Airy Stress Func. Polynomial order to satisfy the biharmonic equation

Thread starter StevenScott
Start date Dec 29, 2017
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Polynomial Stress Stress analysis

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SUMMARY

The discussion focuses on selecting the appropriate polynomial order for the stress function Φ to satisfy the biharmonic equation in elasticity problems. It is established that the order of the polynomial directly correlates with the number of boundary conditions; specifically, a third-order polynomial can satisfy three boundary conditions. This relationship is crucial for ensuring accurate solutions in engineering applications involving stress analysis.

PREREQUISITES

Understanding of biharmonic equations in elasticity theory
Familiarity with polynomial functions and their properties
Knowledge of boundary conditions in mathematical modeling
Basic concepts of stress analysis in engineering

NEXT STEPS

Research the application of polynomial stress functions in finite element analysis
Study the implications of varying polynomial orders on boundary condition satisfaction
Explore advanced topics in elasticity theory, focusing on biharmonic equations
Learn about numerical methods for solving biharmonic equations in engineering contexts

USEFUL FOR

Engineers, researchers, and students in mechanical and civil engineering disciplines who are involved in stress analysis and elasticity theory will benefit from this discussion.

Dec 29, 2017

StevenScott

Hello,

When choosing a polynomial stress function Φ to satisfy the biharmonic equation, how does once decide on which order of the polynomial to choose?
For example, is it based upon the number of boundary conditions, like a 3rd order polynomial would satisfy 3 boundary conditions?