scholarly journals Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Euclides Mesquita ◽  
Edivaldo Romanini ◽  
Josue Labaki
Keyword(s):  
Closed Form ◽  
Integral Transform ◽  
Physical Space ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Constant Load ◽  
Wave Number ◽  
Dynamic Displacement ◽  
Closed Form Solutions ◽  
Fourier Integral Transform

A dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full space is presented. The solution is obtained within the frame of a double Fourier integral transform. Closed-form solutions for general loadings within the full space are furnished in the transformed wave number domain. Expressions for three boundary value problems, associated to a normal and two tangential rectangular loadings in the original physical space, are given in terms of a double inverse Fourier integral. These inverse integral transforms must be evaluated numerically. In the second part of the present paper a strategy to evaluate these integrals is described, the procedure validated and a number of original results are reported.

scholarly journals Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part II: Implementation, Validation, and Numerical Results

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Josue Labaki ◽  
Edivaldo Romanini ◽  
Euclides Mesquita
Keyword(s):  
Present Article ◽  
Integral Transform ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Constant Load ◽  
Numerical Results ◽  
Dynamic Displacement ◽  
Loading Case ◽  
Fourier Integral Transform ◽  
Stationary Loading

In part I of the present article the formulation for a dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full-space has been presented. The solution is obtained within the frame of a double Fourier integral transform. These inverse integral transforms must be evaluated numerically. In the present paper, the technique to evaluate numerically the inverse double Fourier integrals is described. The procedure is validated, and a number of original displacement results for the stationary loading case are reported.

Effects of Interleaves on Fracture of Laminated Composites: Part I—Analysis

1990 ◽  
Vol 57 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. K. Kaw ◽  
J. G. Goree
Keyword(s):  
Composite Laminates ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Elastic Media ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Fourier Integral Transform ◽  
Shaped Crack ◽  
Symmetric Crack

The influence of placing interleaves between fiber-reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as a two-dimensional, isotropic, linearly elastic media consisting of a damaged layer bonded between two half-planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. Fourier integral transform techniques are used to develop the solutions in terms of singular integral equations.

Transient Response of a Periodically Supported Cylindrical Shell Immersed in a Fluid Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 562-568 ◽  
Author(s):  
Harry Herman ◽  
J. M. Klosner
Keyword(s):  
Cylindrical Shell ◽  
Integral Transform ◽  
Circular Cylindrical Shell ◽  
Fourier Integral ◽  
Cylindrical Wave ◽  
Acoustic Medium ◽  
Steel Shell ◽  
Fluid Medium ◽  
Wave Approximation ◽  
Fourier Integral Transform

The dynamic response of a periodically simply supported, infinitely long, circular cylindrical shell to a pressure suddenly applied through the surrounding acoustic medium is investigated. The incident particle velocity is zero, and the pressure is assumed to have a harmonic spatial variation parallel to the shell axis. The exact solution is obtained by use of a Fourier integral transform, and the resulting inversion integral is evaluated by numerical and asymptotic integration. Two solutions to the same problem are obtained by using a plane and cylindrical wave approximation for the radiated field. The range of their applicability is investigated. For a steel shell in water ccs2=0.08815 it is found that, when the supports are placed three shell diameters apart, the use of the cylindrical wave approximation results in a 5-percent underestimation of the maximum deflection, while when the supports are placed one sixth of a shell diameter apart, the approximations are invalid.

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