## Variational principles and hybrid approach for finite deformation analysis of shells.(English)Zbl 0738.73080

Summary: A complementary Hu-Washizu functional $$\Gamma_ 3$$ based on formulae presented by S. N. Atluri [Comput. Struct. 18, 93-116 (1984; Zbl 0524.73043)], is given in dyadic notation. By introducing Legendre transformation, the Heillinger-Reissner functional $$\Pi_ 2$$, $$\Gamma_ 2$$ and the classic potential energy functional $$\Pi_ 1$$ are obtained. An incremental modelling of functional $$\Gamma_ 3$$ for the analysis of finite deformation and finite rotations of arbitrarily shaped shells is presented. The numerical results are shown to be in good agreement with those found in published literature.

### MSC:

 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics 74K15 Membranes 74B20 Nonlinear elasticity

Zbl 0524.73043
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### References:

 [1] Atluri, Comput. Struct. 18 pp 93– (1984) [2] and , AMD-48, 233 (1981). [3] Ph.D thesis, Huazhong University of Science & Technology, 1990. [4] Zhengxing, Comput. Struct. 30 pp 995– (1988)
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