Thermal Stresses in Elastic Plates With Elliptic Holes

1974 ◽  
Vol 96 (3) ◽  
pp. 827-832 ◽  
Author(s):  
K. S. Rao ◽  
M. N. Bapu Rao ◽  
T. Ariman
Keyword(s):  
Temperature Distribution ◽  
Thermal Stresses ◽  
Elliptic Hole ◽  
Major Axis ◽  
Free Edge ◽  
Least Square ◽  
Elastic Plates ◽  
Edge Conditions ◽  
Method Of Least Square ◽  
Steady State Heat

The temperature and membrane stress distributions in an elastic square plate with an insulated central elliptic hole are investigated. The temperature varies along coordinates within the plane. The temperature distribution is determined as the solution of the steady state heat conduction equation, then the membrane stresses due to the temperature are analyzed. For both steps, the free edge conditions around the insulated elliptic hole as well as the boundary conditions at the fully restrained outer edges of the plate are satisfied at selected points by the method of least square point matching. The formulation is valid for any arbitrary orientation of the major axis of the elliptic hole. The numerical results for temperature distribution and membrane stresses are presented for two orientations and compared with the corresponding results for a circular hole.

Axisymmetric Elasticity Solutions of Spherical Shell Segments

1971 ◽  
Vol 38 (1) ◽  
pp. 197-208 ◽  
Author(s):  
H. S. Levine ◽  
J. M. Klosner
Keyword(s):  
Free Edge ◽  
External Pressure ◽  
Spherical Segment ◽  
Least Square ◽  
Shear Stresses ◽  
Spherical Surfaces ◽  
Edge Conditions ◽  
Layer Effect ◽  
Elasticity Solutions ◽  
Axisymmetric Elasticity

A series solution for the stresses and displacements of a spherical segment subjected to arbitrary axisymmetric surface tractions and edge boundary conditions is presented. A least-square point-matching technique is used to satisfy the specified edge conditions. The general solution for the axisymmetric case has been obtained by utilizing two sets of functions, namely, the Lure´ homogeneous functions and the full sphere functions used by Sternberg, Eubanks, and Sadowsky. In particular, solutions to the following problems have been obtained: (a) the spherical segment with a stress free edge subjected to a centrifugal force field; (b) the spherical segment subjected to an external pressure varying as cos2N θ supported on a rigid surface with no shear resistance; and (c) the hemisphere having zero traction on its spherical surfaces subjected to edge shear stresses. The results are presented in graphic form, which demonstrate the boundary-layer effect. Heretofore solutions to these types of problems have been obtained by using shell theory approximations.

Steady-State Thermal Stresses in Wedge-Shaped Cutting Tools

1975 ◽  
Vol 97 (3) ◽  
pp. 1060-1066
Author(s):  
P. F. Thomason
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Heat Conduction Problem ◽  
Equivalent Stress ◽  
Cutting Tools ◽  
Thermoelastic Stress ◽  
Plastic State ◽  
Steady State Heat

Closed form expressions for the steady-state thermal stresses in a π/2 wedge, subject to constant-temperature heat sources on the rake and flank contact segments, are obtained from a conformal mapping solution to the steady-state heat conduction problem. It is shown, following a theorem of Muskhelishvili, that the only nonzero thermal stress in the plane-strain wedge is that acting normal to the wedge plane. The thermal stress solutions are superimposed on a previously published isothermal cutting-load solution, to give the complete thermoelastic stress distribution at the wedge surfaces. The thermoelastic stresses are then used to determine the distribution of the equivalent stress, and this gives an indication of the regions on a cutting tool which are likely to be in the plastic state. The results are discussed in relation to the problems of flank wear and rakeface crater wear in metal cutting tools.

Application of High-Linearity Analog Optocoupler in DSP Acquisition Circuit

2012 ◽  
Vol 232 ◽  
pp. 944-948 ◽  
Author(s):  
Ying Qi Tan ◽  
Xiang Yang Liu ◽  
Bao Qing Den
Keyword(s):  
High Accuracy ◽  
Least Square ◽  
Experiment Data ◽  
Good Linearity ◽  
High Linearity ◽  
Analog Signals ◽  
Noisy Signals ◽  
Method Of Least Square ◽  
Proper Design ◽  
Hardware Circuit

An applied hardware circuit for detecting the AGC signals isolated with DSP is designed based on a high-linearity analog optocoupler. The problem of narrow measuring scope, low linearity and instability which caused by noisy signals is resolved when collects industrial analog signals into DSP. The practical circuit with proper design of components is designed through repeated experiments. The experiment data are analyzed by the method of least-square. The analyzed results show this circuit has the high accuracy and good linearity.

