
• Successfully validated the symbolic results against commercial finite element software and literature data, confirming accuracy and reliability.

Conclusions:

• The developed symbolic computation approach is reliable, scalable, and broadly applicable to 2D truss analysis.
• The open-source MATLAB tool enhances both engineering practice and education by clarifying parameter relationships.
• Symbolic analysis offers significant advantages over numerical methods for understanding and optimizing structural systems.