Stress distributions in an elastic body due to molecular interactions considering one-dimensional periodic material distribution based on Mindlin’s solution

2019 ◽  
Vol 26 (1) ◽  
pp. 139-156 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Toshiki Otani ◽  
Shigehisa Fukui
Keyword(s):  
Elastic Body ◽  
Molecular Interactions ◽  
Material Distribution ◽  
Stress Distributions ◽  
One Dimensional

Stress Distributions in an Elastic Body due to Molecular Interactions Considering One-Dimensional Periodic Material Distribution Based on Mindlin Solution

2018 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Toshiki Otani ◽  
Shigehisa Fukui
Keyword(s):  
Stress Distribution ◽  
Elastic Body ◽  
Molecular Interactions ◽  
Material Distribution ◽  
Stress Distributions ◽  
One Dimensional ◽  
Calculation Results ◽  
Basic Characteristics ◽  
The One

A method to calculate the stress distributions in the elastic body caused by the molecular interactions has been established. The stress distribution was calculated based on the Mindlin’s solution considering the one-dimensional periodic material distribution. The calculation results for a distribution of two materials were presented. The basic characteristics of the stress distribution in the elastic body were quantitatively clarified.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Nonlinear vibrations of a one-dimensional elastic body

1967 ◽  
Vol 3 (3) ◽  
pp. 73-77
Author(s):  
R. F. Il'in ◽  
S. V. Kagadii
Keyword(s):  
Elastic Body ◽  
Nonlinear Vibrations ◽  
One Dimensional

Numerical Simulation of a Thermal Shock in an Elastic Body Considering Non-Locality Effects in the Medium

2020 ◽  
pp. 20-29
Author(s):  
I.Yu. Savelyeva
Keyword(s):  
Thermal Shock ◽  
Elastic Body ◽  
Numerical Solutions ◽  
Internal State ◽  
Temperature Fields ◽  
Stress Distributions ◽  
External Effects ◽  
Analytical Simulation ◽  
Wide Range ◽  
Non Locality

Creating mathematical simulations that allow material behaviour to be described for a wide range of variable external effects is an important stage of developing and utilising new structurally sensitive materials. At present, there exist several approaches to analytical simulation of materials featuring a complex internal structure. We used methods of generalized thermomechanics to derive constitutive equations for a mathematical model describing the temperature and dynamic stress distributions for the case of a thermal shock on the surface of an elastic body, taking spatial non-locality into account. We employed a medium model featuring internal state parameters to describe the process of non-steady-state thermal conductivity. The model proposed makes it possible to account for the spatial and temporal non-locality effects found in structurally sensitive materials; this may be used in further investigations of temperature fields and stresses occurring in structural elements as a result of various external effects. We propose an algorithm for developing numerical solutions based on a Galerkin finite element method. The paper presents temperature field and stress computations for a one-dimensional problem and analyses the effect the non-locality parameters have on these solutions

Impact of Elastic Body on the Deep and Shallow Water

2013 ◽  
Author(s):  
Alexander A. Korobkin ◽  
Tatyana I. Khabakhpasheva
Keyword(s):  
Shallow Water ◽  
Elastic Body ◽  
Water Depth ◽  
The Body ◽  
Complex Structures ◽  
Water Impact ◽  
One Dimensional ◽  
Mode Method ◽  
Bending Stresses ◽  
The Impact

Two-dimensional unsteady problem of elastic body impact on liquid free surface is considered. The water is either of infinite depth or shallow. We are concerned with the effect of the water depth on the bending stresses in the structure caused by the fluid-structure interaction. The Wagner model is used for infinite water depth. In the case of shallow water impact, the hydrodynamic problem is one-dimensional but nonlinear. Both problems for deep and shallow waters are solved numerically by the normal mode method. Two shapes of the body, cylindrical shell and elastic wedge, are considered. The impact conditions and the structural characteristic are identical. The bending stresses in the structure are investigated. It is shown that the bending stresses for impact on shallow water are greater than those for the infinite water depth. The developed methods and approaches can be combined with FFM to include complex structures.

Effective Static and Dynamic Finite Element Modeling of a Double Swept Composite Rotor Blade

2020 ◽  
Vol 65 (3) ◽  
pp. 1-12 ◽  
Author(s):  
Matteo Filippi ◽  
Enrico Zappino ◽  
Erasmo Carrera ◽  
Bruno Castanié
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Stress Distributions ◽  
One Dimensional ◽  
Helicopter Blades ◽  
Mechanical Responses ◽  
Solid Finite Elements ◽  
The One ◽  
Complicated Geometries

The paper concerns mechanical responses of helicopter blades made of composite materials. Structures with complicated geometries are modeled by using both beam and solid finite elements. The adopted one-dimensional kinematics only encompasses pure displacements; therefore, the connection with three-dimensional elements can be carried out with ease. Contributions to elastic and inertial matrices deriving from nodes shared by beams and solids are merely summed together through a standard assembling procedure. Stress, free vibration, and time response analyses have been performed on different configurations. A straight metallic rotating structure and a swept-tip blade made of an orthotropic material have been considered for verification and validation purposes. Current results have been compared with experimental data and numerical solutions available in the literature. Furthermore, a straight and a double-swept blade with a realistic airfoil have been studied. For the straight configuration, the one-dimensional results have been compared with finite element solutions obtained with commercial software. The methodology enabled complicated stress distributions and coupling phenomena to be predicted with reasonable accuracy and affordable computational efforts.

Analysis of stresses in elastic body due to molecular interactions with periodic distribution

2018 ◽  
Vol 2018.56 (0) ◽  
pp. 309
Author(s):  
Toshiki OTANI ◽  
Satoru MAEGAWA ◽  
Hiroshige MATSUOKA ◽  
Shigehisa FUKUI
Keyword(s):  
Elastic Body ◽  
Molecular Interactions ◽  
Periodic Distribution
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