The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

Comparison of Static and Dynamic Stiffness for Beams Undergoing Flexural and Torsional Loading With an Intermediate Mass

2000 ◽  
Author(s):  
Arnoldo Garcia ◽  
Arnold Lumsdaine ◽  
Ying X. Yao
Keyword(s):  
Closed Form ◽  
Natural Frequency ◽  
Cross Sections ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Torsional Loading ◽  
Intermediate Mass ◽  
Form Equation

Abstract Many studies have been performed to analyze the natural frequency of beams undergoing both flexural and torsional loading. For example, Adam (1999) analyzed a beam with open cross-sections under forced vibration. Although the exact natural frequency equation is available in literature (Lumsdaine et al), to the authors’ knowledge, a beam with an intermediate mass and support has not been considered. The models are then compared with an approximate closed form solution for the natural frequency. The closed form equation is developed using energy methods. Results show that the closed form equation is within 2% percent when compared to the transcendental natural frequency equation.

scholarly journals FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250037 ◽  
Author(s):  
ALESSANDRO RAMPONI
Keyword(s):  
Fourier Transform ◽  
Regime Switching ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Transform Method ◽  
Finite State ◽  
Jump Diffusion Model ◽  
Log Price ◽  
The Fourier Transform

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

Calculation of Discharge Current Waveforms in High Voltage Spark Sources. II. Extensions and Limitations of Closed-Form Solution

1982 ◽  
Vol 36 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Alexander Scheeline ◽  
T. V. Tran
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Closed Form ◽  
High Voltage ◽  
Discharge Current ◽  
Closed Form Solution ◽  
Approximate Model ◽  
Form Solution ◽  
Dynamic Impedance ◽  
Numerical Integration Methods

Simulation of gap breakdown and dynamic impedance effects in high voltage spark sources is performed using an algebraically exact solution to an approximate model of source behavior. The importance of diode shunt capacitance in determining gap breakdown behavior is shown. Limitations in generality and implicit use of numerical methods in dynamic situations lead naturally to consideration of numerical integration methods. Comparisons to hardware sources are made.

scholarly journals Closed form solution in buckling optimization problem of twisted rod

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimal Shape ◽  
Actual Problem ◽  
The Cross ◽  
Simply Connected

Abstract The applications of this method for stability problems are illustrated in this manuscript. In the context of twisted rods, the counterpart for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under torsion (Greenhill, 1883). We search the optimal shape of the rod along its axis. A priori form of the cross-section remains unknown. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. Thus, we drop the assumption about the equality of principle moments of inertia for the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The distribution of material along the length of a twisted rod is optimized so that the rod is of the constant volume T and will support the maximal moment without spatial buckling. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. We demonstrate at the beginning the validity of static Euler’s approach for simply supported rod (hinged), twisted by the conservative moment. The applied method for integration of the optimization criteria delivers different length and volumes of the optimal twisted rods. Instead of the seeking for the twisted rods of the fixed length and volume, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for twisted rod is stated in closed form in terms of the higher transcendental functions. In the torsion stability problem, the optimal shape of cross-section is the equilateral triangle.

Exact solution for time exponentially varying pulsed laser heating: Convective boundary condition case

2001 ◽  
Vol 215 (5) ◽  
pp. 591-606 ◽  
Author(s):  
M Kalyon ◽  
B S Yilbas
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Closed Form ◽  
Temperature Rise ◽  
Laser Heating ◽  
Closed Form Solution ◽  
Convective Boundary Condition ◽  
Form Solution ◽  
Heating Process ◽  
Convective Boundary

Laser heating offers considerable advantages over conventional methods. The closed-form solution for the temperature rise in the substrate during the laser heating process gives insight into the physical phenomena involving during the heating process and the material response to a laser heating pulse. In the present study, the exact solution for the temperature rise due to a time exponentially varying pulse and convective boundary condition at the surface is obtained. The closed-form solution to the solutions available in the literature for a step input intensity pulse with a convective boundary condition at the surface as well as a time exponentially varying pulse with a non-convective boundary condition at the surface is deduced. A Laplace transformation method is used in the analysis. In order to account for a pulse resembling a typical laser pulse, an intensity function resulting in exponentially increasing and decaying intensity distribution is employed in the source term in the governing transport equation. The effects of the pulse parameters β′, β′/γ′ and Biot number Bi on the resulting temperature profiles are presented and the material response to a pulse profile resembling a typical actual laser pulse is discussed. It is found that the closed-form solution obtained in the present study becomes identical with those presented in the previous studies for different pulse and boundary conditions. Moreover, the coupling effect of pulse parameter β and Bi is significant for the temperature rise at the surface.

Formulation of surface temperature for laser evaporative pulse heating: The time exponentially decaying pulse case

2002 ◽  
Vol 216 (3) ◽  
pp. 289-299 ◽  
Author(s):  
B S Yilbas ◽  
M Kalyon
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Solid Substrate ◽  
Form Solution ◽  
Solution Temperature ◽  
Heating Process ◽  
Pulse Parameter ◽  
Pulse Profile ◽  
Transform Method

Modelling of the laser heating process is fruitful, since it enhances the understanding of the physical processes involved and minimizes the experimental cost. In the present study, an analytical solution for the temperature distribution inside the solid substrate is obtained using a Laplace transform method. A time exponentially decaying laser pulse profile is introduced in the analysis. The phase change process and recession velocity are accommodated to account for the evaporation at the surface. The closed-form solution obtained is compared with the analytical solution obtained previously for a conduction limited heating case. It is found that the closed-form solution obtained from the present study reduces to a previously obtained analytical solution when the pulse parameter, β∗, is set to zero in the closed-form solution. Temperature predictions from simulations agree well with the results obtained from the closed-form solution.

Extension of the Circle Theorems by Surface Source Distribution

1989 ◽  
Vol 111 (3) ◽  
pp. 243-247 ◽  
Author(s):  
O. Rand
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strength Distribution ◽  
Form Solution ◽  
Source Distribution ◽  
Arbitrary Distribution ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Source

The paper presents a closed-form analytical solution for the source strength distribution along the circumference of a two-dimensional circular cylinder that is required for producing an arbitrary distribution of normal velocity. Being suitable to be used with flows having arbitrary vorticity distribution, the present formulation can be considered as an alternative and extensive form of the circle theorems. Using the conformal transformation technique, the formulation also serves as a closed-form solution of Laplace’s equation in any two-dimensional flow domain that is reducible to the outer or inner region of a circular cylinder having arbitrary prescribed normal velocity over its boundary.

On Some Problems in Transversely Isotropic Elastic Materials

1966 ◽  
Vol 33 (2) ◽  
pp. 347-355 ◽  
Author(s):  
W. T. Chen
Keyword(s):  
Circular Cylinder ◽  
Potential Function ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Static Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Concentrated Force ◽  
Applied Forces ◽  
Discontinuous Pressure

This paper treats some problems in a homogeneous transversely isotropic elastic material, occupying an infinite space, or an infinitely long circular cylinder. The analysis is based upon the potential function method by Elliott, with the addition of another potential function. The static solution is extended to include quasi-static, or steady-state problems. Closed-form solution is found for the problem of an arbitrarily oriented concentrated force in an infinite medium. The case of discontinuous pressure over an infinitely long circular cylinder is also studied with the aid of a numerical method of integration. The applied forces are assumed to be moving with uniform velocity along the anisotropic direction.

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