A finite element formulation for problems of large strain and large displacement

1970 ◽  
Vol 6 (8) ◽  
pp. 1069-1086 ◽  
Author(s):  
H.D. Hibbitt ◽  
P.V. Marcal ◽  
J.R. Rice
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Large Displacement ◽  
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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