On the Buckling of Axially Compressed Imperfect Cylindrical Shells

1974 ◽  
Vol 41 (3) ◽  
pp. 737-743 ◽  
Author(s):  
J. Arbocz ◽  
E. E. Sechler
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Limit Point ◽  
Axial Load ◽  
Shooting Method ◽  
Response Pattern ◽  
Load Level ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary ◽  
Buckling Behavior

A theoretical investigation of the buckling behavior of imperfect isotropic shells with edge constraints and under axial compression was carried out. The nonlinear Donnell equations for imperfect isotropic shells have been reduced to an equivalent set of nonlinear ordinary differential equations. The resulting two-point boundary-value problem was solved numerically by the “shooting method.” The use of this method made it possible to investigate how the axial load level at the limit point is affected by the following factors: the rigorous enforcing of the experimental boundary conditions, the prebuckling growth caused by the edge constraint, the overall symmetry of the response pattern, and the orientation and shape of the axisymmetric and asymmetric imperfection components.

Finite Deflections and Snap-Through of High Circular Arches

1968 ◽  
Vol 35 (4) ◽  
pp. 763-769 ◽  
Author(s):  
J. V. Huddleston
Keyword(s):  
Boundary Value Problem ◽  
Cross Section ◽  
Digital Computer ◽  
Shooting Method ◽  
Point Boundary ◽  
Finite Deflections ◽  
Plane Shear ◽  
First Order ◽  
Buckling Behavior ◽  
First Order Differential Equations

The buckling behavior of two-hinged circular arches with any height-to-span ratio is studied by formulating the problem as a two-point boundary-value problem consisting of six nonlinear, first-order differential equations and appropriate boundry conditions. The theory is exact in the sense that no restrictions are placed on the size of the deflections or on the thickness of the arch. It is approximate in the sense that plane sections are assumed to remain plane, shear deformation is neglected, and the geometric properties of each cross section are assumed to remain constant during the deflection. The problem is solved on a digital computer by a shooting method that uses two levels of regula falsi and one of iteration. Selected results as plotted by the computer are shown and interpreted.

Adjoint Interior-Point Boundary Conditions for Linear Differential Operators

1977 ◽  
Vol 20 (4) ◽  
pp. 447-450 ◽  
Author(s):  
Robert Neff Bryan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Interior Point ◽  
Differential Operators ◽  
Boundary Value ◽  
Point Boundary ◽  
Linear Differential Operators ◽  
Linear Differential

The investigations reported in this paper were prompted by a remark by A. M. Krall in [2] that certain functional which appear in the boundary conditions of the system adjoint to a given linear differential boundary value problem seem artificial in that setting.

Effects of Friction on Post-Buckling Behavior and Axial Load Transfer in a Horizontal Well

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1104-1118 ◽  
Author(s):  
Guohua Gao ◽  
Stefan Miska
Keyword(s):  
Boundary Conditions ◽  
Critical Load ◽  
Axial Load ◽  
Load Transfer ◽  
Experimental Studies ◽  
Proper Solution ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Helical Buckling ◽  
Lateral Friction

Summary In this paper, the buckling equation and natural boundary conditions are derived with the aid of calculus of variations. The natural and geometric boundary conditions are used to determine the proper solution that represents the post-buckling configuration. Effects of friction and boundary conditions on the critical load of helical buckling are investigated. Theoretical results show that the effect of boundary conditions on helical buckling becomes negligible for a long pipe with dimensionless length greater than 5π Velocity analysis shows that lateral friction becomes dominant at the instant of buckling initiation. Thus, friction can increase the critical load of helical buckling significantly. However, once buckling is initiated, axial velocity becomes dominant again and lateral friction becomes negligible for post-buckling behavior and axial-load-transfer analysis. Consequently, it is possible to seek an analytical solution for the buckling equation. Analytical solutions for both sinusoidal and helical post-buckling configurations are derived, and a practical procedure for modeling of axial load transfer is proposed. To verify the proposed model and analytical results, the authors also conducted experimental studies. Experimental results support the proposed solutions.

scholarly journals The Solutions of Mixed Monotone Fredholm-Type Integral Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hua Su
Keyword(s):  
Boundary Value Problem ◽  
Banach Spaces ◽  
Unique Solution ◽  
Integral Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary ◽  
Fredholm Type ◽  
Monotone Iterative ◽  
Type Integral ◽  
Ordered Banach Spaces

By introducing new definitions ofϕconvex and-φconcave quasioperator andv0quasilower andu0quasiupper, by means of the monotone iterative techniques without any compactness conditions, we obtain the iterative unique solution of nonlinear mixed monotone Fredholm-type integral equations in Banach spaces. Our results are even new toϕconvex and-φconcave quasi operator, and then we apply these results to the two-point boundary value problem of second-order nonlinear ordinary differential equations in the ordered Banach spaces.

A two point boundary value problem for neutral functional differential equations

1983 ◽  
Vol 94 (3-4) ◽  
pp. 331-338
Author(s):  
Y. G. Sficas ◽  
S. K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Shooting Method ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Point Boundary ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Image Position

SynopsisThis paper is concerned with the existence of solutions of a two point boundary value problem for neutral functional differential equations. We consider the problemwhere M and N are n × n matrices. This is examined by using the “shooting method”. Also, an example is given to illustrate how our result can be applied to yield the existence of solutions of a periodic boundary value problem.

scholarly journals NONLOCAL THIRD ORDER BOUNDARY VALUE PROBLEMS WITH SOLUTIONS THAT CHANGE SIGN

2014 ◽  
Vol 19 (2) ◽  
pp. 145-154
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Scaling Method ◽  
Number Of Solutions

We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.

Existence and uniqueness for two-point boundary value problems

1981 ◽  
Vol 88 (3-4) ◽  
pp. 219-234 ◽  
Author(s):  
John V. Baxley ◽  
Sarah E. Brown
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Point Boundary ◽  
Initial Value

SynopsisBoundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

Nonlinear Analysis of Steep, Compressible Arches of Any Shape

1971 ◽  
Vol 38 (4) ◽  
pp. 942-946 ◽  
Author(s):  
J. V. Huddleston
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Nonlinear Analysis ◽  
Shooting Method ◽  
Point Boundary ◽  
Concentrated Load ◽  
First Order ◽  
Newton Raphson ◽  
Parabolic Arch ◽  
First Order Differential Equations

The buckling and snap-through behavior of steep arches is studied by treating the arch as a compressible, curved elastica. A technique previously developed for circular arches is here generalized for arches of any shape. As before, the system is described by a two or three-point boundary-value problem containing simultaneous, nonlinear, first-order differential equations. This problem is solved by a shooting method augmented by a Newton-Raphson technique for finding the original curvature at any point along the arch. Selected results for a circular and a parabolic arch under concentrated load are given, including symmetric and unsymmetric modes of buckling.

scholarly journals A shooting method for singular nonlinear second order Volterra integro-differential equations

1997 ◽  
Vol 20 (3) ◽  
pp. 589-598 ◽  
Author(s):  
R. E. Shaw ◽  
L. E. Garey
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Second Order ◽  
Point Boundary

The method of parallel shooting will be employed to solve nonlinear second order singular Volterra integro-differential equations with two point boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document