Square Of Strain Research Articles

Experimental Investigation on Vortex Induced Vibration of Marine Risers with Different Wall Thicknesses

In this paper, the vortex-induced vibration experiment of the risers with different wall thicknesses in wave-flow combined water flume was carried out. The dynamic strain sensing technology was adopted. The sensitivity and micro evolution pattern of riser VIV response relative to wall thickness were examined by varying the wall thickness of various riser models, comparing the dimensionless root mean square of strain, vibration frequencies and trajectories by varying different wall thicknesses of the risers. The results indicate that the wall thickness does not have a large influence on the Strouhal numbers of the vibration of the risers, which are always around 0.18; the larger the wall thickness is, the earlier the lock-in region is jumped out, as wall thickness increases, the outflow velocity corresponding to the occurrence of an “8” or oblique “8” shape vibration trajectory continues to delay, and the velocity range for such trajectories gradually narrows.

Modes of grain growth and mechanism of dislocation reaction under applied biaxial strain: Atomistic and continuum modeling

The phase field crystal method and Continuum Modeling are applied to study the cooperative dislocation motion of the grain boundary (GB) migration, the manner of the nucleation of the grain and of the grain growth in two dimensions (2D) under the deviatoric deformation at high temperature. Three types of the nucleation modes of new finding are observed by the phase field crystal simulation: The first mode of the nucleation is generated by the GB splitting into two sub-GBs; the second mode is of the reaction of the sub-GB dislocations, such as, the generation and annihilation of a pair of partial Frank sessile dislocation in 2D. The process can be considered as the nucleation of dynamic recrystallization; the third mode is caused by two oncoming rows of the dislocations of these sub-GBs, crossing and passing each other to form new gap which is the nucleation place of the new deformed grain. The research is shown that due to the nucleation of different modes the mechanism of the grain growth by means of the sub-GB migration is different, and therefore, the grain growth rates are also different. Under the deviatoric deformation of the applied biaxial strain, the grain growth is faster than that of the grain growth without external applied stress. It is observed that the cooperative dislocation motion of the GB migration under the deviatoric deformation accompanies with local plastic flow and the state of the stress of the system changes sharply. When the system is in the process of recrystallized grain growth, the system energy is in an unstable state due to the release of the strain energy to cause that the reverse movement of the plastic flow occurs. The area growth of the deformed grain is approximately proportional to the strain square and also to the time square. The rule of the time square of the deformed grain growth can also be deduced by establishing the continuum dynamic equation of the biaxial strain-driven migration of the GB. The copper metal is taken as an example of the calculation, and the obtained result is a good agreement with that of the experiment.

Development the Fourier analysis method of x-ray diffraction to calculate variables in crystal structure as well as calculation of some lattice parameters

The Fourier method was developed to calculate other important variables in the crystalline structure, such a strain, which is equal to 7.4828 x 10−3 instead of the mean square strain and the energy density of the strain, which is equal to 2799614.7 dyne / cm2 and the stress equal to 7.4828 x 108 dyne/cm2. The results obtained from the Fourier method for calculating other parameters of the manganese oxide lattice for each peak of x-ray diffraction peaks such as the texture coefficient, its mean value equal to 0.99999 and the micro strains, which its mean value equal to 4.47 × 10−3 dislocation density, its mean value are equal to 37.3 (lines .m−2) and the specific surface area its mean value is equal to 19,58432 of crystalline volume. A comparison was also made between the values of the square of strain and the apparent strain.

STABILITY CHART FOR UNSUPPORTED SQUARE TUNNELS IN HOMOGENEOUS UNDRAINED CLAY

This short technical note investigates the stability of a plane strain square tunnel in homogeneous undrained clay using shear strength reduction technique. The finite difference program FLAC is used to determine the factor of safety for unsupported square tunnels where an automatic generation of program script is developed using FISH programming. This developed procedure enables parametric studies to be conducted in an effective way with great efficiency. Numerical results, expressed in term of factor of safety, are compared with published classical upper and lower bound limit solutions. The comparison between these two numerical methods finds a very good agreement and the confidence level of the current FLAC model has increased significantly. With the success of model validations, a number of stability design charts for square tunnels using dimensionless ratios are presented for practical scenarios in a similar way to Taylor's slope stability charts. Examples are illustrated to show the potential usefulness of the produced design charts for practicing engineers.

