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 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 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.

scholarly journals Complete Riemann Solvers for the Hyperbolic GPR Model of Continuum Mechanics

2021 ◽  
Vol 35 ◽  
pp. 60-72
Author(s):  
U. Ariunaa ◽  
◽  
M. Dumbser ◽  
Ts. Sarantuya ◽  
◽  
...  
Keyword(s):  
Continuum Mechanics ◽  
Riemann Solver ◽  
Governing Equations ◽  
Overdetermined System ◽  
Riemann Solvers ◽  
First Order ◽  
Conservative Schemes ◽  
Solid Dynamics ◽  
First Time ◽  
Better Than

In this paper, complete Riemann solver of Osher-Solomon and the HLLEM Riemann solver for unified first order hyperbolic formulation of continuum mechanics, which describes both of fluid and solid dynamics, are presented. This is the first time that these types of Riemann solvers are applied to such a complex system of governing equations as the GPR model of continuum mechanics. The first order hyperbolic formulation of continuum mechanics recently proposed by Godunov S. K., Peshkov I. M. and Romenski E. I., further denoted as GPR model includes a hyperbolic formulation of heat conduction and an overdetermined system of PDE. Path-conservative schemes are essential in order to give a sense to the non-conservative terms in the weak solution framework since governing PDE system contains non-conservative products, too. New Riemann solvers are implemented and tested successfully, which means it certainly acts better than standard local Lax-Friedrichs-type or Rusanov-type Riemann solvers. Two simple computational examples are presented, but the obtained computational results clearly show that the complete Riemann solvers are less dissipative than the simple Rusanov method that was employed in previous work on the GPR model.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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