Hu–Washizu principle

In continuum mechanics, and in particular in finite element analysis, the Hu–Washizu principle is a variational principle which says that the action

∫ V e [ 1 2 ε T C ε − σ T ε + σ T ( ∇ u ) − p ¯ T u ] d V − ∫ S σ e T ¯ T u   d S {\displaystyle \int _{V^{e}}\left[{\frac {1}{2}}\varepsilon ^{T}C\varepsilon -\sigma ^{T}\varepsilon +\sigma ^{T}(\nabla u)-{\bar {p}}^{T}u\right]dV-\int _{S_{\sigma }^{e}}{\bar {T}}^{T}u\ dS}

is stationary, where C {\displaystyle C} is the elastic stiffness tensor. The Hu–Washizu principle is used to develop mixed finite element methods.[1] The principle is named after Hu Haichang and Kyūichirō Washizu.

References

  1. ^ Jihuan, He (June 1997). "Equivalent theorem of Hellinger–Reissner and Hu–Washizu variational principles". Journal of Shanghai University. 1 (1). Shanghai University Press: 36–41. doi:10.1007/s11741-997-0041-1. ISSN 1007-6417. S2CID 119852325.

Further reading

  • K. Washizu: Variational Methods in Elasticity & Plasticity, Pergamon Press, New York, 3rd edition (1982)
  • O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu : The Finite Element Method: Its Basis and Fundamentals, Butterworth–Heinemann, (2005).
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