Deriving analytical solutions using symbolic matrix structural analysis for continuous beams

Area of Science:

• Structural Engineering
• Computational Mechanics
• Symbolic Computation

Background:

• Traditional Matrix Structural Analysis (MatSA) often relies on numerical methods.
• Deriving analytical expressions for complex structures like continuous beams can be challenging.
• Limited tools exist for in-depth, symbolic-driven sensitivity analysis in structural mechanics.

Purpose of the Study:

• To investigate the application of symbolic computation in MatSA for continuous beams.
• To develop an open-source MATLAB program for symbolic analysis of continuous beams.
• To demonstrate the benefits of symbolic MatSA for design exploration and education.

Main Methods:

• Utilizing the MATLAB Symbolic Math Toolbox for symbolic computation.
• Applying symbolic MatSA to derive analytical expressions for displacements, reactions, and internal forces.
• Implementing the derived methodology into an open-source MATLAB program.

Main Results:

• Analytical expressions for displacements, support reactions, and internal forces were successfully derived.
• Efficient and scalable sensitivity analysis capabilities were achieved through direct computation of partial derivatives.
• An open-source MATLAB program was developed for symbolic analysis of continuous beams under various loads.
• The program facilitates the derivation of influence lines and identification of maximum response values.

Conclusions:

• Symbolic computation offers a powerful approach to MatSA for continuous beams, providing deeper insights into structural behavior.
• This methodology enhances design exploration and aids in engineering education by clarifying parameter relationships.
• The developed open-source tool promotes wider adoption and understanding of symbolic MatSA in structural engineering.