Application of Short and Long (Enhanced Vlasov's) Solutions for Cylindrical Shell on Example of Concentrated Radial Force

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Andrii Oryniak ◽  
Igor Orynyak
Keyword(s):  
Cylindrical Shell ◽  
Efficient Solution ◽  
Radial Force ◽  
Circumferential Direction ◽  
Axial Line ◽  
Eighth Order ◽  
Concentrated Force ◽  
Accuracy Of Results ◽  
Analytical Approaches ◽  
Asme Paper

Abstract Analytical approaches for cylindrical shell are mostly based on expansion of all variables in Fourier series in circumferential direction. This leads to eighth-order differential equation with respect to axial coordinate. Here it is approximately treated as a sum of two fourth-order biquadratic equations. First one assumes that all variables change more quickly in circumferential direction than in axial one (long solution), while the second (short) one is based on opposite assumption. The accuracy and applicability of this approach were demonstrated (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032) on example of action of one or two concentrated radial forces and compared with finite element method results. This paper is an improvement of our previous work (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032). Two amendments are made. The first is insignificant one and use slightly modified expressions for bending strains, while the second one relates to the short solution. Here we do not consider any more that circumferential displacement is negligible as compared with radial one. Eventually this improves the accuracy of results, as compared with previous work. For example, for cylinder with radius, R, to wall thickness, h, ratio equal to 20, the maximal inaccuracy for radial displacement in point of force application decreases from 5% to 3%. For thinner cylinder with R/h = 100, this inaccuracy decreases from 2.5% to 1.25%. These inaccuracies are related to larger terms in Fourier expansion, the significance of which decrease when length or area of outer loading becomes greater. The last conclusion is demonstrated for the case of distributed concentrated force acting along short segment on axial line.

Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov’s) Solutions on Example of Concentrated Radial Force

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Andrii Oryniak
Keyword(s):  
Cylindrical Shell ◽  
Axial Force ◽  
Shear Force ◽  
Radial Force ◽  
Circumferential Direction ◽  
Practical Significance ◽  
Geometrical Parameters ◽  
Practical Consideration ◽  
Simplified Approach ◽  
Circumferential Displacement

There is the general feeling among the scientists that everything what could be performed by theoretical analysis for cylindrical shell was already done in last century, or at least, would require so tremendous efforts, that it will have a little practical significance in our era of domination of powerful and simple to use commercial software. Present authors partly support this point of view. Nevertheless there is one significant mission of theory which is not exhausted yet, but conversely is increasingly required for engineering community. We mean the educational one, which would provide by rather simple means the general understanding of the patterns of deformational behavior, the load transmission mechanisms, and the dimensionless combinations of physical and geometrical parameters which governs these patterns. From practical consideration it is important for avoiding of unnecessary duplicate calculations, for reasonable restriction of the geometrical computer model for long structures, for choosing the correct boundary conditions, for quick evaluation of the correctness of results obtained. The main idea of work is expansion of solution in Fourier series in circumferential direction and subsequent consideration of two simplified differential equations of 4th order (biquadratic ones) instead of one equation of 8th order. The first equation is derived in assumption that all variables change more quickly in axial direction than in circumferential one (short solution), and the second solution is based on the opposite assumption (long solution). One of the most novelties of the work consists in modification of long solution which in fact is well known Vlasov’s semi-membrane theory. Two principal distinctions are suggested: a) hypothesis of inextensibility in circumferential direction is applied only after the elimination of axial force; b) instead of hypothesis zero shear deformation the differential dependence between circumferential displacement and axial one is obtained from equilibrium equation of circumferential forces by neglecting the forth order derivative. The axial force is transmitted to shell by means of short solution which gives rise (as main variables in it) to a radial displacement, its angle of rotation, bending radial moment and radial force. The shear force is also generated by it. The latter one is equilibrated by long solution, which operates by circumferential displacement, axial one, axial force and shear force. The comparison of simplified approach consisted from short solution and enhanced Vlasov’s (long) solution with FEA results for a variety of radius to wall thickness ratio from big values and up to 20 shows a good accuracy of this approach. So, this rather simple approach can be used for solution of different problems for cylindrical shells.

