scholarly journals SAINT-VENANT'S TORSION PROBLEM WITH STRESS FUNCTION IN THE FORM OF A THIRD DEGREE POLYNOMIAL

1953 ◽  
Vol 9 (4) ◽  
pp. 255
Author(s):  
YEH KAI-YUAN
Keyword(s):  
Stress Function ◽  
Torsion Problem ◽  
Degree Polynomial

Torsion of a Prismatical Bar Whose Section Is a Crescent

1959 ◽  
Vol 81 (4) ◽  
pp. 428-432
Author(s):  
F. Sisto
Keyword(s):  
Stress Function ◽  
Approximate Formula ◽  
Fourier Integral ◽  
Infinite Strip ◽  
Torsion Problem ◽  
Circular Arcs ◽  
Infinite Integral

The Saint Venant torsion problem is solved for a region bounded by two circular arcs forming a crescent. The region is conformally transformed to an infinite strip and the stress function is obtained by Fourier integral. Subsequent quadratures for evaluation of the torsion constant are obtained explicitly with the exception of a single infinite integral which may easily be evaluated numerically. Some values of the torsion constant are given, and an approximate formula valid for small “camber” is presented.

Application of the R-Function Theory and Least Square Method for Torsion Problem with H-Shaped Cross-Section

2012 ◽  
Vol 217-219 ◽  
pp. 2313-2316
Author(s):  
Ping Ping Li ◽  
Hong Yuan ◽  
Shan Qing Li
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Stress Function ◽  
Present Method ◽  
Function Theory ◽  
Least Square Method ◽  
Least Square ◽  
Torsion Problem ◽  
Function Form ◽  
Shaped Cross Section

The R-function theory and least square method are employed to solve the torsion problem of the bar with H-shaped cross-section. When the least square method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the H-shaped cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe H-shaped cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of H-shaped cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

Application of the R-Function Theory and Variational Method for Torsion Problem with Complicated Cross-Section

2013 ◽  
Vol 353-356 ◽  
pp. 3320-3323 ◽  
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Boundary Condition ◽  
Variational Method ◽  
Cross Section ◽  
Stress Function ◽  
Present Method ◽  
Function Theory ◽  
Implicit Function ◽  
Torsion Problem ◽  
Function Form ◽  
Numerical Example

The R-function theory and variational method are employed to solve the torsion problem of the bar with a complicated cross-section. When the variational method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the complicated cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe the complicated cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of the complicated cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

Optimization of performance in multi-cell beams with different surface slopes for use in vehicle structure using a multi-objective evolutionary algorithm based on decomposition

2021 ◽  
pp. 146442072199784
Author(s):  
S Chahardoli ◽  
Mohammad Sheikh Ahmadi ◽  
TN Tran ◽  
Afrasyab Khan
Keyword(s):  
Decomposition Method ◽  
Experimental Tests ◽  
Surface Slope ◽  
Optimal Model ◽  
Degree Polynomial ◽  
Numerical Tests ◽  
Numerical Studies ◽  
Surface Slopes ◽  
Vehicle Structure ◽  
Number Of Cells

This study examined the effect of the upper surface slope and the number of cells in the side beams on the collapse properties using experimental and numerical tests. The numerical studies were conducted with LS-DYNA software, and the accuracy of numerical results was investigated by experimental tests. Using MATLAB software, the second-degree polynomial functions were obtained for the collapse properties of the specimens. Also, after the optimization by the decomposition method, the best mode was introduced for the specimens. The studies on collapse properties showed that increasing the number of cells leads to a decrease in all collapse properties, and increasing the upper surface slope leads to an increase in the collapse properties. Moreover, the optimization results by decomposition method showed that this method could suggest the most optimal model for multi-cell and sloping beams.

scholarly journals Data-driven graph drawing techniques with applications for conveyor systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Simone Göttlich ◽  
Sven Spieckermann ◽  
Stephan Stauber ◽  
Andrea Storck
Keyword(s):  
Real World ◽  
Connected Graph ◽  
Stress Function ◽  
Graph Drawing ◽  
Point Of View ◽  
Data Driven ◽  
Challenging Problem ◽  
Conveyor System ◽  
System Graph ◽  
Real World Problems

AbstractThe visualization of conveyor systems in the sense of a connected graph is a challenging problem. Starting from communication data provided by the IT system, graph drawing techniques are applied to generate an appealing layout of the conveyor system. From a mathematical point of view, the key idea is to use the concept of stress majorization to minimize a stress function over the positions of the nodes in the graph. Different to the already existing literature, we have to take care of special features inspired by the real-world problems.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

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