An explicit boussinesq solution for a polynomial distribution of pressure over a triangular region

1971 ◽  
Vol 1 (2) ◽  
pp. 167-170 ◽  
Author(s):  
Otto J. Svec ◽  
G. M. L. Gladwell
Keyword(s):  
Triangular Region ◽  
Boussinesq Solution ◽  
Polynomial Distribution

scholarly journals A Simplified Analysis Method for the Deformation Response of an Existing Tunnel to Ground Surcharge Based on the Pasternak Model

2021 ◽  
Vol 11 (7) ◽  
pp. 3255
Author(s):  
Zheng Wei ◽  
Yusheng Jiang
Keyword(s):  
Longitudinal Displacement ◽  
Maximum Displacement ◽  
Deformation Response ◽  
Reaction Coefficient ◽  
Element Simulation ◽  
Tunnel Model ◽  
Calculation Results ◽  
Pasternak Model ◽  
Boussinesq Solution ◽  
Euler Bernoulli Beam

Surface surcharge changes the existing equilibrium stress field of the stratum and adversely affects the existing tunnel. This paper presents a simplified analytical solution for calculating the longitudinal displacement of existing tunnels that are subjected to adjacent surcharge loading. Based on the Boussinesq solution, the distribution of the additional load matrix caused by the surface surcharge on the existing tunnel was obtained. A Euler–Bernoulli beam with a Pasternak foundation was used as a simplified model for tunnel stress analysis. Using the corrected reaction coefficient of the foundation bed, the differential equation of tunnel deformation was established, and the solution matrix of the longitudinal displacement of the tunnel was obtained by using the finite difference method. The reliability and applicability of the proposed method were verified by comparing the results with finite element simulation results, field test data, and the calculation results of three simplified elastic analysis methods with different foundation bed coefficients. On this basis, the parameters of the load–tunnel model were analyzed, and the effects of the buried depth, the size of the load, the relative positions of the load and the tunnel, and the relative stiffness of the tunnel soil on the maximum displacement of the existing tunnel were calculated. An empirical formula is proposed for calculating the maximum longitudinal displacement of the existing tunnel subjected to surface surcharge. The findings of this research can provide a basis for the theoretical verification of the deformation response of an existing tunnel subjected to adjacent surface surcharge.

scholarly journals Analytical Solutions of Spherical Cavity Expansion Near a Slope due to Pile Installation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jingpei Li ◽  
Yaguo Zhang ◽  
Haibing Chen ◽  
Fayun Liang
Keyword(s):  
Free Boundary ◽  
Inclination Angle ◽  
Spherical Cavity ◽  
Theoretical Method ◽  
Cavity Expansion ◽  
Sloping Ground ◽  
Present Solution ◽  
Image Technique ◽  
Boussinesq Solution ◽  
Spherical Cavity Expansion

Based on the hypothesis that the penetration of a single pile can be simulated by a series of spherical cavity expansions, this paper presents an analytical solution of cavity expansion near the sloping ground. Compared with the cavity expansion in the half-space, the sloping free boundary has been taken into account as well as the horizontal free boundary. The sloping and horizontal free surfaces are considered by the introduction of a virtual image technique, the harmonic function, and the Boussinesq solution. The results show that the sloping free boundary and the variation of the inclination angle have pronounced influences on the distribution of the stress and displacement induced by the spherical cavity expansion. The present solution provides a simplified and realistic theoretical method to predict the soil behaviors around the spherical cavity near the sloping ground. The approach can also be used for the determination of the inclination angle of the slope according to the maximum permissible displacement.

