Application of Vector Calculus to Numerical Simulation of Continuum Mechanics Problems

2001 ◽  
Vol 167 (1) ◽  
pp. 22-38 ◽  
Author(s):  
Nicholas M. Bessonov ◽  
Dong Joo Song
Keyword(s):  
Numerical Simulation ◽  
Continuum Mechanics ◽  
Vector Calculus

Fractional Vector Calculus and Fractional Continuum Mechanics

2016 ◽  
Vol 2 (2) ◽  
pp. 85-104 ◽  
Author(s):  
Konstantinos A. Lazopoulos ◽  
Anastasios A. Lazopoulos
Keyword(s):  
Continuum Mechanics ◽  
Vector Calculus ◽  
Fractional Continuum

A Theory of Fracture Based Upon an Extension of Continuum Mechanics to the Nanoscale

2005 ◽  
Vol 73 (5) ◽  
pp. 792-798 ◽  
Author(s):  
Eun-Suok Oh ◽  
Jay R. Walton ◽  
John C. Slattery
Keyword(s):  
Numerical Simulation ◽  
Long Range ◽  
Continuum Mechanics ◽  
Bulk Material ◽  
Stress Singularity ◽  
Intermolecular Forces ◽  
Square Root ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Root Stress

A theory of fracture is presented that is based upon an extension of continuum mechanics to the nanoscale through the incorporation of long-range intermolecular forces which correct bulk material descriptions near interfaces. The surface energy on crack surfaces, which is given in terms of the long-range intermolecular forces, plays an important role in an expression for the stress distribution near the crack tip. It is observed through numerical simulation that the incorporation of these long-range intermolecular forces removes the square-root stress singularity predicted by classical linear elastic fracture mechanics.

scholarly journals О постановке экспериментов по определению пробивной способности хвостовых участков кумулятивных струй

2021 ◽  
Vol 91 (5) ◽  
pp. 793
Author(s):  
С.В. Федоров
Keyword(s):  
Numerical Simulation ◽  
Continuum Mechanics ◽  
Short Distance ◽  
Axisymmetric Problem ◽  
High Strength ◽  
Shaped Charge ◽  
Two Dimensional ◽  
Penetration Effect ◽  
Steel Target ◽  
Shaped Charge Jet

According to the calculations, the penetration effect of shaped charges can be significantly increased (by 40–50 % in the case of a high-strength steel target) if due increasing the accuracy of their manufacture the lower speed threshold is reduced at which the penetration of the tail sections of the shaped-charge jet into the target is stopped. For experimental confirmation of these data, it is proposed to study in detail the penetrability of the tail sections of shaped-charge jets using cut-off rods made of high-density material located at a short distance from the shaped charge (less than its diameter) and designed to eliminate the faster part of the jet. Based on numerical simulation in the framework of a two-dimensional axisymmetric problem of continuum mechanics, possible parameters of the cut-off rods for generating solitary "tails" of shaped-charge jets with different velocities of the leading element are predicted.

scholarly journals Developing a module to convert OpenFOAM computational meshes to the msh format

2021 ◽  
Vol 2094 (3) ◽  
pp. 032022
Author(s):  
D Chitalov
Keyword(s):  
Numerical Simulation ◽  
Continuum Mechanics ◽  
Performance Test ◽  
Technical Support ◽  
Practical Significance ◽  
Ansys Fluent

Abstract The paper reveals the features of developing an application for conversion of computational meshes built in OpenFOAM to the msh format applied for numerical simulation of continuum mechanics (CM) problems with the ANSYS FLUENT platform. Some companies apply this platform in parallel with OpenFOAM that requires a mesh conversion module. Although there are program tools capable to solve this problem, their application involves some difficulties, mainly the necessity to pay for a license, absence of complete documentation, paid technical support. Thus, the described problem is actual and its solution – developing a conversion module – is the study purpose. The article discloses features of the OpenFOAM utility for conversion, a list of technologies to develop a module, module action, results of its performance test using a CM problem. The study findings are statements of scientific novelty and expected practical significance.

scholarly journals A primer on exterior differential calculus

2003 ◽  
pp. 85-162 ◽  
Author(s):  
D.A. Burton
Keyword(s):  
Continuum Mechanics ◽  
Differential Calculus ◽  
Differential Forms ◽  
Lie Derivative ◽  
Exterior Differential ◽  
Exterior Calculus ◽  
Vector Calculus ◽  
Exterior Forms ◽  
Pedagogical Application

A pedagogical application-oriented introduction to the cal?culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con?nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi?tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma?chinery, are stressed throughout the article. .

A First Course in Continuum Mechanics

2001 ◽  
Author(s):  
Oscar Gonzalez ◽  
Andrew M. Stuart
Keyword(s):  
Continuum Mechanics
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