Cantilever Rod in Cross Wind

1989 ◽  
Vol 56 (3) ◽  
pp. 639-643 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Numerical Integration ◽  
Large Deformation ◽  
Aerodynamic Drag ◽  
Flexural Rigidity ◽  
Relative Importance ◽  
Elastic Rod ◽  
Nondimensional Parameter ◽  
Cantilever Rod ◽  
Thin Elastic Rod

A thin elastic rod is held at one end in a strong cross wind. The nonlinear large deformation equations are formulated and solved by perturbation and numerical integration. The problem is governed by a nondimensional parameter K representing the relative importance of aerodynamic drag to flexural rigidity. For large K, phenomena such as nonuniqueness, instability, and hysteresis may occur.

Unfolding a Curved Elastic Sheet

1981 ◽  
Vol 23 (5) ◽  
pp. 217-219 ◽  
Author(s):  
C.-Y. Wang
Keyword(s):  
Flat Plate ◽  
Numerical Integration ◽  
Flexural Rigidity ◽  
Elliptic Functions ◽  
Applied Force ◽  
Relative Importance ◽  
Dimensional Parameter ◽  
Elastic Sheet ◽  
Leaf Springs ◽  
Force Displacement

A curved elastic sheet is flattened on a rigid flat plate by vertical end forces. The problem is governed by a non-dimensional parameter, B, which signifies the relative importance of flexural rigidity to the applied force and the natural radius. The elastica equations are solved by elliptic functions, perturbation for small B, and numerical integration. Force-displacement characteristics and sheet configurations are found. The results may be applied to sandwiched leaf springs.

Equilibrium of Heavy Elastic Cylindrical Shells

1981 ◽  
Vol 48 (3) ◽  
pp. 582-586 ◽  
Author(s):  
C.-Y. Wang ◽  
L. T. Watson
Keyword(s):  
General Solution ◽  
Numerical Integration ◽  
Newton Method ◽  
Perturbation Analysis ◽  
Similarity Solution ◽  
Flexural Rigidity ◽  
Equilibrium Shape ◽  
Elastic Shell ◽  
Relative Importance ◽  
Quasi Newton

An originally circular, heavy elastic shell rests on a horizonal surface. The equilibrium shape is governed by the heavy elastica equations. The solutions depend heavily on the parameter B, which represents the relative importance of density and perimeter length to flexural rigidity. There are four distinct cases. A perturbation analysis is obtained for small B while a similarity solution exists for large B. The general solution is obtained by accurate numerical integration using a least change secant update quasi-Newton method and a new homotopy method.

scholarly journals Existence and uniqueness of equilibrium states of a rotating elastic rod

1994 ◽  
Vol 17 (2) ◽  
pp. 315-322
Author(s):  
M. B. M. Elgindi
Keyword(s):  
Equilibrium Equation ◽  
Existence And Uniqueness ◽  
Flexural Rigidity ◽  
Rotation Axis ◽  
Critical Value ◽  
Uniqueness Of Solution ◽  
Bifurcation Problem ◽  
Elastic Rod ◽  
Two Parameters ◽  
Uniqueness Of Equilibrium

A flexible rod is rotated from one end. The equilibrium equation is a fourth order nonlinear two-point boundary value problem which depends on two parametersλandαrepresenting the importance of centrifugal effects to flexural rigidity and the angle between the rotation axis and the clamped end, respectively. Previous studies on the existence and uniqueness of solution of the equilibrium equation assumedα=0. Among the findings of these studies is the existence of a critical valueλcbeyond which the uniqueness of the “trivial” solution is lost. The computations ofλcrequired the solution of a nonlinear bifurcation problem. On the other hand, this work is concerned with the existence and uniqueness of solution of the equilibrium equation whenα≠0and in particular in the computations of a critical valueλcsuch that the equilibrium equation has a unique solution for eachα≠0providedλ<λc. For smallα≠0this requires the solution of a nonlinear perturbed bifurcation problem.

Melting From a Horizontal Rotating Disk

1989 ◽  
Vol 56 (1) ◽  
pp. 47-50 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Heat Transfer ◽  
Numerical Integration ◽  
Stokes Equations ◽  
Rotating Disk ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Relative Importance ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Transfer Rates

Melting of a disk is facilitated by rotation. The problem is governed by a nondimensional parameter α which represents the relative importance of injection (melt) rate and rotation times viscosity. The nonlinear governing equations are solved by perturbations for small α and numerical integration for arbitrary α. Torque and heat transfer rates are found. The solution is one of the rare exact similarity solutions of the Navier-Stokes equations.

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