scholarly journals To the solution of the problem of bending of a cylindrical shell by the boundary elements method

2018 ◽  
Vol 230 ◽  
pp. 02032 ◽  
Author(s):  
Mykola Surianinov ◽  
Yurii Krutii
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Boundary Elements ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Various Boundary Conditions ◽  
Analytical Construction ◽  
Load Vector ◽  
Plates And Shells ◽  
Boundary Elements Method

The solution of the problem of the long cylindrical shell bending by a numerical and analytical boundary elements method is considered. The method is based on the analytical construction of a fundamental system of solutions and Green’s functions for the differential equation of the problem under consideration. This paper is devoted to the determination of these expressions. The semi-moment theory of the cylindrical shell calculation, proposed by V.Z. Vlasov, which for the problem under consideration leads to one eighth-order partial differential equation is used. The problem of the bending of a cylindrical shell is twodimensional, and in the numerical and analytical boundary elements method, plates and shells are considered as generalized one-dimensional modules, so the variational method of Kantorovich-Vlasov was applied to this equation to obtain an ordinary differential equation of the eighth order. Sixty-four expressions of all the fundamental functions of the problem are constructed, as well as an analytic expression for the Green’s function, which makes it possible to construct a load vector (without any restrictions on the nature of its application), and then proceed to the solution of boundary-value problems for the bending of long cylindrical shells under various boundary conditions.

Analysis of a cylindrical shell reinforced with a stringer loaded by a radial force

1966 ◽  
Vol 2 (4) ◽  
pp. 20-22
Author(s):  
E. V. Binkevich ◽  
A. L. Gashko ◽  
V. P. Manza
Keyword(s):  
Cylindrical Shell ◽  
Radial Force

scholarly journals A system of two infinite beams separated by an elastic core under moving load

2018 ◽  
Vol 19 (12) ◽  
pp. 285-288
Author(s):  
Magdalena Ataman ◽  
Wacław Szcześniak
Keyword(s):  
Differential Equations ◽  
Moving Load ◽  
Fourier Integral ◽  
Winkler Foundation ◽  
Eighth Order ◽  
Concentrated Force ◽  
Moving Force ◽  
Elastic Core ◽  
Lower Beam ◽  
Extensive List

The paper discussed the analytical solution of a dynamic problem of a system of two infinite beams separated by an elastic core. The beams’ system rests on the Winkler foundation and is loaded with a moving concentrated force. Because the problem is stationary for an observer moving with the load, partial differential equations, describing the vibrations of the system, were transformed into ordinary differential equations in the coordinate system related to the moving force. The system of equations was transformed to one differential equation of an eighth order. The equation defines deflection of the lower beam. The solution of the problem was resulted to the simple infinite Fourier integral. An extensive list of publications on the related literature is presented in the paper [1-45].

Geometric Elements in the Elastic-Plastic Analysis of a Cylindrical Shell

1991 ◽  
Vol 44 (11S) ◽  
pp. S181-S193 ◽  
Author(s):  
S. Lukasiewicz ◽  
J. Nowinka
Keyword(s):  
Cylindrical Shell ◽  
Deformation Behavior ◽  
Geometric Approach ◽  
Radial Force ◽  
Deformation Pattern ◽  
Element Solution ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Plastic Zones ◽  
Geometric Elements

The paper deals with an elastic-plastic analysis of a cantilever cylindrical shell loaded at its free end by a concentrated radial force. The problem is solved by means of the so-called “geometric elements” which conform to the deformation pattern of the shell. The results obtained define the large deformation behavior and the motion of plastic zones over the surface of the shell. A comparison with a standard finite element solution is made, and the advantages of the geometric approach are shown.

