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.

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.

The Compressible Elastica on an Elastic Foundation

1982 ◽  
Vol 49 (3) ◽  
pp. 577-583 ◽  
Author(s):  
A. M. Nicolau ◽  
J. V. Huddleston
Keyword(s):  
Boundary Value Problem ◽  
Elastic Foundation ◽  
Shooting Method ◽  
Initial Point ◽  
Terminal Point ◽  
Point Boundary ◽  
System Parameters ◽  
First Order ◽  
Technical Theory ◽  
First Order Differential Equations

The nonlinear two-point boundary-value problem describing the compressible elastica on an elastic foundation is formulated exactly within the context of the technical theory of bending as a set of eight first-order differential equations plus appropriate initial-point conditions and terminal-point conditions. The problem is then solved by a shooting method that determines two missing quantities. Graphs of load versus displacements and load versus the missing quantities are presented for various combinations of the system parameters. These results show that the presence of the elastic foundation enables the member to sustain unsymmetric (as opposed to antisymmetric) shapes in its postbuckled state, and that bifurcations from the straight configuration to symmetric buckled modes and bifurcations from symmetric buckled modes to unsymmetric ones depend on two system parameters—a compressibility measure and the foundation modulus. For a given compressibility and foundation stiffness, equilibrium paths are plotted globally, enabling unsymmetric paths to be extended from one bifurcation point to another, with the result that the complete postbuckling process can be traced. Finally, a discussion of path shapes as a function of foundation stiffness is given.

The Iterative Shooting Method Applied to the Modeling of the In-Run Profile of a Ski Jumping Hill

2015 ◽  
Vol 712 ◽  
pp. 37-42 ◽  
Author(s):  
Renata Filipowska
Keyword(s):  
Shooting Method ◽  
Order Differential Equation ◽  
Reaction Force ◽  
Point Boundary ◽  
Normal Reaction ◽  
Initial Value ◽  
First Order ◽  
Sensitivity Functions ◽  
Ski Jumping ◽  
First Order Differential Equations

This paper treats an iterative shooting method based on sensitivity functions for solving non–linear two–point boundary value problems (BVPs), in the form of a second–order differential equation and four boundary conditions. The solution of this BVP constitutes an in–run profile of a ski jumping hill. It is characterized by reduced a normal reaction force, which has impact on ski jumper’s legs during sliding downhill. In order to use this method, it is necessary to convert the BVP to an appropriate initial value problem (IVP). Consequently, in each iteration, we must solve a system of six first–order differential equations.

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.

scholarly journals Discrete First-Order Three-Point Boundary Value Problem

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Mohamed ◽  
H. B. Thompson ◽  
M. S. Jusoh ◽  
K. Jusoff
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
First Order

scholarly journals Application of The Riccati Method to The Adiabatic Oscillations of Stars

2004 ◽  
Vol 193 ◽  
pp. 483-486
Author(s):  
M. Takata ◽  
W. Löffler
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Shooting Method ◽  
Relaxation Method ◽  
Linear Differential Equations ◽  
Matrix Riccati Equation ◽  
First Order ◽  
Nonlinear Matrix ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractThe eigenmodes of the adiabatic oscillations of stars are usually calculated numerically by solving the system of the four linear first-order differential equations using either the relaxation method or the shooting method. Finding some shortcomings in these conventional methods, we adopt another method, namely the Riccati method, in which it is not the system of the linear differential equations but the nonlinear matrix Riccati equation that is solved numerically. After describing the method, we discuss its advantages and give some demonstrations.

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.

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