Solution of Thermal Stress Problems in Tube Sheets by the Boundary Point Least Squares Method

1970 ◽  
Vol 92 (2) ◽  
pp. 339-349 ◽  
Author(s):  
L. E. Hulbert
Keyword(s):  
Thermal Stress ◽  
Least Squares ◽  
Boundary Point ◽  
Thermal Stresses ◽  
Least Squares Method ◽  
Tube Sheet ◽  
Point Matching ◽  
Stress Functions ◽  
Plane Stress Analysis ◽  
Least Squares Approach

This paper describes the application of the boundary point least squares approach to the plane stress analysis of tube sheets with either mechanical or thermal loads. The paper includes a derivation of appropriate stress functions, a discussion of the point matching and boundary point least squares methods, and a description of the application of the method to the analysis of different hole configurations in tube sheets. It concludes with numerical results obtained from the analysis of the thermal stresses near the divider lane of a tube sheet from a two-pass heat exchanger.

Thermal Stress Analysis of Multiholed Composite Plates and Cylinders by the Boundary-Point-Least-Squares Method

1974 ◽  
Vol 96 (3) ◽  
pp. 214-219 ◽  
Author(s):  
L. E. Hulbert ◽  
S. G. Sampath
Keyword(s):  
Least Squares ◽  
Boundary Point ◽  
Thermal Stresses ◽  
Least Squares Method ◽  
Composite Plates ◽  
Multiply Connected Domains ◽  
Series Solutions ◽  
Thermally Induced ◽  
Multiply Connected

The paper describes the application of the boundary-point-least-squares method (BPLS) to the determination of the two-dimensional temperatures and thermal stresses in composite multiply connected domains. Series solutions are first determined for the steady-state temperatures. Using these temperature solutions, the solution to the thermally-induced stresses is automatically found in terms of Airy stress function series. Applications are described which illustrate use of the method in specific problems.

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

scholarly journals Derivation of a Bayes Factor to Distinguish Between Linked or Pleiotropic Quantitative Trait Loci

Genetics ◽  
2004 ◽  
Vol 166 (2) ◽  
pp. 1025-1035
Author(s):  
L Varona ◽  
L Gómez-Raya ◽  
W M Rauw ◽  
A Clop ◽  
C Ovilo ◽  
...  
Keyword(s):  
Fatty Acids ◽  
Linoleic Acid ◽  
Least Squares ◽  
Bayes Factor ◽  
Least Squares Method ◽  
Simple Procedure ◽  
Pleiotropic Qtl ◽  
Using Data ◽  
Landrace Pig ◽  
Least Squares Approach

Abstract A simple procedure to calculate the Bayes factor between linked and pleiotropic QTL models is presented. The Bayes factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes factor approach was more powerful than the multivariate least-squares approach.

Stress Response Functions to Multi-Dimensional Spatial Fluctuations of Fluid Temperature

2002 ◽  
Author(s):  
Naoto Kasahara ◽  
Hideki Takasho
Keyword(s):  
Thermal Stress ◽  
Temperature Fluctuation ◽  
Thermal Stratification ◽  
Thermal Stresses ◽  
Fluid Mixing ◽  
Cold Spot ◽  
Fluid Temperature ◽  
Response Functions ◽  
Spatial Fluctuations ◽  
Stress Functions

Temperature fluctuation from incomplete fluid mixing induces fatigue damages on structures of nuclear components, which should be prevented. For rational analyses of this phenomenon, the authors have developed a frequency response function of thermal stress and extended to multi-dimensional spatial fluctuations of fluid temperature. This function is formulated by a product of the effective heat transfer and the effective thermal stress functions, and enables us to quickly calculate the thermal stresses induced by both local and global temperature distributions in structures. Furthermore, it can evaluate sensitivities of thermal stress to frequencies of temperature fluctuation, Biot number and constraint conditions of structures. Applicability of this function was verified for multi-dimensional problems such as thermal stratification problems and hot/cold spot ones.

Analysis of Multiholed Orthotropic Laminated Plates by the Boundary-Point-Least-Squares Method

1975 ◽  
Vol 97 (2) ◽  
pp. 118-122 ◽  
Author(s):  
S. G. Sampath ◽  
L. E. Hulbert
Keyword(s):  
Least Squares ◽  
Boundary Point ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Elliptical Hole ◽  
Laminated Plates ◽  
Series Solutions ◽  
Orthotropic Plates ◽  
Multiply Connected

The paper describes the application of boundary-point-least-squares method (BPLS) for the determination of stresses in multiply connected finite orthotropic plates under plane stress. Series solutions composed of mapping functions are employed. Numerical solutions presented include the case of an orthotropic plate with an elliptical hole with orientation noncoincident with the material axes.

scholarly journals A Regularised Total Least Squares Approach for 1D Inverse Scattering

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 216
Author(s):  
Andreas Tataris ◽  
Tristan van Leeuwen
Keyword(s):  
Integral Equation ◽  
Least Squares ◽  
Inverse Scattering ◽  
Least Squares Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Stability Estimate ◽  
Total Least Squares ◽  
Scattering Data ◽  
Least Squares Approach

We study the inverse scattering problem for a Schrödinger operator related to a static wave operator with variable velocity, using the GLM (Gelfand–Levitan–Marchenko) integral equation. We assume to have noisy scattering data, and we derive a stability estimate for the error of the solution of the GLM integral equation by showing the invertibility of the GLM operator between suitable function spaces. To regularise the problem, we formulate a variational total least squares problem, and we show that, under certain regularity assumptions, the optimisation problem admits minimisers. Finally, we compute numerically the regularised solution of the GLM equation using the total least squares method in a discrete sense.

scholarly journals Robust Estimations of Current Velocities with Four-Beam Broadband ADCPs

2009 ◽  
Vol 26 (12) ◽  
pp. 2642-2654 ◽  
Author(s):  
M. Gilcoto ◽  
Emlyn Jones ◽  
Luis Fariña-Busto
Keyword(s):  
Least Squares ◽  
Covariance Matrix ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Robust Solution ◽  
Least Squares Solution ◽  
Weighted Least Squares Method ◽  
Radial Beam ◽  
Least Squares Approach ◽  
Variance Covariance Matrix

Abstract An extended explanation of the hypothesis and equations traditionally used to transform between four-beam ADCP radial beam velocities and current velocity components is presented. This explanation includes a dissertation about the meaning of the RD Instrument error velocity and a description of the standard beam-to-current components transformation as a least squares solution. Afterward, the variance–covariance matrix associated with the least squares solution is found. Then, a robust solution for transforming radial beam velocities into current components is derived under the formality of a weighted least squares approach. The associated variance–covariance matrix is also formulated and theoretically proves that the modulus of its elements will be generally lower than the corresponding modulus of the variance–covariance matrix associated with the standard least squares solution. Finally, a comparison between the results obtained using the standard least squares solution and the results of the weighted least squares method, using a high-resolution ADCP dataset, is presented. The results show that, in this case, the weighted least squares solution provides variance estimations that are 4% lower over the entire record period (8 days) and 7% lower during a shorter, more energetic period (12 h).

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method
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