Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

Area of Science:

• Solid Mechanics
• Composite Materials Engineering
• Applied Mathematics

Background:

• Analyzing the static deflection of anisotropic composite beams is crucial for structural integrity.
• Elastic foundations with variable stiffness introduce complexity to beam deflection analysis.
• Existing analytical methods may face challenges with convergence and accuracy for such complex systems.

Purpose of the Study:

• To derive new analytical solutions for the static deflection of anisotropic composite beams on variable stiffness elastic foundations.
• To investigate the efficiency and convergence of the Homotopy Analysis Method (HAM) and its iterative variant (iHAM).
• To validate the accuracy of the developed HAM solutions against existing literature and numerical methods.

Main Methods:

• The Homotopy Analysis Method (HAM) was employed to obtain closed-form series solutions.
• Two algorithms were utilized: conventional HAM and iterative HAM (iHAM).
• Solutions were verified using the Chebyshev Collocation Method and comparison with literature data.

Main Results:

• The iterative HAM (iHAM) algorithm showed improved convergence compared to conventional HAM for achieving similar accuracy.
• New analytical solutions were successfully obtained for composite beams on variable stiffness elastic foundations.
• Numerical experiments confirmed the accuracy and efficiency of HAM for static beam deflection problems.

Conclusions:

• The Homotopy Analysis Method, particularly the iterative approach, provides an accurate and efficient tool for analyzing the static deflection of anisotropic composite beams on complex elastic foundations.
• The study offers valuable new analytical results for a challenging problem in composite structure analysis.
• The findings support the applicability of HAM in solving advanced problems in structural mechanics.