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Related Concept Videos

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Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
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Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method.

Olga Doeva1, Pedram Khaneh Masjedi1, Paul M Weaver1

  • 1Bernal Institute, School of Engineering, University of Limerick, Limerick, Ireland.

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Summary

New analytical solutions using the Homotopy Analysis Method (HAM) were developed for anisotropic composite beams on elastic foundations. The iterative HAM (iHAM) approach demonstrated superior convergence for analyzing static deflection problems.

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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.