Analytic solutions for Euler-Bernoulli beams with axial compression resting on a nonlinear elastic foundation using...

Area of Science:

• Structural Mechanics
• Applied Mathematics
• Continuum Mechanics

Background:

• Euler-Bernoulli beams are fundamental in structural analysis.
• Understanding deflection under combined axial compression and nonlinear elastic foundations is crucial for engineering applications.
• Existing analytical methods may face challenges with such complex boundary conditions.

Purpose of the Study:

• To investigate the deflection behavior of Euler-Bernoulli beams under axial compression and nonlinear elastic foundations.
• To introduce and validate the Modified Adomian Decomposition Method (MADM) for this specific problem.
• To provide an accurate and efficient analytical framework for predicting beam deflection.

Main Methods:

• The Modified Adomian Decomposition Method (MADM) was employed.
• An initial polynomial ansatz was used to optimize Adomian polynomial construction.
• The method's accuracy was verified against an analytical benchmark and compared with existing published solutions.

Main Results:

• MADM demonstrated rapid convergence and an accurate series solution for beam deflection.
• The proposed formulation showed excellent agreement with both the analytical benchmark and previous studies.
• The method proved to be stable and efficient for modeling coupled effects.

Conclusions:

• MADM is a reliable and effective analytical technique for analyzing Euler-Bernoulli beams with axial compression on nonlinear elastic foundations.
• The study confirms the validity and efficiency of MADM in predicting complex beam deflection behaviors.
• This approach offers a valuable tool for engineers and researchers dealing with similar structural mechanics problems.