Thermal Stresses in Moderately Thick Elastic Plates

1959 ◽  
Vol 26 (3) ◽  
pp. 432-436
Author(s):  
B. E. Gatewood
Keyword(s):  
Temperature Gradient ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Elastic Plates ◽  
Plate Length ◽  
Moderately Thick Plates ◽  
Thick Elastic Plates ◽  
Thickness Variable

Abstract The three-dimensional stresses in the plate are investigated without using the plane-stress or plane-strain assumptions, the thickness of the plate being limited so that the normal stress in the thickness direction can be taken as a polynomial in the thickness variable. The temperature is taken as a polynomial in the thickness variable but with relatively large, though restricted, gradients with respect to the co-ordinates of the plane of the plate. For the case of the temperature constant in thickness variable, the stresses in the plane of the plate are presented as the plane-stress solution plus correcting terms due to the plate thickness, where the correcting terms involve the product of the temperature gradient and the ratio of the plate thickness to the plate length in the direction of the temperature gradient. In many cases the corrections are small even for moderately thick plates.

scholarly journals Numerical solution of acoustic scattering by finite perforated elastic plates

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150767 ◽  
Author(s):  
A. V. G. Cavalieri ◽  
W. R. Wolf ◽  
J. W. Jaworski
Keyword(s):  
Boundary Conditions ◽  
Acoustic Scattering ◽  
Free Edge ◽  
Solution Procedure ◽  
Sound Level ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Beneficial Effects ◽  
Plate Length ◽  
Radiated Sound

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

scholarly journals Determining the AMSR-E SST Footprint from Co-located MODIS SSTs

2018 ◽  
Author(s):  
Brahim Boussidi ◽  
Peter Cornillon ◽  
Gavino Puggioni ◽  
Chelle Gentemann
Keyword(s):  
Aspect Ratio ◽  
Ground Truth ◽  
Major Axis ◽  
Sampling Procedure ◽  
Least Square ◽  
Gaussian Kernel ◽  
Bootstrap Sampling ◽  
Semi Major Axis ◽  
Linear Inversion ◽  
Precise Knowledge

This study was undertaken to derive and analyze the Advanced Microwave Scanning Radiometer - EOS (AMSR-E) sea surface temperature (SST) footprint associated with the Remote Sensing Systems (RSS) Level-2 (L2) product. The footprint, in this case, is characterized by the weight attributed to each 4 4 km square contributing to the SST value of a given AMSR-E pixel. High-resolution L2 SST fields obtained from the MODerate-resolution Imaging Spectroradiometer (MODIS), carried on the same spacecraft as AMSR-E, are used as the sub-resolution “ground truth“ from which the AMSR-E footprint is determined. Mathematically, the approach is equivalent to a linear inversion problem, and its solution is pursued by means of a constrained least square approximation based on the bootstrap sampling procedure. The method yielded an elliptic-like Gaussian kernel with an aspect ratio 1.58, very close to the AMSR-E 6.93GHz channel aspect ratio, 1.7. (The 6.93GHz channel is the primary spectral frequency used to determine SST.) The semi-major axis of the estimated footprint is found to be alignedwith the instantaneous field-of-view of the sensor as expected fromthe geometric characteristics of AMSR-E. Footprintswere also analyzed year-by-year and as a function of latitude and found to be stable – no dependence on latitude or on time. Precise knowledge of the footprint is central for any satellite-derived product characterization and, in particular, for efforts to deconvolve the heavily oversampled AMSR-E SST fields and for studies devoted to product validation and comparison. A preliminarly analysis suggests that use of the derived footprint will reduce the variance between AMSR-E and MODIS fields compared to the results obtained.

scholarly journals A Method for Reconstruction of Boiler Combustion Temperature Field Based on Acoustic Tomography

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuhui Wu ◽  
Xinzhi Zhou ◽  
Li Zhao ◽  
Chenlong Dong ◽  
Hailin Wang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Optimal Parameter ◽  
Interpolation Method ◽  
Least Square Method ◽  
Reconstruction Algorithm ◽  
Least Square ◽  
Temperature Fields ◽  
Acoustic Tomography ◽  
Measured Temperature

Acoustic tomography (AT), as a noninvasive temperature measurement method, can achieve temperature field measurement in harsh environments. In order to achieve the measurement of the temperature distribution in the furnace and improve the accuracy of AT reconstruction, a temperature field reconstruction algorithm based on the radial basis function (RBF) interpolation method optimized by the evaluation function (EF-RBFI for short) is proposed. Based on a small amount of temperature data obtained by the least square method (LSM), the RBF is used for interpolation. And, the functional relationship between the parameter of RBF and the root-mean-square (RMS) error of the reconstruction results is established in this paper, which serves as the objective function for the effect evaluation, so as to determine the optimal parameter of RBF. The detailed temperature description of the entire measured temperature field is finally established. Through the reconstruction of three different types of temperature fields provided by Dongfang Boiler Works, the results and error analysis show that the EF-RBFI algorithm can describe the temperature distribution information of the measured combustion area globally and is able to reconstruct the temperature field with high precision.

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