General solution for dynamical problem of infinite beam on an elastic foundation

1991 ◽  
Vol 12 (7) ◽  
pp. 633-637 ◽  
Author(s):  
Zheng Xiao-ping ◽  
Wang Shang-wen ◽  
Chen Bai-ping
Keyword(s):  
General Solution ◽  
Elastic Foundation ◽  
Dynamical Problem ◽  
Infinite Beam

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Numerical investigation of non-linear deflections of an infinite beam on non-linear and discontinuous elastic foundation

2014 ◽  
Vol 15 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Hyoungsu Baek ◽  
Jinsoo Park ◽  
T.S. Jang ◽  
H.G. Sung ◽  
Jeom Kee Paik
Keyword(s):  
Numerical Investigation ◽  
Elastic Foundation ◽  
Infinite Beam ◽  
Non Linear
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