Correlation Parameters for Eliminating the Effect of Pulse Shape on Dynamic Plastic Deformation

1970 ◽  
Vol 37 (3) ◽  
pp. 744-752 ◽  
Author(s):  
C. K. Youngdahl
Keyword(s):  
Plastic Deformation ◽  
Cylindrical Shell ◽  
Pulse Shape ◽  
Circular Cylindrical Shell ◽  
Strong Dependence ◽  
Uniform Pressure ◽  
Concentrated Force ◽  
Total Impulse ◽  
The Mean ◽  
Mean Time

The solutions to four classical problems in dynamic plasticity—the circular plate under uniform pressure, the reinforced circular cylindrical shell under uniform pressure, the free-free beam with a central concentrated force, and the circular cylindrical shell with a ring load—are examined to determine the effect of pulse shape on final plastic deformation. It is found that there is a strong dependence on pulse shape for pulses which have the same total impulse and maximum load; however, the effect of the pulse shape is virtually eliminated if the pulses have the same total impulse and “effective load.” The “effective load” is defined as the impulse divided by twice the mean time of the pulse, where the mean time is the interval between the onset of plastic deformation and the centroid of the pulse.

Bubble-induced noise and vibration in cylindrical shell filled with liquid nitrogen

2017 ◽  
Vol 232 (5) ◽  
pp. 804-814
Author(s):  
Manoj Kumar Gupta ◽  
Dharmendra S Sharma ◽  
VJ Lakhera
Keyword(s):  
Black Holes ◽  
Cylindrical Shell ◽  
Gravitational Wave ◽  
Liquid Nitrogen ◽  
Laser Interferometer ◽  
Noise Spectrum ◽  
Radial Force ◽  
Critical Systems ◽  
Displacement Effect ◽  
Acoustic Effect

Bubble-induced vibration is a very crucial aspect in some critical systems like laser interferometer gravitational-wave observatory. Recently, laser interferometer gravitational-wave observatory detected the gravitational wave produced due to the merger of two black holes. To detect the other universe collision event due to other binary pairs like neutron stars, black holes or combination, the sensitivity of the detector should be very high. The sensitivity depends on the reduction of the noise present in the detector system / components. Liquid nitrogen cryopump is also one of the sources for the noise. This noise has been produced due to the bubble structure interaction. The present work analyzes the bubble generated noise spectrum level and its acoustic effect due to induced vibration. The spectrum levels considering force, acceleration, velocity, and displacement effect have been studied in detail for a thin annular fluid (LN2) filled cylindrical shell. It is assumed that the structure of cylindrical shell is homogeneous as well as isotropic. The noise level generated due to radial force excitation resulting from bubble collision has been found to be in the range of −85 dB to −45 dB at a lower resonance frequency.

Effect of Volumetric Fiber Fraction on Failure Strength of Thin-Walled GFRP Composite Cylindrical Shell Externally Pressurized

2012 ◽  
Vol 488-489 ◽  
pp. 530-536 ◽  
Author(s):  
Soheil Gohari ◽  
Abolfazl Golshan ◽  
Farzin Firouzabadi ◽  
Navid Hosseininezhad
Keyword(s):  
Cylindrical Shell ◽  
Shear Deformation ◽  
Failure Criteria ◽  
Failure Strength ◽  
Composite Cylindrical Shell ◽  
Fiber Angle ◽  
Fiber Fraction ◽  
Gfrp Composite ◽  
Thin Walled ◽  
Analytical Approaches

Externally pressurized thin-walled GFRP composite cylindrical shell strength was studied against failure. Fiber breakage, matrix breakage, interlaminate shear deformation, delamination shear deformation and micro buckling failure were investigated employing maximum failure criteria as volumetric fiber fraction factor varied. One-ply cylindrical shell with fiber angle orientation of 0 degree was modeled in ABAQUS finite element simulation and the result was varied using analytical approaches. Moreover, the pressure fluctuations for various volumetric fiber fraction factors were quadratic according to plotted graphs obtained. Meanwhile, MATLAB software was used for theoretical analysis. The comparison of two approaches was proved to be accurate. Subsequently, failure strength of various laminated GFRP cylindrical shell with different fiber angle orientations at each ply was studied for diverse volumetric fiber fraction factors. Stacking sequence, fiber angle orientations were mainly effective on failure strength.

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