Autism Spectrum Disorder Identification Using Polynomial Distribution based Convolutional Neural Network

2021 ◽  
Vol 19 (2) ◽  
pp. 19-30
Author(s):  
G. Nagarajan ◽  
Dr.A. Mahabub Basha ◽  
R. Poornima
Keyword(s):  
Neural Network ◽  
Prediction Models ◽  
Autism Spectrum ◽  
Spectrum Disorder ◽  
Machine Learning Techniques ◽  
Hybrid Technique ◽  
Learning Techniques ◽  
Chicken Swarm Optimization ◽  
Sensitivity Specificity ◽  
Polynomial Distribution

One main psychiatric disorder found in humans is ASD (Autistic Spectrum Disorder). The disease manifests in a mental disorder that restricts humans from communications, language, speech in terms of their individual abilities. Even though its cure is complex and literally impossible, its early detection is required for mitigating its intensity. ASD does not have a pre-defined age for affecting humans. A system for effectively predicting ASD based on MLTs (Machine Learning Techniques) is proposed in this work. Hybrid APMs (Autism Prediction Models) combining multiple techniques like RF (Random Forest), CART (Classification and Regression Trees), RF-ID3 (RF-Iterative Dichotomiser 3) perform well, but face issues in memory usage, execution times and inadequate feature selections. Taking these issues into account, this work overcomes these hurdles in this proposed work with a hybrid technique that combines MCSO (Modified Chicken Swarm Optimization) and PDCNN (Polynomial Distribution based Convolution Neural Network) algorithms for its objective. The proposed scheme’s experimental results prove its higher levels of accuracy, precision, sensitivity, specificity, FPRs (False Positive Rates) and lowered time complexity when compared to other methods.

scholarly journals Organic aerosol components observed in Northern Hemispheric datasets from Aerosol Mass Spectrometry

2010 ◽  
Vol 10 (10) ◽  
pp. 4625-4641 ◽  
Author(s):  
N. L. Ng ◽  
M. R. Canagaratna ◽  
Q. Zhang ◽  
J. L. Jimenez ◽  
J. Tian ◽  
...  
Keyword(s):  
Mass Spectrum ◽  
Organic Aerosol ◽  
Total Signal ◽  
Mass Spectral ◽  
Aerosol Mass ◽  
Aerosol Mass Spectrometry ◽  
Wide Range ◽  
Triangular Region ◽  
Photochemical Aging ◽  
Spectral Diagnostic

Abstract. In this study we compile and present results from the factor analysis of 43 Aerosol Mass Spectrometer (AMS) datasets (27 of the datasets are reanalyzed in this work). The components from all sites, when taken together, provide a holistic overview of Northern Hemisphere organic aerosol (OA) and its evolution in the atmosphere. At most sites, the OA can be separated into oxygenated OA (OOA), hydrocarbon-like OA (HOA), and sometimes other components such as biomass burning OA (BBOA). We focus on the OOA components in this work. In many analyses, the OOA can be further deconvolved into low-volatility OOA (LV-OOA) and semi-volatile OOA (SV-OOA). Differences in the mass spectra of these components are characterized in terms of the two main ions m/z 44 (CO2+) and m/z 43 (mostly C2H3O+), which are used to develop a new mass spectral diagnostic for following the aging of OA components in the atmosphere. The LV-OOA component spectra have higher f44 (ratio of m/z 44 to total signal in the component mass spectrum) and lower f43 (ratio of m/z 43 to total signal in the component mass spectrum) than SV-OOA. A wide range of f44 and O:C ratios are observed for both LV-OOA (0.17±0.04, 0.73±0.14) and SV-OOA (0.07±0.04, 0.35±0.14) components, reflecting the fact that there is a continuum of OOA properties in ambient aerosol. The OOA components (OOA, LV-OOA, and SV-OOA) from all sites cluster within a well-defined triangular region in the f44 vs. f43 space, which can be used as a standardized means for comparing and characterizing any OOA components (laboratory or ambient) observed with the AMS. Examination of the OOA components in this triangular space indicates that OOA component spectra become increasingly similar to each other and to fulvic acid and HULIS sample spectra as f44 (a surrogate for O:C and an indicator of photochemical aging) increases. This indicates that ambient OA converges towards highly aged LV-OOA with atmospheric oxidation. The common features of the transformation between SV-OOA and LV-OOA at multiple sites potentially enable a simplified description of the oxidation of OA in the atmosphere. Comparison of laboratory SOA data with ambient OOA indicates that laboratory SOA are more similar to SV-OOA and rarely become as oxidized as ambient LV-OOA, likely due to the higher loadings employed in the experiments and/or limited oxidant exposure in most chamber experiments.

