The Side-Force Problem for Shallow Helicoidal Shells

1969 ◽  
Vol 36 (2) ◽  
pp. 292-295 ◽  
Author(s):  
F. Y. M. Wan
Keyword(s):  
Computer Program ◽  
Numerical Results ◽  
Elementary Functions ◽  
Pure Bending ◽  
Side Force ◽  
Force Problem ◽  
Geometric Duality

The side-force problem for a shallow helicoidal shell is shown to be the complete static-geometric analog of the pure bending problem for the same shell. The solution of the former in terms of elementary functions is obtained, without another set of independent calculations, simply by applying the rules of the static-geometric duality to that of the latter. The analogy also enables us to use the same computer program developed for the pure bending problem (without any modification) to generate numerical results for the side-force problem.

Drifting Force and Moment on Ships in Oblique Waves

1966 ◽  
Vol 10 (01) ◽  
pp. 18-24
Author(s):  
Pung Nien Hu ◽  
King Eng
Keyword(s):  
Potential Theory ◽  
General Expression ◽  
Phase Angle ◽  
Analytical Solutions ◽  
Vertical Axis ◽  
Long Waves ◽  
Elementary Functions ◽  
Oblique Waves ◽  
Side Force ◽  
Yaw Moment

A general expression for the drifting moment about the vertical axis of an oscillating ship in regular oblique waves is derived from the potential theory, following a similar procedure developed by Maruo for drifting force. Explicit analytical solutions for the drifting side force and yaw moment on thin ships in long waves are obtained in terms of simple elementary functions. The effect of the wave frequency, the draft of the ship, the displacement, and the phase angle of the ship oscillation are discussed.

A Point Heat Source on the Surface of a Semi-Infinite Transversely Isotropic Piezothermoelastic Material

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Peng-Fei Hou ◽  
Wei Luo ◽  
Andrew Y. T. Leung
Keyword(s):  
Heat Source ◽  
Cadmium Selenide ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Point Heat Source ◽  
Elementary Functions ◽  
General Solutions ◽  
Coupled Field

We use the compact harmonic general solutions of transversely isotropic piezothermoelastic materials to construct the three-dimensional Green’s function of a steady point heat source on the surface of a semi-infinite transversely isotropic piezothermoelastic material by four newly introduced harmonic functions. All components of the coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for cadmium selenide are given graphically by contours.

A Large Rotation Matrix for Nonlinear Framed Structures, Part 2: Numerical Verification

2014 ◽  
Vol 1065-1069 ◽  
pp. 2034-2039
Author(s):  
Jin Duan ◽  
Yun Gui Li
Keyword(s):  
Cantilever Beam ◽  
Numerical Results ◽  
Rotation Matrix ◽  
Numerical Verification ◽  
Structural Stiffness ◽  
Pure Bending ◽  
Large Rotation ◽  
Framed Structures ◽  
Analytical Results ◽  
Good Agreement

In this paper, some numerical verifications would be presented and discussed, mainly including the following three types: (1) the pure bending beam in which the structural stiffness would maintain the original value and not change along with the load; (2) the clamped arc-beam in which the structural stiffness would decrease gradually with the increment of load and the structure would be buckling at some certain load value; and (3) the cantilever beam in which the structural stiffness would increase significantly with the increment of load. For all of the above examples, the present results are in good agreement with the analytical results and numerical results in other literatures, testifying and illustrating the validity of the large rotation matrix for nonlinear framed structure, which is developed in the part 1 of this paper.

scholarly journals Three-loop cusp anomalous dimension and a conjecture for n loops

2016 ◽  
Vol 31 (13) ◽  
pp. 1650076 ◽  
Author(s):  
Nikolaos Kidonakis
Keyword(s):  
Top Quark ◽  
Anomalous Dimension ◽  
Numerical Results ◽  
Elementary Functions ◽  
Top Quark Production ◽  
Quark Production ◽  
Lower Loop ◽  
Analytical Expressions ◽  
Cusp Anomalous Dimension ◽  
Approximate Formulas

I present analytical expressions for the massive cusp anomalous dimension in QCD through three loops, first calculated in 2014, in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a conjecture for the n-loop cusp anomalous dimension in terms of the lower-loop results. I also present numerical results and simple approximate formulas for the cusp anomalous dimension relevant to top-quark production.

Influence of imperfections on the maximum strength of biaxially bent columns

1976 ◽  
Vol 3 (2) ◽  
pp. 186-197 ◽  
Author(s):  
Sriramulu Vinnakota
Keyword(s):  
Residual Stresses ◽  
Computer Program ◽  
Design Methods ◽  
Numerical Results ◽  
Maximum Strength ◽  
Simply Supported

The effect of imperfections on the maximum strength of isolated, simply supported biaxially bent steel H-columns is studied with the help of a computer program. The influence of the pattern and intensity of residual stresses is considered first. The effect of the sign and magnitude of initial crookedness is then examined. Finally, the variation of the influence of residual stresses and initial crookedness with slenderness is presented. It is indicated that the numerical results given and the computer program, could be used to check the validity of the existing design methods, after selecting the representative imperfections.

