A Solution for the Thin Elastic Shell With Surface Loads

1964 ◽  
Vol 31 (1) ◽  
pp. 91-96 ◽  
Author(s):  
C. R. Steele
Keyword(s):  
Temperature Distribution ◽  
Elastic Foundation ◽  
Wide Class ◽  
Elastic Shell ◽  
Asymptotic Series ◽  
Surface Load ◽  
Thin Elastic Shell ◽  
Curvature Coordinate ◽  
Particular Solution ◽  
Surface Loads

The problem considered is the thin elastic shell described by the equations of Novozhilov with an arbitrary but smooth midsurface that has a surface load and/or temperature distribution which varies rapidly with respect to one curvature coordinate. The particular solution is obtained in the form of an asymptotic series in powers of a parameter which is a measure of the rapidity of variation in the distribution. The wide class of problems, for which only the first term of the asymptotic series need be retained, is analogous to the beam on an elastic foundation. However, the advantage of the complex representation of Novozhilov is demonstrated by an example in which the shell is loaded and heated on strips with several conditions of constraint.

scholarly journals Acoustic Scattering by an Axisymmetric Thin Elastic Shell

1971 ◽  
Vol 50 (1A) ◽  
pp. 153-153
Author(s):  
S. Chang ◽  
B. S. Chambers ◽  
B. J. Maxum
Keyword(s):  
Elastic Shell ◽  
Acoustic Scattering ◽  
Thin Elastic Shell

Static and Dynamic Buckling of a Compressed Narrow Rectangular Plate on an Elastic Foundation

2008 ◽  
Author(s):  
Leonid Srubshchik ◽  
Issac Herskowitz ◽  
Irina Peckel ◽  
Edward Potetyunko
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Isotropic Plate ◽  
Vertical Direction ◽  
Dynamic Buckling ◽  
Initial Time ◽  
Asymptotic Formulas ◽  
Surface Load ◽  
Small Surface ◽  
Asymptotic Values

In this paper we consider a thin narrow rectangular isotropic plate subjected to a small surface load and supported laterally by a continuous nonlinear elastic foundation. The both short ends of plate are clamped while the longitudinal sides are completely free, so that their points can move along the boundary, along the normal to the boundary, and in a vertical direction. At initial time the uniformly distributed in-plane compressive stresses are suddenly applied to the short ends in the longitudinal direction. Our goal is to find the asymptotic formulas for values of static and dynamic buckling load in the case of the narrow elastic plate and estimate their values as function of the imperfection parameter. We apply the geometrically nonlinear theory for the thin rectangular isotropic plate laterally supported by the continuous softening or stiffening foundation to formulate an associated nonlinear spectral problem for the load parameter. This problem contains a small natural parameter δ - the ratio of the width of the rectangular plate to its length and can be integrated using the asymptotic method developed in the work by Srubshchik, Stolyar and Tsibulin [1]. Accordingly we approximate the solution of the original problem by the leading term of the finite expansion in δ which is described by the motion equations of an axially compressed elastic column on the nonlinear continuous elastic foundation which has only one spatial dimension and can be investigated more comprehensively. The formulas for asymptotic values of the static and dynamic buckling compressive loads are obtained by means of the perturbation theory and by one-term Fourier’s approximation respectively. The specific numerical results for these asymptotic values are presented.

Modelling the transient interaction of a thin elastic shell with an exterior acoustic field

2008 ◽  
Vol 75 (3) ◽  
pp. 275-290 ◽  
Author(s):  
David J. Chappell ◽  
Paul J. Harris ◽  
David Henwood ◽  
Roma Chakrabarti
Keyword(s):  
Acoustic Field ◽  
Elastic Shell ◽  
Thin Elastic Shell ◽  
Transient Interaction

The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response

1996 ◽  
Vol 118 (3) ◽  
pp. 277-284 ◽  
Author(s):  
S. F. Felszeghy
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
State Solution ◽  
Actual Problem ◽  
State Response ◽  
Particular Solution

The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.

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