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This chapter presents analytical solutions for linear elastic plane stress and strain problems. We introduce and develop the Airy stress function method, a powerful technique specifically designed for solving two-dimensional boundary value problems. Using this method, we explore several classic problems and derive analytical solutions in both Cartesian and polar coordinate systems, showcasing the versatility and applicability of the Airy function approach in the realm of plane stress and strain analysis.

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Solutions for Infinitesimal Plane Stress and Strain Problems

  • 章节

  • 发表日期：

    2025年

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  • Junqian Zhang,
  • Yicheng Song,
  • Bo Lu

摘要

This chapter presents analytical solutions for linear elastic plane stress and strain problems. We introduce and develop the Airy stress function method, a powerful technique specifically designed for solving two-dimensional boundary value problems. Using this method, we explore several classic problems and derive analytical solutions in both Cartesian and polar coordinate systems, showcasing the versatility and applicability of the Airy function approach in the realm of plane stress and strain analysis.