MATLAB Program for Elastoplastic Analysis of Frame Structures (Structural Top Displacement)

Elastoplastic analysis of frame structures holds significant importance in structural engineering, particularly for evaluating structural performance under extreme loads such as earthquakes. Implementing this analysis through MATLAB programs enables efficient calculation of structural top displacements, assisting engineers in assessing structural deformation capacity and safety.

The fundamental approach for elastoplastic analysis involves discretizing the structure into multiple elements while considering material nonlinear behavior during loading. The program typically includes these core computational steps:

Model Establishment: Define structural geometry, material properties (such as elastic modulus and yield strength), and boundary conditions using matrix-based data structures. Element Stiffness Matrix Calculation: Construct element stiffness matrices based on different mechanical responses during elastic and plastic phases, implementing material constitutive models through conditional statements. Global Stiffness Matrix Assembly: Integrate all element stiffness matrices into a global stiffness matrix using sparse matrix storage (`sparse` function) for efficient memory usage in large-scale problems. Incremental Loading and Iteration: Employ step-by-step loading combined with iterative methods like Newton-Raphson to handle nonlinear problems, implementing convergence checks until reaching target loads or structural failure. Top Displacement Extraction: Solve global equilibrium equations using linear algebra solvers (`\` operator or `mldivide` function) to obtain structural top displacements for deformation capacity evaluation.

MATLAB's advantages lie in its robust matrix operation capabilities and flexible programming environment, which efficiently handle complex elastoplastic computations. Key functions involved may include sparse matrix operations for large systems, nonlinear equation solvers for iterative procedures, and custom plasticity criterion algorithms using logical comparisons and state variables.

Through such analysis, engineers can optimize structural design to ensure controlled deformations during elastoplastic phases, thereby enhancing seismic performance. The program typically outputs displacement-load curves and plastic hinge formation patterns for comprehensive structural assessment.