scholarly journals Solution of the Boussinesq’s problem in evaluating ratio between shear stress and contact pressure

2020 ◽  
pp. 139-151
Author(s):  
Е.Г. Хитров ◽  
А.В. Андронов ◽  
Е.В. Нестерова
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Normal Stress ◽  
Contact Pressure ◽  
Stress Function ◽  
Average Pressure ◽  
Normal Stress Distribution ◽  
Contact Patch ◽  
Wide Range ◽  
Boussinesq’S Problem

Решение фундаментальной задачи Буссинеска широко используется в технических науках и позволяет эффективно решать широкий спектр задач науки о лесозаготовительном производстве. На его основе удается получить практически значимые результаты в области оценки распределения напряжений, возникающих в обрабатываемом материале под воздействием рабочего органа. Цель нашего исследования - проанализировать результаты расчетов и установить соотношение максимального значения касательного напряжения и среднего значения давления по пятну контакта рабочего органа с обрабатываемом материалом. Теоретическую основу работы составляют уравнения распределения нормальных и касательных напряжений, возникающих в упругом полупространстве при вдавливании в него жесткого клина. В результате анализа теоретических расчетов показано, что характер затухания нормального напряжения по глубине деформируемого массива материала с высокой точностью аппроксимируется квадратичной функцией (на основе полученной приближенной функции выполнено сопоставление среднего давления по пятну контакта индентора с массивом и нормального напряжения по глубине массива). При этом, как показали результаты расчетов, функция распространения касательного напряжения в деформируемом массиве имеет экстремум. Выполнено сопоставление полученных данных по значению экстремума функции касательного напряжения со значением приближенной функции нормального напряжения на границе контакта индентора сдеформируемым массивом. В результате показано, что максимальное по модулю касательное напряжение составляет 11-12% среднего контактного давления. Расчеты проведены при варьировании коэффициента Пуассона материала массива, установленное соотношение остается практически неизменным. Solution of fundamental Boussinesq’s problem is widely used in technical sciences and allows effectively solving a wide range of problems in forestry science. On its basis, it is possible to obtain practically significant results in the field of assessing the distribution of stresses arising in processed material under the influence of a working body. The purpose of our study is to analyze the results of calculations and establish the ratio of the maximum value of the shear stress and the average pressure over the contact patch of the working body with the material being processed. The theoretical basis of the work is formed by the equations for the distribution of normal and tangential stresses arising in an elastic half-space when a rigid cone is pressed into it. As a result of the analysis of the results of theoretical calculations, it was shown that the character of the normal stress distribution over the depth of the deformed massif of material is approximated with high accuracy by a quadratic function (based on the obtained approximate function, the average pressure over the contact patch of the indenter with the massif and the normal stress over the depth of the massif were compared). In this case, as shown by the results of calculations, the function of the shear stress distribution in the deformed massif has the extremum. Comparison of the obtained data on the value of the extremum of the shear stress function with the value of the approximate normal stress function at the interface of the indenter contact with the deformable mass is performed. As a result, it is shown that the maximum shear stress in absolute value is 11-12% of the average contact pressure. The calculations were carried out with varying Poisson's ratio of the massif material; the established ratio remains practically unchanged.

Stress in Bonded Adherends for Single Lap Joints

1996 ◽  
Vol 12 (03) ◽  
pp. 167-171
Author(s):  
G. Bezine ◽  
A. Roy ◽  
A. Vinet
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Numerical Model ◽  
Stress Distribution ◽  
Normal Stress ◽  
Lap Joints ◽  
Axial Loads ◽  
Normal Stress Distribution ◽  
Single Lap Joints ◽  
Element Technique

A finite-element technique is used to predict the shear stress and normal stress distribution in adherends for polycarbonate/polycarbonate single lap joints subjected to axial loads. Numerical and photoelastic results are compared so that a validation of the numerical model is obtained. The influences on stresses of the overlap length and the shape of the adherends are studied.

