Dynamics of Rods: Numerical Formulation

2009 ◽  
Author(s):  
A.D. Campos ◽  
F.A. Rochinha
Keyword(s):  
Numerical Formulation

scholarly journals Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

2020 ◽  
Vol 42 (4) ◽  
pp. 415-426
Author(s):  
Canh V. Le ◽  
Phuc L. H. Ho
Keyword(s):  
Optimization Problem ◽  
Shape Function ◽  
Limit State ◽  
Great Accuracy ◽  
Homogenization Theory ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Second Order Cone ◽  
Numerical Formulation ◽  
Element Free

This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.

Numerical formulation for constant-gain chemical laser calculations

1973 ◽  
Vol 11 (1) ◽  
pp. 15-27 ◽  
Author(s):  
Emily B Turner ◽  
W Dallas Adams ◽  
George Emanuel
Keyword(s):  
Chemical Laser ◽  
Numerical Formulation

Platonism and Mathematical Explanations

2021 ◽  
Vol 13 (2) ◽  
pp. 113-122
Author(s):  
Fabrice Pataut ◽  
Keyword(s):  
Mathematical Theory ◽  
Causal Explanation ◽  
Applied Mathematics ◽  
Propositional Attitude ◽  
Abstract Objects ◽  
Mathematical Explanations ◽  
Parsimony Principle ◽  
The Face ◽  
Numerical Formulation ◽  
The One

Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a non numerical formulation of some explanans may be obtained so that the platonistic force of the best numerical-based account of the explanandum is also undermined (Rizza), the parsimony principle has been respected. Since derivations resorting to conservative mathematics and proofs involved in non numerical best explanations also require abstract objects, concepts, and principles under the usual reading of “abstract,” one might complain that such accounts turn out to be as metaphysically loaded as their platonistic counterparts. One might then urge that ontological parsimony is also required of these nominalistic accounts. It might, however, prove more fruitful to leave this particular worry to the side, to free oneself, as it were, from parsimony thus construed and to look at other important aspects of the defeating or undermining strategies that have been lavished on the disposal of platonism. Two aspects are worthy of our attention: epistemic cost and debunking claims. Our knowledge that applied mathematics is conservative is established at a cost, and so is our knowledge that nominalistic proofs play a genuine theoretical role in best explanations. I will suggest that the knowledge one must acquire to show that nominalistic deductions and explanations do indeed play their respective theoretical role involves some question-begging assumptions regarding the nature and validity of proofs. As for debunking, even if the face value content of either non numerical claims, or conservative mathematical claims, or platonistic mathematical claims didn’t figure in our causal explanation of why we hold the mathematical beliefs that we do, construed or understood as beliefs about such contents, or as beliefs held in either of these three ways, we could still be justified in holding them, so that the distinction between nominalistic deductions or non numerical explanations on the one hand and platonistic ones on the other turns out to be spurious with respect to the relevant propositional attitude, i.e., with respect to belief.

Impact—Response Behavior of Offshore Pipelines

1982 ◽  
Vol 104 (4) ◽  
pp. 325-329 ◽  
Author(s):  
P. G. Bergan ◽  
E. Mollestad
Keyword(s):  
Plastic Material ◽  
Material Behavior ◽  
Hydrodynamic Drag ◽  
Offshore Pipelines ◽  
Sea Floor ◽  
Drag Forces ◽  
Sea Bottom ◽  
Nonlinear Dynamic Equations ◽  
Numerical Formulation ◽  
Inertia Forces

A method for analyzing the dynamic behavior of marine pipelines subjected to impact loads or sudden forced movements is outlined. Inertia forces (also from hydrodynamic mass), hydrodynamic drag forces as well as friction and lift effects for a pipe at the sea bottom are accounted for. An extensive nonlinear formulation is used for the pipe itself; it includes large displacements and elasto-plastic material behavior. Aspects of the numerical formulation of the problem and the solution of the nonlinear dynamic equations are discussed. The examples show computed dynamic response for pipelines lying on the sea floor and for a pipe section freely submerged in water when subjected to various force and displacement histories.

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