DEFORMATION ANALYSIS by ENERGY METHOD USING SERIES VELOCITY FIELD

1993 ◽  
pp. 949-956
Author(s):  
Tomoyuki Wada
Keyword(s):  
Velocity Field ◽  
Energy Method ◽  
Deformation Analysis

scholarly journals Blow-up criterion for the density dependent inviscid Boussinesq equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Li Li ◽  
Yanping Zhou
Keyword(s):  
Velocity Field ◽  
Energy Method ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Boussinesq Equations ◽  
Smooth Solutions ◽  
Density Dependent ◽  
Priori Estimates ◽  
Blow Up Criterion

Abstract In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in $\mathbb{R}^{N}\ (N\geq 2)$ R N ( N ≥ 2 ) . By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq equations. Our result extends the known blow-up criteria.

Estimation of Dynamic Forces in Very High-Speed Impact Forging

1966 ◽  
Vol 88 (4) ◽  
pp. 369-372 ◽  
Author(s):  
M. J. Hillier
Keyword(s):  
Approximate Solution ◽  
Velocity Field ◽  
Plane Strain ◽  
Energy Method ◽  
Coulomb Friction ◽  
High Speed ◽  
Admissible Velocity ◽  
High Speed Impact ◽  
Dynamic Forces ◽  
Very High

A study is made of three methods of estimating die loads in impact forging: By approximate solution of the equations of equilibrium; by an energy method, assuming plane sections remain plane; and using the energy method in association with a kinematically admissible velocity field. Results are given for die pressures and die loads for axisymmetric and plane-strain forging of disks and slabs with smooth dies, perfectly rough dies, and for the case of Coulomb friction.

scholarly journals Machining Deformation Analysis of Aircraft Monolithic Components based on the Energy Method

2021 ◽  
Author(s):  
Xiaoming Huang ◽  
Xiaoliang Liu ◽  
Jiaxing Li ◽  
Yongbin Chen ◽  
Dechen Wei ◽  
...  
Keyword(s):  
Initial Stress ◽  
Analytical Model ◽  
Energy Method ◽  
Fem Simulation ◽  
Deformation Energy ◽  
Deformation Analysis ◽  
Layer By Layer ◽  
Theoretical Approaches ◽  
Machining Deformation ◽  
Monolithic Components

Abstract In the process of machining aircraft monolithic components, the initial stress in the blank will cause machining deformation. Based on the energy method, an analytical mathematical model of machining deformation is presented in this paper. The key point is to transform the energy in the removed material into the deformation energy of the part after machining. The initial residual stress of 7050-T7451 aluminum alloy blank and single frame part are used as investigated case in the analytical model. For layer by layer machining, the deformation evolution is closely related to the tensile or compressive properties of the initial stress of removed material. Combined with the change of neutral axis position, The machining deformation is calculated by theoretical model. Then, FEM simulation is carried out to analyze the influence of stiffening ribs on machining deformation utilizing the semi-analytical model of equivalent bending stiffness. Furthermore, experiments are set up to verify the validity of the theory and FEM data. The results indicate that the deformation results of the experiment are consistent with that of theory and FEM model. Deformation is determined by energy of removed material. This paper provides a novel theoretical approaches for the further investigation of this issue.

scholarly journals Machining Deformation Analysis of Aircraft Monolithic Components Based on the Energy Method

2021 ◽  
Author(s):  
Xiaoming Huang ◽  
Xiaoliang Liu ◽  
Weitao Sun ◽  
Jiaxing Li ◽  
Yongbin Chen ◽  
...  
Keyword(s):  
Initial Stress ◽  
Analytical Model ◽  
Energy Method ◽  
Fem Simulation ◽  
Deformation Energy ◽  
Deformation Analysis ◽  
Layer By Layer ◽  
Theoretical Approaches ◽  
Machining Deformation ◽  
Monolithic Components

