scholarly journals A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme

2016 ◽  
Vol 109 (3) ◽  
pp. 407-456 ◽  
Author(s):  
Jibran Haider ◽  
Chun Hean Lee ◽  
Antonio J. Gil ◽  
Javier Bonet
Keyword(s):  
Large Strain ◽  
First Order ◽  
Solid Dynamics ◽  
Lagrangian Scheme

scholarly journals A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity

2015 ◽  
Vol 283 ◽  
pp. 689-732 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil ◽  
Chun Hean Lee ◽  
Miquel Aguirre ◽  
Rogelio Ortigosa
Keyword(s):  
Large Strain ◽  
First Order ◽  
Solid Dynamics

scholarly journals A first order hyperbolic framework for large strain computational solid dynamics. Part III: Thermo-elasticity

2021 ◽  
Vol 373 ◽  
pp. 113505
Author(s):  
Javier Bonet ◽  
Chun Hean Lee ◽  
Antonio J. Gil ◽  
Ataollah Ghavamian
Keyword(s):  
Large Strain ◽  
First Order ◽  
Solid Dynamics

scholarly journals An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations

2012 ◽  
Vol 55 (3) ◽  
pp. 575-605 ◽  
Author(s):  
Olivier Bokanowski ◽  
Jochen Garcke ◽  
Michael Griebel ◽  
Irene Klompmaker
Keyword(s):  
Sparse Grid ◽  
Bellman Equations ◽  
First Order ◽  
Hamilton Jacobi Bellman ◽  
Lagrangian Scheme

scholarly journals The semi-Lagrangian method on curvilinear grids

2016 ◽  
Vol 7 (3) ◽  
pp. 99-137 ◽  
Author(s):  
Adnane Hamiaz ◽  
Michel Mehrenberger ◽  
Hocine Sellama ◽  
Eric Sonnendrücker
Keyword(s):  
Lagrangian Method ◽  
Cubic Splines ◽  
Time Step ◽  
Spatial Error ◽  
Conservation Of Mass ◽  
First Order ◽  
Curvilinear Grids ◽  
Order Reconstruction ◽  
Odd Order ◽  
Lagrangian Scheme

Abstract We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

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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