Large‐Deflection Analysis of Eccentrically Compressed Beams Under Thermal Effects: A Least‐Squares Optimization Framework

ABSTRACT This study proposes a novel nonlinear modeling and solution approach to analyze the geometrically nonlinear behavior of beams subjected to combined eccentric compressive loads and thermal effects. General governing equations for large‐displacement beams under the simultaneous action of eccentric compression and temperature fields are formulated analytically. A numerical solution procedure for the nonlinear governing equations is developed by transforming the system of nonlinear equations into a least‐squares optimization problem. Based on the Levenberg–Marquardt algorithm, a computational code is implemented in MATLAB to solve the proposed nonlinear optimization problem. The accuracy of the developed method is verified through comparison with classical solutions using elliptic integrals, showing excellent agreement. The influences of load eccentricity and temperature on the nonlinear response of beams are also investigated in detail. The simple and efficient approach proposed in this study offers a promising tool for practicing engineers in the design of beams with large displacements under combined eccentric and thermal loading.