A general high-order finite element formulation for shells at large strains and finite rotations

2003 ◽  
Vol 57 (15) ◽  
pp. 2147-2175 ◽  
Author(s):  
Y. Başar ◽  
U. Hanskötter ◽  
Ch. Schwab
Keyword(s):  
Finite Element ◽  
High Order ◽  
Finite Element Formulation ◽  
Large Strains ◽  
Element Formulation ◽  
Finite Rotations

Finite Element Formulation Based on the Extended High-Order Sandwich Panel Theory

AIAA Journal ◽  
2015 ◽  
Vol 53 (10) ◽  
pp. 3006-3015 ◽  
Author(s):  
Zhangxian Yuan ◽  
George A. Kardomateas ◽  
Yeoshua Frostig
Keyword(s):  
Finite Element ◽  
Sandwich Panel ◽  
High Order ◽  
Finite Element Formulation ◽  
Element Formulation

scholarly journals A component-free Lagrangian finite element formulation for large strain elastodynamics

2021 ◽  
Author(s):  
Miguel Martín Stickle ◽  
Miguel Molinos ◽  
Pedro Navas ◽  
Ángel Yagüe ◽  
Diego Manzanal ◽  
...  
Keyword(s):  
Finite Element ◽  
Weighting Function ◽  
Large Strain ◽  
Finite Element Formulation ◽  
Large Strains ◽  
Element Formulation ◽  
New Approach ◽  
Symmetric Structure ◽  
Lagrangian Finite Element ◽  
Solid Dynamics

AbstractStandard finite element formulation and implementation in solid dynamics at large strains usually relies upon and indicial-tensor Voigt notation to factorized the weighting functions and take advantage of the symmetric structure of the algebraic objects involved. In the present work, a novel component-free approach, where no reference to a basis, axes or components is made, implied or required, is adopted for the finite element formulation. Under this approach, the factorisation of the weighting function and also of the increment of the displacement field, can be performed by means of component-free operations avoiding both the use of any index notation and the subsequent reorganisation in matrix Voigt form. This new approach leads to a straightforward implementation of the formulation where only vectors and second order tensors in $${\mathbb {R}}^3$$ R 3 are required. The proposed formulation is as accurate as the standard Voigt based finite element method however is more efficient, concise, transparent and easy to implement.

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