Abstract In the process of machining aircraft monolithic components, the initial stress in the blank will cause machining deformation. Based on the energy method, an analytical mathematical model of machining deformation is presented in this paper. The key point is to transform the energy in the removed material into the deformation energy of the part after machining. The initial residual stress of 7050-T7451 aluminum alloy blank and single frame part are used as investigated case in the analytical model. For layer by layer machining, the deformation evolution is closely related to the tensile or compressive properties of the initial stress of removed material. Combined with the change of neutral axis position, The machining deformation is calculated by theoretical model. Then, FEM simulation is carried out to analyze the influence of stiffening ribs on machining deformation utilizing the semi-analytical model of equivalent bending stiffness. Furthermore, experiments are set up to verify the validity of the theory and FEM data. The results indicate that the deformation results of the experiment are consistent with that of theory and FEM model. Deformation is determined by energy of removed material. This paper provides a novel theoretical approaches for the further investigation of this issue.

scholarly journals Designing a kinematic module with rounding to model the processes of combined radial-longitudinal extrusion involving a tool whose configuration is complex

2021 ◽  
Vol 2 (1 (110)) ◽  
pp. 81-89
Author(s):  
Natalia Hrudkina ◽  
Igramotdin Aliiev ◽  
Oleg Markov ◽  
Iurii Savchenko ◽  
Liudmyla Sukhovirska ◽  
...  
Keyword(s):  
Velocity Field ◽  
Energy Method ◽  
Cutting Forces ◽  
Complex Form ◽  
Cold Extrusion ◽  
Preliminary Assessment ◽  
Industrial Implementation ◽  
Optimal Value ◽  
Estimation Scheme ◽  
Force Mode

It is advisable that parts whose shape is complex and which are made from solid or hollow blanks should be made by means of transverse and combined radial-longitudinal extrusion. The variation of manufacturing modes, tool configurations (in the form of chambers and rounding of the transitional sections of matrices) requires an adequate preliminary assessment of the force regime and the features of part shape formation. This paper has proposed a curvilinear kinematic module of the trapezoidal form for modeling radial-longitudinal extrusion processes in the presence of matrix rounding. Given the impossibility of using a quarter-circle boundary for the kinematically assigned possible velocity field, it has been proposed to use approximate curves in the form of z1(r) and z2(r). Taking into account the slightest deviation in the length of the arc of the approximate curve z1(r) and the area of the curvilinear trapezoid bounded by it relative to a quarter of the circle (not exceeding 0.8 % for any ratio), it has been recommended using this particular replacement. We have performed calculations of the value of the reduced deformation pressure inside the kinematic module with rounding taking into consideration the power of cutting forces at the border with adjacent kinematic modules. As an example, the devised module with rounding embedded in the estimation scheme of radial extrusion was analyzed. A significant impact of friction conditions on the force mode and the corresponding optimal value of the rounding radius have been identified. The resulting kinematic module makes it possible to expand the capabilities of the energy method for modeling cold extrusion processes involving the tools of complex form according to new deformation schemes. That could contribute to preparing recommendations on the optimal tool configuration and more active industrial implementation of these processes

Dynamic Deformation Analysis of a Red Blood Cell in Steady and Unsteady Shear Flows

2008 ◽  
Author(s):  
Sadao Bessho ◽  
Masanori Nakamura ◽  
Kenichirou Koshiyama ◽  
Shigeo Wada
Keyword(s):  
Velocity Field ◽  
Blood Cells ◽  
Predictive Accuracy ◽  
Dynamic Deformation ◽  
Artificial Organs ◽  
Deformation Analysis ◽  
Flow Conditions ◽  
Flow Velocity Field ◽  
Dynamical Deformation ◽  
Simple Flow

Quantitative evaluation of hemolysis, the breaking open of red blood cells (RBCs), is essential in designing artificial organs. Recently, numerical methods to quantify hemolysis from a measured or calculated macroscopic flow velocity field have been proposed [1]. Nevertheless, their predictive accuracy has not reached a satisfactory level required in practice. This would be because the conventional methods are mostly established based on the hemolysis tests under simple flow conditions and have not well considered deformation of RBCs. For further amelioration of the predictive accuracy, it would be necessary to take into account motion and dynamical deformation of individual RBCs in a flow field.

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