Transient Response of an Elastic Homogeneous Half-Space to Suddenly Applied Rectangular Loading

1994 ◽  
Vol 61 (2) ◽  
pp. 256-263 ◽  
Author(s):  
F. Guan ◽  
M. Novak
Keyword(s):  
Laplace Transform ◽  
Half Space ◽  
Transient Response ◽  
Integral Kernel ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Inverse Laplace Transform ◽  
Line Load ◽  
Homogeneous Half Space

A closed-form solution of transient response to suddenly applied loading distributed over a rectangular area on the surface of an elastic homogeneous half-space is developed for special purposes such as analysis of dynamic soil-structure interaction or contact problems. The solution is obtained using Laplace transform with respect to time and Fourier transform with respect to space. Inverse Laplace transform is implemented analytically. As extreme cases of rectangular loading, the solutions for a point force or finite line load can also be obtained. The advantages of this solution over most other solutions by numerical analyses are that the multiple integrations are reduced by one order, the singularity is removed from the integral kernel, and no additional discretization in the vicinity of the region of interest is required.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

Response of an Elastic Half Space to Impulsive Stationary Finite Line Sources

1971 ◽  
Vol 38 (2) ◽  
pp. 549-550 ◽  
Author(s):  
F. R. Norwood
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Elastic Half Space ◽  
Line Load ◽  
Finite Line ◽  
Infinite Line

This Note considers the transient response in the interior of a half space acted upon by a normal impulsive stationary semi-infinite line load. The solution for the corresponding infinite line load problem is contained in the solution for the case of a semi-infinite line load. By a simple superposition, the solution is obtained for a half space acted upon by a finite line load.

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