Numerical Study of Cruciform Specimens for Biaxial Tensile Tests

2016 ◽  
Author(s):  
Luis F. Puente Medellín ◽  
Antonio Balvantin ◽  
J. A. Diosdado-De la Peña
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Normal Stress ◽  
Sheet Metal ◽  
Numerical Study ◽  
Tensile Tests ◽  
Thickness Reduction ◽  
Shear Stresses ◽  
Normal Stress Distribution ◽  
Biaxial Tensile

This paper presents a numerical study of different geometries of cruciform specimens for biaxial tensile tests. The aim of these specimens is to be used on fixtures for biaxial tests mounted in universal testing machines. For the study, a model of isotropic material for steel sheet metal specimens was considered. Thus, only the mechanical properties of the sheet metal in the rolling direction were considered in the simulations. In this numerical analysis, the normal stress distribution and the consequent shear stress were studied. Additionally, the effect of the inclusion of multiple slots as well as a thickness reduction on the normal and shear stresses were assessed. Hence, a specimen in which a uniform normal stress distribution with zero shear stress, is necessary. The results of the analysis show that a specimen with features, multiple slots and a thickness reduction in the central area, provides a better performance in the simulations than dismissing any of these characteristics. Finally, a specimen model suitable for the mentioned test is proposed according to the obtained numerical results and the feasibility of manufacture of the experimental sample-test.

Normal stress distribution adjacent to optimum holes in composite plates

1994 ◽  
Vol 29 (4) ◽  
pp. 393-398 ◽  
Author(s):  
R. Ramesh Kumar ◽  
G. Venkateswara Rao ◽  
K.S. Suresh
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Composite Plates ◽  
Normal Stress Distribution

scholarly journals Entropy-Based Shear Stress Distribution in Open Channel for all types of Flow using Experimental Data

2021 ◽  
Author(s):  
Hae Seong Jeon ◽  
Ji Min Kim ◽  
Yeon Moon Choo
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Turbulent Flow ◽  
Correlation Coefficient ◽  
Open Channel ◽  
Shear Stress Distribution ◽  
Entropy Theory ◽  
Tractive Force ◽  
Design Standards ◽  
Wide Range

Abstract Korea’s river design standards set general design standards for river and river-related projects in Korea, which systematize the technologies and methods involved in river-related projects. This includes measurement methods for parts necessary for river design, but do not include information on shear stress. Shear Stress is to one of the factors necessary for river design and operation. Shear stress is one of the most important hydraulic factors used in the fields of water especially for artificial channel design. Shear stress is calculated from the frictional force caused by viscosity and fluctuating fluid velocity. Current methods are based on past calculations, but factors such as boundary shear stress or energy gradient are difficult to actually measure or estimate. The point velocity throughout the entire cross section is needed to calculate the velocity gradient. In other words, the current Korea’s river design standards use tractive force, critical tractive force instead of shear stress because it is more difficult to calculate the shear stress in the current method. However, it is difficult to calculate the exact value due to the limitations of the formula to obtain the river factor called the tractive force. In addition, tractive force has limitations that use empirically identified base value for use in practice. This paper focuses on the modeling of shear stress distribution in open channel turbulent flow using entropy theory. In addition, this study suggests shear stress distribution formula, which can be easily used in practice after calculating the river-specific factor T. and that the part of the tractive force and critical tractive force in the Korea’s river design standards should be modified by the shear stress obtained by the proposed shear stress distribution method. The present study therefore focuses on the modeling of shear stress distribution in open channel turbulent flow using entropy theory. The shear stress distribution model is tested using a wide range of forty-two experimental runs collected from the literature. Then, an error analysis is performed to further evaluate the accuracy of the proposed model. The results revealed a correlation coefficient of approximately 0.95–0.99, indicating that the proposed method can estimate shear stress distribution accurately. Based on this, the results of the distribution of shear stress after calculating the river-specific factors show a correlation coefficient of about 0.86 to 0.98, which suggests that the equation can be applied in practice.

Analysis of Deep Beams

1951 ◽  
Vol 18 (2) ◽  
pp. 163-172
Author(s):  
H. D. Conway ◽  
L. Chow ◽  
G. W. Morgan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Stress Distribution ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Normal Stress ◽  
Stress Function ◽  
Beam Theory ◽  
Deep Beam ◽  
Stress Functions

Abstract This paper presents a method of analyzing the stress distribution in a deep beam of finite length by superimposing two stress functions. The first stress function is chosen in the form of a trigonometric series which satisfies all but one of the boundary conditions—that of zero normal stress on the ends of the beam. The principle of least work is then used to obtain a second stress function giving the distribution of normal stress on the ends which is left by the first stress function. By superimposing the two solutions, all the boundary conditions are satisfied. Two particular cases of a given type of loading are solved in this way to investigate the stresses in a deep beam and their deviation from the ordinary beam theory. In addition, an approximate solution by the numerical method of finite difference is worked out for one of the two cases. Results from the two methods are compared and discussed. A method of obtaining an exact solution to the problem is given in an Appendix.

