Prediction of Cylinder Flow Pressures in Mass-Flow Bins Using Minimum Strain Energy

1976 ◽  
Vol 98 (4) ◽  
pp. 1370-1374 ◽  
Author(s):  
A. G. McLean ◽  
P. C. Arnold
Keyword(s):  
Mass Flow ◽  
Strain Energy ◽  
Plane Flow ◽  
Geometry Design ◽  
Numerical Effort ◽  
Minimum Strain Energy ◽  
Flow Pressure ◽  
Energy Theory ◽  
Cylinder Flow ◽  
Complete Variation

Jenike, et al. [1] have presented a minimum strain energy theory to predict cylinder flow pressures in mass-flow bins. The complete variation of strain energy pressures is depicted by bounds requiring considerable numerical effort to develop for a specific cylinder geometry. Design charts are presented, but these are available for only two circular cylinder geometries. This paper summarizes and clarifies the minimum strain energy theory for predicting cylinder flow pressures. A single bound approximation which allows the magnitude of the peak flow pressure to be determined for both axisymmetric and plane flow cylinders is presented. This peak pressure may also be estimated by a single calculation of strain energy pressure. The usefulness and accuracy of these procedures are illustrated by reworking the example presented by Jenike, et al. [1].

scholarly journals Mass Flow, Pressure Drop, and Leakage Dependent Modeling and Characterization of Solar Air Collectors

2014 ◽  
Vol 48 ◽  
pp. 250-263 ◽  
Author(s):  
Christian Welz ◽  
Christoph Maurer ◽  
Paolo Di Lauro ◽  
Gerhard Stryi-Hipp ◽  
Michael Hermann
Keyword(s):  
Pressure Drop ◽  
Mass Flow ◽  
Flow Pressure

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

Recent Results on the Elasticity Theory of Inclusions

1994 ◽  
Vol 47 (1S) ◽  
pp. S10-S17 ◽  
Author(s):  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Composite Materials ◽  
Work Hardening ◽  
Strain Energy ◽  
Volume Fraction ◽  
Exact Formula ◽  
Stress And Strain ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Work Hardening Rate ◽  
Minimum Strain Energy

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.

Exploration of Local Blade Motions During Blade Shaping for Thick Layered Foam Cutting

2004 ◽  
Author(s):  
J. J. Broek ◽  
A. Kooijman
Keyword(s):  
Strain Energy ◽  
Cutting Tool ◽  
Cutting Speed ◽  
General Rule ◽  
Free Form ◽  
Linear Change ◽  
Minimum Strain Energy ◽  
Blade Cutting ◽  
Tool Position ◽  
Cutting Direction

The FF-TLOM (Free Form Thick Layered Object Manufacturing) technology is a Rapid Prototyping process based on flexible blade cutting of polystyrene foam. The heated blade is shaped by three parameters, which allows an infinite amount of minimum strain energy blade shapes with none, one or two inflexions. In the shaping domain stable and unstable blade shapes can exist. Stable shapes are defined as curves with none and one-inflexion and are applied for operational cutting of foam layers with the FF-TLOM technology. The tool motions are generated from the static tool poses and are calculated for a linear change of the flexible blade, when the cutting tool moves from one tool position to the next. The cutting blade is positioned to the foam slab with help of a point relative positioned on the flexible blade. The tool frame is positioned with a point fixed relatively to the tool frame. During the tool motions the blade curvature is changed and will introduce a shift of the half way point fixed on the blade (especially in the case of asymmetrical support inclinations and high curvature). Next the local displacement of the blade points in the bending plane of the blade due to blade shaping and tool pitching are quantified during the tool motions. These displacements induce an angle of attack of the blade in cutting direction, and will influence cutting speed and cutting accuracy. The quantification software is developed and will be used in the future for an overall prediction of the total tool curve displacements due to blade shaping, such as roll, pitch, yaw and linear positioning motions of the tool. A general rule for FF-TLOM cutting is minimization of all tool motions, which are not related to the forward cutting motion.

Directional Coarsening of γ′ Phase Induced by Phase Transformation Stress

2005 ◽  
Vol 20 (9) ◽  
pp. 2314-2321 ◽  
Author(s):  
K. Zhao ◽  
Y.H. Ma ◽  
L.H. Lou ◽  
Z.Q. Hu
Keyword(s):  
Free Energy ◽  
Phase Transformation ◽  
Uniform Distribution ◽  
Strain Energy ◽  
Coherency Strain ◽  
Preferential Direction ◽  
Nickel Based Superalloy ◽  
Directional Coarsening ◽  
Energy Theory ◽  
Transformation Stress

It was found that directional coarsening was induced by phase transformation stress due to non-uniform distribution of μ phase in an experimental nickel-based superalloy. The mechanism based on the existing diffusion and coherency strain energy theory has been discussed. It was concluded that directional coarsening was the course of dissolving of γ′ portion with high free energy, diffusing and growing on the existed γ′ particles along a preferential direction.

On Energy Strength Theories for Geomaterials

2013 ◽  
Vol 353-356 ◽  
pp. 901-904
Author(s):  
Shou Yi Xue
Keyword(s):  
Energy Density ◽  
Shear Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Volumetric Strain ◽  
Dissipated Energy ◽  
Energy Theory ◽  
Shear Strain Energy ◽  
Shear Energy ◽  
Strain Energy Density Theory

The composition of the energy in the process of material deformation and failure and the relationship between energy and strength were summarized; the features, essences and main problems of the energy release rate theory, the three-shear energy theory and the net shear strain energy density theory were illustrated. It is pointed out that the roles of distortion strain energy, volumetric strain energy and dissipated energy are not identical, especially distortion strain energy and volumetric strain energy must be separately processed. The three-shear energy theory and the net shear strain energy density theory can properly deal with the problems, and also well reflect the intermediate principal stress effect. The above research results can provide references for further discussions.

Fracture of aluminum-epoxy layered composites containing cracks

1982 ◽  
Vol 17 (2) ◽  
pp. 75-78 ◽  
Author(s):  
E E Gdoutos
Keyword(s):  
Composite Plate ◽  
Strain Energy ◽  
Crack Extension ◽  
Critical Value ◽  
Layered Composites ◽  
Parallel Cracks ◽  
Two Parallel Cracks ◽  
Minimum Strain Energy ◽  
Uniaxial Compressive Stress ◽  
Strain Energy Density Theory

The plane problem of a composite plate consisting of two aluminum half-planes bonded together through an epoxy layer and containing two parallel cracks, one in the layer and the other in one of the half-planes was considered. The composite plate was loaded by a uniform uniaxial compressive stress distribution applied along the surfaces of the crack of either the layer or the half-plane. The critical value of the applied stress as well as the corresponding angle for crack extension were determined by using the minimum strain energy density theory. Valuable results governing the dependence of the critical failure stress of the composite plate as well as the angle of crack extension from the more vulnerable crack on the geometry of the plate were derived.

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