Stresses in Soils Due to External Loading

2015 ◽  
pp. 180-248
Keyword(s):  
Isotropic Material ◽  
Influence Factor ◽  
Plane Surface ◽  
External Loading ◽  
Concentrated Load ◽  
Distributed Load ◽  
Boussinesq Solution ◽  
Mathematical Definitions ◽  
Semi Empirical ◽  
Irregular Loading

Stress analysis is often necessary in the design of foundations of all types of structures, particularly buildings, retaining structures, dams, highway pavements, and embankments. In this chapter, the mathematical definitions of stress and strain and the elasticity of an isotropic material are first treated. This is followed by the classical theory of Boussinesq for the stress in a semi-infinite, elastic, isotropic, and homogeneous continuum loaded normally on its upper plane surface by a concentrated load. The Boussinesq solution is later extended to analyze the stresses produced by a uniformly distributed load over a flexible circular foundation, rectangular loading, strip loading, line loading, triangular loading, and embankment loading. The case of irregular loading using the Newmark's Chart is also considered. The settlement of a foundation under external loadings by the use of both the Boussinesq theory and the semi-empirical strain influence factor method proposed by Schmertmann et al. (1978) are considered.

Friction Structure Effect Analysis of Granular Materials in Foundation Soil

2012 ◽  
Vol 591-593 ◽  
pp. 1083-1088
Author(s):  
Chang Dan Wang ◽  
Shun Hua Zhou ◽  
Hui Su
Keyword(s):  
Stress Distribution ◽  
Granular Materials ◽  
Soil Layer ◽  
Stress Transfer ◽  
Fine Sand ◽  
Structure Effect ◽  
Additional Stress ◽  
Foundation Soil ◽  
Effect Analysis ◽  
Boussinesq Solution

To research and analyze the additional stress distribution and change of granular materials, the model tests are used to observe vertical additional stress in different position and depth. And the comparison between observed values and theoretical values is conducted to analyze the transmission and attenuation of additional stress in granular materials. The research results show that calculated values are based on Boussinesq solution which ignores the property of soil layer (materials), the distribution of additional stress for fine sand which belongs to granular materials is largely deviated from theoretical value. For granular materials, inner friction structure effect is evident influence to additional stress transfer. And continue using calculation method which is based on continuum materials will have bigger difference and even wrong.

A Flexible Facial Feature Replacement System

2011 ◽  
Vol 403-408 ◽  
pp. 2958-2961
Author(s):  
Jih Pin Yeh ◽  
Chen Yu Kao ◽  
Chung Yung Chen ◽  
Hwei Jen Lin
Keyword(s):  
Facial Feature ◽  
Experimental Results ◽  
Control Points ◽  
Plane Rotation ◽  
Triangular Region ◽  
Replacement System ◽  
Feature Replacement ◽  
Natural Composite

In this study, we propose a facial feature replacement system, which uses the triangulation algorithm to perform facial feature replacement in each segmented triangular region associated with control points. The experimental results show that our system provides quite natural composite images. In addition, the system is flexible and has no limit in the shape, size, and plane rotation of the faces which are processed.

Sharing Teaching Ideas: The Equation of a Triangle

2001 ◽  
Vol 94 (5) ◽  
pp. 362-364
Author(s):  
Miriam Amit ◽  
Michael N. Fried ◽  
Pavel Satianov
Keyword(s):  
High School ◽  
High School Teachers ◽  
Mathematical Expression ◽  
Number Line ◽  
Convex Region ◽  
School Teachers ◽  
Twelfth Graders ◽  
Triangular Region ◽  
System Of Inequalities ◽  
Teaching Ideas

In studying algebra, a segment of the number line is inevitably related to a system of inequalities in one variable. Similarly, a convex region of the plane is inevitably related to a system of inequalities in two variables. Indeed, we drew this unsurprising conclusion from a questionnaire that we gave to a group of high school teachers and a large group of advanced twelfth graders. In the questionnaire, we simply asked what kind of mathematical expression is needed to determine the points in a line segment and in a triangular region.

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