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<p>This paper develops accurate and innovative nonlinear analytical solutions for higher-order shear deformation beams. The key contributions include the representation of deflection through classical beam eigenfunction expansions, the explicit determination of rotations tailored to specific boundary conditions, and the derivation of nonlinear algebraic governing equations via the energy variational method. These solutions achieve unprecedented accuracy, establishing the most reliable theoretical foundation for engineering design and providing benchmark references for validating nonlinear numerical and approximate analytical methods. In the author’s computations, even under deliberately conservative estimates, the deflection errors remain below 0.01%. By rigorously addressing complex boundary conditions and diverse loading cases, this work strengthens the theoretical framework of analytical mechanics and delivers substantial academic value for a wide range of nonlinear structural problems.</p>

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Accurate nonlinear analytical solutions of higher order shear deformation beams using classical beam eigen functions

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Da-Guang Zhang

摘要

This paper develops accurate and innovative nonlinear analytical solutions for higher-order shear deformation beams. The key contributions include the representation of deflection through classical beam eigenfunction expansions, the explicit determination of rotations tailored to specific boundary conditions, and the derivation of nonlinear algebraic governing equations via the energy variational method. These solutions achieve unprecedented accuracy, establishing the most reliable theoretical foundation for engineering design and providing benchmark references for validating nonlinear numerical and approximate analytical methods. In the author’s computations, even under deliberately conservative estimates, the deflection errors remain below 0.01%. By rigorously addressing complex boundary conditions and diverse loading cases, this work strengthens the theoretical framework of analytical mechanics and delivers substantial academic value for a wide range of nonlinear structural problems.