The Determination of Stresses and Temperatures in Cooling Bodies by Finite Elements

1976 ◽  
Vol 98 (3) ◽  
pp. 478-484 ◽  
Author(s):  
R. W. Lewis ◽  
B. R. Bass
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Physical And Mechanical Properties ◽  
Complex Geometries ◽  
Linear Boundary ◽  
Non Linear

This paper presents a finite element method for solving non-linear heat conduction and thermal stress problems. The nonlinearity is caused by the variation of thermo-physical and mechanical properties of the material with respect to temperature. The distribution of temperature and stress in a cooling body can be followed from the onset of solidification. The method is capable of handling complex geometries and initial non-linear boundary conditions.

Simultaneous Determination of Steady Temperatures and Heat Fluxes on Surfaces of Three Dimensional Objects Using FEM

2001 ◽  
Author(s):  
Brian H. Dennis ◽  
George S. Dulikravich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Multiply Connected ◽  
Three Dimensional Objects ◽  
Solid Objects ◽  
System Solution

Abstract A finite element method (FEM) formulation is presented for the prediction of unknown steady boundary conditions in heat conduction on multiply connected three-dimensional solid objects. The present FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-specified on other boundaries. Details of the discretization, linear system solution techniques, regularization, and sample results for 3-D problems are presented.

scholarly journals Specific solution of problem of water filtering in the rocks by the finite element method

2019 ◽  
Vol 109 ◽  
pp. 00093 ◽  
Author(s):  
Olena Slashchova ◽  
Ihor Slashchov ◽  
Iryna Sapunova
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Strain State ◽  
Water Saturation ◽  
Physical And Mechanical Properties ◽  
Critical Parameters ◽  
The Finite Element Method ◽  
Water Saturated ◽  
Element Method

The article is devoted to development of methods for geofiltration calculations with taking into account peculiarities of changes of the rock physical and mechanical properties at water saturation. Methods: mathematical modeling of geomechanical and filtration processes with the help of finite element method and laboratory and underground studies. A mathematical model was formulated for solving a problem of elasticity theory by the finite element method, which took into account peculiarities of water-saturated rocks. Pattern of stress-strain state changing in the fractured water-saturated rocks under the action of critical loads, which occurred around the preparatory roadways during their operation, were established. In order to solve the filtration problems, a bank of collected initial data on physical and mechanical properties of water-saturated rocks was processed with the help of variation coefficients, which were taken into account by the method, which assumed calculation of the model loading with critical parameters.

scholarly journals A New Approach of Mathematical Analysis of Structure of Graphene as a Potential Material for Composites

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 3918
Author(s):  
Mieczysław Jaroniek ◽  
Leszek Czechowski ◽  
Łukasz Kaczmarek ◽  
Tomasz Warga ◽  
Tomasz Kubiak
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Graphene Sheets ◽  
Superposition Method ◽  
Plane Model ◽  
New Approach ◽  
Element Method

The new analysis of a simplified plane model of single-layered graphene is presented in this work as a potential material for reinforcement in ultralight and durable composites. However, owing to the clear literature discrepancies regarding the mechanical properties of graphene, it is extremely difficult to conduct any numerical analysis to design parts of machines and devices made of composites. Therefore, it is necessary to first systemize the analytical and finite element method (FEM) calculations, which will synergize mathematical models, used in the analysis of mechanical properties of graphene sheets, with the very nature of the chemical bond. For this reason, the considered model is a hexagonal mesh simulating the bonds between carbon atoms in graphene. The determination of mechanical properties of graphene was solved using the superposition method and finite element method. The calculation of the graphene tension was performed for two main directions of the graphene arrangement: armchair and zigzag. The computed results were verified and referred to articles and papers in the accessible literature. It was stated that in unloaded flake of graphene, the equilibrium of forces exists; however, owing to changes of inter-atom distance, the inner forces occur, which are responsible for the appearance of strains.

A Three-Dimensional Finite Element Method for Nonsteady State Temperature Distribution in the Rolling Process

2011 ◽  
Vol 101-102 ◽  
pp. 521-524
Author(s):  
Shu Ni Song ◽  
Jing Yi Liu
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Temperature Distribution ◽  
Three Dimensional ◽  
Rolling Process ◽  
Linear Boundary ◽  
Linear Boundary Condition ◽  
Non Linear ◽  
Metal Deformation

The temperature is a key factor that affects the metal deformation and the material property in the rolling process. The metal deformation is often carried along with the variety of temperature. Moreover, the plastic work is converted into the thermal energy during the process of the metal deformation. Therefore, the numerical simulation of the rolling process should take the temperature factors into consideration to improve the prediction accuracy. In this paper, we use the full three-dimensional Rigid-plastic finite element method to predict the temperature distribution which relate to linear or non-linear boundary condition of the free surface. Based on the simulation, the impact of radiant heat-transfer coefficient on the temperature prediction can be obtained. The comparison of the calculated results between the linear and non-linear boundary conditions demonstrates that the temperature obtained on the linear boundary condition has higher accurateness than that obtained on the non-linear boundary condition.

Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries

1999 ◽  
Vol 121 (3) ◽  
pp. 537-545 ◽  
Author(s):  
B. H. Dennis ◽  
G. S. Dulikravich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Linear System ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
System Solution ◽  
Method Formulation ◽  
Element Method

A finite element method formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and combined thermoelasticity continuum problems is presented. The present finite element method formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently overspecified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for two-dimensional problems are presented.

EFFECT OF MECHANICAL PROPERTIES OF THE SUBSTRATE TISSUES ON THE DETERMINATION OF ELASTIC MODULUS OF THE SCLERA USING INDENTATION TEST

2016 ◽  
Vol 16 (07) ◽  
pp. 1650085
Author(s):  
XIUQING QIAN ◽  
KUNYA ZHANG ◽  
ZHICHENG LIU
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Elastic Moduli ◽  
Indentation Depth ◽  
Vitreous Body ◽  
Indentation Test ◽  
Posterior Pole

The sclera is an important connective tissue that protects the sensitive layers within the eyeball. Identifying the mechanical properties of the sclera near the posterior pole is necessary to analyze the deformation of the sclera and stresses changing in the optic nerve head tissues. We propose a method to determine the mechanical properties of the sclera using dimensional analysis, finite element method and the indentation test. The elastic moduli of the sclera for different indentation depths and positions were identified. We found that the elastic moduli of the sclera varied with indentation depth. This was due to the effect of the mechanical properties of the substrate tissues inside the sclera. The elastic modulus of the choroid had the biggest effect on the determination of elastic modulus of the sclera, whereas that of the vitreous body could be ignored when the ratio of the indentation depth to the thickness of the sclera was less than 0.5. The effects of mechanical properties of the substrate tissues become more pronounced at greater indentation depths.

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