The shape and orientation of the minimum strain energy of coherent ellipsoidal precipitate in an anisotropic cubic material

1995 ◽  
Vol 43 (12) ◽  
pp. 4495-4503 ◽  
Author(s):  
I.S. Suh ◽  
J.K. Park
Keyword(s):  
Strain Energy ◽  
Minimum Strain Energy

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.

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].

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.

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.

Optimization Research on Geometric Parameters of Scallop-Shaped Lattice Shells

2015 ◽  
Vol 724 ◽  
pp. 192-196
Author(s):  
Na Li ◽  
Ren An Chang ◽  
Wei Zong ◽  
Qi Hang Yu
Keyword(s):  
Mechanical Properties ◽  
Strain Energy ◽  
Geometric Parameters ◽  
Free Form ◽  
Spatial Structures ◽  
Shaped Surface ◽  
Minimum Strain Energy ◽  
Optimal Values ◽  
Lattice Shells

<p>Free-form and bionic spatial shells are popular in the area of spatial structures. Scallop-shaped surface is the product of evolution and a kind of spatial shells that can satisfy the mechanical requirements. Based on the scallop-shaped lattice shells, this paper focused on the optimization of geometric parameters. The principle of minimum strain energy was applied to conclude the influence law of the geometric parameters on mechanical properties. Finally the optimal values of geometric parameters were obtained. The results show that the optimization of geometric parameters presents the integrated significance to improve scallop-shaped lattice shells.</p>

A Minimum Strain Energy Approach for Obtaining Optimal Unbalance Distribution in Flexible Rotors

1982 ◽  
Vol 104 (4) ◽  
pp. 875-880 ◽  
Author(s):  
T. F. Conry ◽  
P. R. Goglia ◽  
C. Cusano
Keyword(s):  
Strain Energy ◽  
Critical Speed ◽  
Optimization Problem ◽  
Equations Of Motion ◽  
Rotor System ◽  
Quadratic Program ◽  
Unique Minimum ◽  
Flexible Rotors ◽  
Minimum Strain Energy ◽  
Selection Of

A method is developed to design for optimal unbalance distribution in a rotor system which has elements that are assembled on the shaft and operates above the first critical speed. This method can also be used for computing the optimal selection of balance weights in specified planes for a rotor with a known distribution of unbalance—the classic balancing problem. The method is an optimization problem where the strain energy of the rotor and its supports are minimized subject to the constraints of the equations of motion of the rotor system at a particular balancing speed. The problem is a quadratic program that has a unique minimum.

A Framework for Energy-Based Kinetostatic Modeling of Compliant Mechanisms

2017 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Minimum Strain Energy ◽  
Constraint Model ◽  
Future Work

Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano’s first theorem and the Crotti-Engesser theorem, which don’t require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of using Castigliano’s first theorem and the Crotti-Engesser theorem with the explicit formulations in this framework. Future work will be focused on incorporating use of the principle of minimum strain energy and the principle of minimum complementary strain energy.

scholarly journals Effects of Fibre Architecture on Deformation during Preform Manufacture

1999 ◽  
Vol 8 (6) ◽  
pp. 096369359900800 ◽  
Author(s):  
A.C. Long ◽  
B.J. Souter ◽  
F. Robitaille ◽  
C.D. Rudd
Keyword(s):  
Strain Energy ◽  
Geometric Model ◽  
Knitted Fabrics ◽  
Fabric Deformation ◽  
Kinematic Mapping ◽  
Forming Characteristics ◽  
Minimum Strain Energy ◽  
Draping Simulation ◽  
Fabric Construction ◽  
Shear Strain Energy

Simulations of fabric deformation during preform manufacture are usually based on a kinematic mapping of the fibres onto the component. Whilst this approach can anticipate excessive deformation, it takes no account of the effect of fabric construction on subsequent forming characteristics. The aim of this study is to establish a relationship between fibre architecture and formability, and to incorporate this within an enhanced draping simulation. The approach utilises a geometric model for woven or warp-knitted fabrics, which forms the basis of a mechanical model for fabric deformation. The model is then used to determine the shear strain energy required to produce a particular draped fibre pattern. This is implemented within an iterative procedure to determine the draped pattern resulting in minimum strain energy. The results compare favourably with experiments for hemispherical preforms, where initial fabric construction is shown to have a significant effect on the resulting fibre orientations.

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