Mathematical models and numerical methods for the simulation of adaptive inflatable structures for impact absorption

2016 ◽  
Vol 174 ◽  
pp. 3-20 ◽  
Author(s):  
C. Graczykowski
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Inflatable Structures ◽  
Impact Absorption

scholarly journals RESIDUAL DISPLACEMENTS‘ PROGRESIVE ANALYSIS OF THE MULTISUPPORTED BEAM / DAUGIAATRAMĖS SIJOS LIEKAMŲJŲ POSLINKIŲ PROGRESINĖ ANALIZĖ

2014 ◽  
Vol 6 (5) ◽  
pp. 461-467 ◽  
Author(s):  
Liudas Liepa ◽  
Agnė Gervytė ◽  
Ela Jarmolajeva ◽  
Juozas Atkočiūnas
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Analysis Problem ◽  
Residual Displacements ◽  
Repeated Load ◽  
Energy Principles

This paper focuses on a shakedown behaviour of the ideally elasto-plastic beams system under variable repeated load. The mathematical models of the analysis problems are created using numerical methods, extremum energy principles and mathematic programming. It is shown that during the shakedown process the residual displacements vary non-monotonically. By solving analysis problem, where the load locus is being progressively expanded, it is possible to determine the upper and lower bounds of residual displacements. Suggested methods are ilustrated by solving multisupported beam example problem. The results are obtained considering principle of the small displacements. Nagrinėjamas idealiai tampriai plastinės lenkiamos strypinės sistemos prisitaikomumo būvis, veikiant kartotinei kintamajai apkrovai. Analizės uždavinių matematiniai modeliai sudaromi, pasitelkus skaitinius metodus, ekstreminius energinius principus ir matematinį programavimą. Parodoma, kad prisitaikant konstrukcijai jos liekamieji poslinkiai gali kisti nemonotoniškai. Išsprendus analizės uždavinį, kuriame progresyviai plečiama apkrovos veikimo sritis, galima nustatyti viršutines ir apatines liekamųjų poslinkių kitimo ribas. Siūloma metodika iliustruota daugiaatramės sijos liekamųjų poslinkių skaičiavimo pavyzdžiu. Rezultatai gauti, esant mažų poslinkių prielaidai.

Modelling and computation of liquid crystals

Acta Numerica ◽  
2021 ◽  
Vol 30 ◽  
pp. 765-851
Author(s):  
Wei Wang ◽  
Lei Zhang ◽  
Pingwen Zhang
Keyword(s):  
Liquid Crystals ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Soft Matter ◽  
Scientific Research ◽  
Crystalline Solids ◽  
The Past ◽  
Tremendous Progress

Liquid crystals are a type of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the past four decades, which is of great importance for fundamental scientific research and has widespread applications in industry. In this paper we review the mathematical models and their connections to liquid crystals, and survey the developments of numerical methods for finding rich configurations of liquid crystals.

Mathematical models and numerical methods for the forward problem in cardiac electrophysiology

2002 ◽  
Vol 5 (4) ◽  
pp. 215-239 ◽  
Author(s):  
G.T. Lines ◽  
M.L. Buist ◽  
P. Grottum ◽  
A.J. Pullan ◽  
J. Sundnes ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Cardiac Electrophysiology ◽  
Forward Problem

scholarly journals Application of quasiconformal mapping methods to the investigation of the explosive processes impact on the environment

2019 ◽  
pp. 17-18
Author(s):  
Kateryna Mykolaiivna Malash ◽  
Andrii Yaroslavovych Bomba
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Quasiconformal Mapping ◽  
Quasiconformal Mappings ◽  
Practical Application

The mathematical models used to study explosive processes are given. A class of problems investigating the influence of explosive processes on the environment by the quasiconformal mappings numerical methods are outlined and their practical application are described

scholarly journals NUMERICAL MODELING OF GAS TURBINE COOLED BLADES

Aviation ◽  
2005 ◽  
Vol 9 (3) ◽  
pp. 9-18
Author(s):  
Arif Pashayev ◽  
Djakhangir Askerov ◽  
Ramiz Ali Cabar oqlu Sadiqov
Keyword(s):  
Numerical Modeling ◽  
Temperature Field ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Gas Turbine ◽  
Point Of View ◽  
Theoretical Substantiation ◽  
Stationary Temperature Field ◽  
Methods Of Calculation ◽  
Effective Combination

In contrast to methods that do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasi‐stationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A. Ziqmound continuity modules have been received.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

scholarly journals Computation method of geometry die of stretch forming press

2018 ◽  
Vol 224 ◽  
pp. 04014
Author(s):  
Konstantin Bormotin ◽  
Win Aung
Keyword(s):  
Numerical Methods ◽  
Inverse Problems ◽  
Mathematical Models ◽  
Computation Method ◽  
Stretch Forming ◽  
Shell Forming ◽  
Punch Shape

Mathematical models and numerical methods for solving inverse problems of shell forming by means of stretching on a die have been developed. The algorithms implemented in MSC.Marc allow to calculate the required punch shape. The results of simulation of the stretching technology are presented.

Numerical Methods for Mathematical Models of Heterogeneous Catalytic Fixed Bed Chemical Reactors

2012 ◽  
Vol 11 (1) ◽  
pp. 49-64
Author(s):  
P. D. Devika ◽  
P. A. Dinesh ◽  
G. Padmavathi ◽  
Rama Krishna Prasad
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Fixed Bed ◽  
Differential Algebraic Equations ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Chemical Reactors ◽  
Catalytic Systems ◽  
Heterogeneous Catalytic ◽  
Catalytic Material

Mathematical modeling of chemical reactors is of immense interest and of enormous use in the chemical industries. The detailed modeling of heterogeneous catalytic systems is challenging because of the unknown nature of new catalytic material and also the transient behavior of such catalytic systems. The solution of mathematical models can be used to understand the interested physical systems. In addition, the solution can also be used to predict the unknown values which would have been otherwise obtained by conducting the actual experiments. Such solutions of the mathematical models involving ordinary/partial, linear/non-linear, differential/algebraic equations can be determined by using suitable analytical or numerical methods. The present work involves the development of mathematical methods and models to increase the understanding between the model parameters and also to decrease the number of laboratory experiments. In view of this, a detailed modeling of heterogeneous catalytic chemical reactor systems has been considered for the present study.

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