An optimal flattening algorithm for ship hull plate fabricated by thermal forming

Normally, ship hull plates contain compound curvature distributions and they can only be fabricated by integrating mechanical rolling with bending and following them with regional heating to achieve required configuration. This paper mainly proposes a comprehensive flattening process to determine optimal planar shape, shrinkage strain distribution and mapping relation for three typical ship hull plates by thermal forming, which practically benefit for automatic forming. An innovative geometric method is first presented to obtain initial planar approximation and strain square sum subject to negative principal strain constraints within each element from planar to desired surface is formulated based on nonlinear kinetic analysis. Then, we employ area equivalent method through transforming spatial quadrilateral into planar quadrilateral to simplify optimization model. Finally, initial planar approximations are regarded as iteration initial points to solve the model based on sequential quadratic programming. The results indicate that the proposed process can effectively achieve optimal planar shape, mapping relation and negative principal strain to help achieve all heating paths and heat source parameters at one time, thus automation.

Effective Young's modulus for a spatially variable soil mass subjected to a simple stress state

ABSTRACTThe effect of spatial variability on the effective Young's modulus of a soil mass is investigated. The soil mass is a two-dimensional plane strain square domain subjected to a simple stress state, with Young's modulus being modelled as a stationary lognormal random field. The effective Young's modulus is simulated by random field finite-element analysis. It is found that under the condition of horizontal scale of fluctuation (SOF) = vertical SOF, the effective Young's modulus can be satisfactorily approximated as the geometric average over the square domain. However, the conclusion changes dramatically when the spatial variability is highly anisotropic, e.g. horizontal scale vertical SOF. In this case, the effective Young's modulus can be approximated as the arithmetic average or harmonic average, depending on the direction of loading. A unified spatial averaging model is further proposed in this study. It is shown that the effective Young's modulus can be satisfactorily approximated by this unified model without the need to switch among arithmetic, geometric and harmonic averages.

Undrained stability of a square tunnel where the shear strength increases linearly with depth

This paper investigates the stability of a plane strain square tunnel in undrained clay, where the shear strength profile increases linearly with depth. The stability for a range of tunnel geometries and soil conditions are found using rigid-block upper bound methods as well as finite element limit analysis. The latter procedures employ a discrete form of the bound theorems of classical plasticity, use a bespoke conic programming scheme to solve the resulting optimisation problems, and bracket the true collapse load with upper and lower bound solutions to within 5% for all the cases considered. Results from the parametric study are summarised in the form of stability charts. An approximate closed-form expression is developed for use by practising engineers.

Atmospheric forcing of the Beaufort Sea ice gyre: Surface‐stratosphere coupling

In a companion article we examined the nature of correspondence between synoptic weather patterns and reversals in the Beaufort Sea ice gyre. In this paper we extend this analysis to examine the role of stratospheric forcing on surface phenomena. Investigated in particular is the correspondence between reversals in stratospheric winds at 10 mbar during winter as defined by stratospheric sudden warmings (SSW) and mean sea level pressure synoptic types in the Beaufort Sea region. Connections between stratospheric and surface events are characterized using relative vorticity and the square of strain computed at different pressure levels from the stratosphere to the surface in the Beaufort Sea region. We quantify the correspondence between stratospheric flow and surface phenomena through investigation of the frequency in synoptic types derived in a companion article during stratospheric sudden warming events. Investigation of stratospheric wind gradients averaged over the Beaufort Sea region demonstrates a prevalence in anticyclonic activity during SSWs that persists for approximately 20 days. Examination of the evolution in synoptic types in the Beaufort Sea region also shows an increase in the number of synoptic types associated with anticyclonic activity during SSWs.

Fundamental laws of fracture region of solids

AbstractThe present paper reports that the deformation is statistically symmetric even in the fracture region of solids. The major factor in the fracture region of brittle solids is the creation of new surfaces. On the basis of the creation of new surfaces, four fundamental laws are derived for the fracture region of brittle solids. These laws are: (i) New surfaces are created only after a particular strain of the crystal. (ii) For the smaller values of compressive strain, the area of newly created surfaces is directly proportional to the square of the strain. (iii) The proportionality constant between the area of the newly created surfaces and the square of strain may be termed as fracture constant. Mathematically the fracture constant is the area of newly created surface for unit compressive strain of the crystal. (iv) For larger values of the compressive strain, the logarithm of newly created surfaces is directly proportional to the strain. The experimental verification of the laws of fracture region of solids are discussed. The value of fracture constant of certain solids are estimated and their significance is discussed.