Stresses in a Thick Plate With Axially Symmetric Loading

1965 ◽  
Vol 32 (2) ◽  
pp. 458-459 ◽  
Author(s):  
T. J. Lardner
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Numerical Integration ◽  
Elastic Plate ◽  
Thick Plate ◽  
Axially Symmetric ◽  
Pressure Loading ◽  
Normal Stress Distribution ◽  
Symmetric Loading

The problem of the thick elastic plate with a symmetric circular pressure loading is considered. The normal stress distribution on the midplane and for two positions off the midplane is obtained by a numerical integration of the solutions. A comparison of the stress distribution on the midplane is made with previous results.

Normal stress distribution in highly concentrated suspensions undergoing squeeze flow

2013 ◽  
Vol 52 (2) ◽  
pp. 155-163 ◽  
Author(s):  
Mohsen Nikkhoo ◽  
Khosrow Khodabandehlou ◽  
LeAnne Brozovsky ◽  
Francis Gadala-Maria
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Squeeze Flow ◽  
Concentrated Suspensions ◽  
Normal Stress Distribution

The Research of Pure Bending Flanged Beam’s Stress Distribution in Civil Engineering

2012 ◽  
Vol 568 ◽  
pp. 168-171
Author(s):  
Jian Ou Pan ◽  
Yu Jing Jia ◽  
Guang Zhen Cheng
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Civil Engineering ◽  
Effective Means ◽  
Measurement Technology ◽  
Stress And Strain ◽  
Test Bed ◽  
Pure Bending ◽  
Normal Stress Distribution ◽  
Measuring Point

Experimental method is an important means to research the mechanical properties of materials in civil engineering. In this paper, first, analyzing the section of pure bending beam’s normal-stress distribution, drafting the measure scheme of flanged beam’s pure bending normal-stress, arranging measuring point in different place about the section of pure bending, adopting multi-function composite test-bed, static strain gauge and other testing instrument, by step loading, to finish the measure of each measuring points’ stress and strain, also, analysis and treatment for test data. According to the result of analysis and treatment, pointing out that measured stress and strain of pure bending beam is proportional to loading. The measured normal-stress distribution of the pure bend beam is uniform with theoretical analysis, which is satisfy the engineering demand. Knowing and mastering multipoint measurement technology and method is an effective means for the scientific research.

Observations by Evaluating the Uncertainty of Stress Distribution in Truss Structures Based on Probabilistic and Possibilistic Methods

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Sushan Li ◽  
Roland Platz
Keyword(s):  
Monte Carlo ◽  
Stress Distribution ◽  
Normal Stress ◽  
Direct Methods ◽  
Truss Structure ◽  
Truss Structures ◽  
Model Parameters ◽  
Normal Stress Distribution ◽  
Fuzzy Analysis ◽  
Input Parameters

Load-bearing mechanical structures like trusses face uncertainty in loading along with uncertainty in stress and strength, which are due to uncertainty in their development, production, and usage. According to the working hypothesis of the German Collaborative Research Center SFB 805, uncertainty occurs in processes that are not or only partial deterministic and can only be controlled in processes. The authors classify, compare, and evaluate four different direct methods to describe and evaluate the uncertainty of normal stress distribution in simple truss structures with one column, two columns, and three columns. The four methods are the direct Monte Carlo (DMC) simulation, the direct quasi-Monte Carlo (DQMC) simulation, the direct interval, and the direct fuzzy analysis with α-cuts, which are common methods for data uncertainty analysis. The DMC simulation and the DQMC simulation are categorized as probabilistic methods to evaluate the stochastic uncertainty. On the contrary, the direct interval and the direct fuzzy analysis with α-cuts are categorized as possibilistic methods to evaluate the nonstochastic uncertainty. Three different truss structures with increasing model complexity, a single-column, a two-column, and a three-column systems are chosen as reference systems in this study. Each truss structure is excited with a vertical external point load. The input parameters of the truss structures are the internal system properties such as geometry and material parameters, and the external properties such as magnitude and direction of load. The probabilistic and the possibilistic methods are applied to each truss structure to describe and evaluate its uncertainty in the developing phase. The DMC simulation and DQMC simulation are carried out with full or “direct” sample sets of model parameters such as geometry parameters and state parameters such as forces, and a sensitivity analysis is conducted to identify the influence of every model and state input parameter on the normal stress, which is the output variable of the truss structures. In parallel, the direct interval and the direct fuzzy analysis with α-cuts are carried out without altering and, therefore, they are direct approaches as well. The four direct methods are then compared based on the simulation results. The criteria of the comparison are the uncertainty in the deviation of the normal stress in one column of each truss structure due to varied model and state input parameters, the computational costs, as well as the implementation complexity of the applied methods.

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