Bending of Superelastic Wires, Part II: Application to Three-Point Bending

1995 ◽  
Vol 62 (2) ◽  
pp. 466-470 ◽  
Author(s):  
B. T. Berg
Keyword(s):  
Numerical Procedure ◽  
Bending Moment ◽  
Numerical Results ◽  
Constitutive Relationship ◽  
Pure Bending ◽  
Three Point Bending ◽  
Rod Theory ◽  
Soft Loading ◽  
Loading And Unloading ◽  
The Relationship

The constitutive relationship between applied pure bending moment and the resulting curvature of a few superelastic alloy wires is applied to the three-point bending problem. Three-point bending experiments on hard and soft loading machines are described. The relationship between the applied deflection and the resulting force in three-point bending is calculated from a nonlinear Euler-Bernoulli rod theory. A numerical procedure used to solve the three-point bending problem for both loading and unloading is briefly described and numerical results are compared with experiment.

Aerodynamics of Fixed and Rotating Spoked Cycling Wheels

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
S. J. Karabelas ◽  
N. C. Markatos
Keyword(s):  
Aerodynamic Performance ◽  
Numerical Results ◽  
Vertical Force ◽  
Side Force ◽  
Magnus Effect ◽  
Angular Velocities ◽  
Ground Effects ◽  
Effects Of Rotation ◽  
Yaw Angle ◽  
Yaw Moment

The performance of a semiracing spoked wheel is numerically and experimentally studied at full size in a wind tunnel. The numerical investigation is divided into two parts. In the first part, the wheel is considered to be fixed (no rotation) and the numerical results are compared to the experimental measurements. The flow past the wheel is treated as stationary and turbulent. The effects of cross wind and the wheel’s speed on the drag, side force, and yaw moment are investigated. Numerical results are presented via diagrams and plots at various yaw angles. Both the measurements and predictions agree quite well and they show a considerable increase in the yaw moment and side force at medium and high yaw angles. The axial drag force initially increases with yaw angle (up to 7.5 deg) and eventually decreases. Ground effects did not affect the overall loads, except for the vertical force at high yaw angles. In the second part, the effects of rotation have been taken into account. The wheel rotates at constant angular velocities and the flow is modeled as nonstationary and turbulent. The aerodynamic performance of the wheel is strongly affected by the rotational speed. In most of the cases, as the latter parameter increases, the loads nonlinearly increase. The rotation generates asymmetrical loading, since the flow is accelerated in one side and decelerated in the other (the Magnus effect). A vertical force is produced, which is dependent on the ratio of the rotational to the free-stream speed. Moreover, in an attempt to assess the effects of the number of spokes to the aerodynamic performance, two other models with 8 and 32 spokes have been numerically tested and compared to the original one (16 spokes). The results revealed, as expected, an increase in the axial drag and vertical force with the number of spokes.

Analysis of Stresses in Shallow Spherical Shells With Periodically Spaced Holes

1970 ◽  
Vol 92 (4) ◽  
pp. 834-840 ◽  
Author(s):  
L. E. Hulbert ◽  
F. A. Simonen
Keyword(s):  
Computer Program ◽  
Spherical Shell ◽  
Numerical Solution ◽  
Least Squares ◽  
Boundary Point ◽  
Numerical Results ◽  
Series Solutions ◽  
Spherical Shells ◽  
Perforated Plates ◽  
Circular Holes

This paper concerns the numerical solution of shallow spherical shell problems by the method of boundary-point-least-squares. The analysis forms the basis of a computer program for the calculation of stresses in curved perforated plates. Multiple-pole series solutions are used, and recursion methods for generating the required Bessel-Kelvin functions are discussed. Numerical results are given for previously unsolved problems involving an array of seven circular holes and for an array of four noncircular holes.

The Elasto-Electric Field for a Rigid Conical Punch on a Transversely Isotropic Piezoelectric Half-Space

1999 ◽  
Vol 66 (3) ◽  
pp. 764-771 ◽  
Author(s):  
W.-Q. Chen ◽  
T. Shioya ◽  
H.-J. Ding
Keyword(s):  
Exact Solution ◽  
Electric Field ◽  
Potential Theory ◽  
Half Space ◽  
Piezoelectric Effect ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Theory Method ◽  
Elementary Functions ◽  
Potential Theory Method

This paper exactly analyzes the problem of a rigid conical punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to include the piezoelectric effect. By using the previous results of pure elasticity, exact solution is derived. It is found that all the elastoelectric variables are expressed in terms of elementary functions. Numerical results are finally performed.

scholarly journals Automatic Differentiation in ROOT

2020 ◽  
Vol 245 ◽  
pp. 02015
Author(s):  
Vassil Vassilev ◽  
Aleksandr Efremov ◽  
Oksana Shadura
Keyword(s):  
Computer Program ◽  
Automatic Differentiation ◽  
Source Code ◽  
Constant Factor ◽  
Control Flow ◽  
Chain Rule ◽  
Elementary Functions ◽  
Arithmetic Operations ◽  
Small Constant ◽  
Derivatives Of

In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.), elementary functions (exp, log, sin, cos, etc.) and control flow statements. AD takes source code of a function as input and produces source code of the derived function. By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program. This paper presents AD techniques available in ROOT, supported by Cling, to produce derivatives of arbitrary C/C++ functions through implementing source code transformation and employing the chain rule of differential calculus in both forward mode and reverse mode. We explain its current integration for gradient computation in TFormula. We demonstrate the correctness and performance improvements in ROOT’s fitting algorithms.

Sign in / Sign up

Export Citation Format

Share Document