Design and Analysis of Composite Structures for Automotive Applications

Appendix CIntegral Transforms in Elasticity

C.1 One‐Dimensional Integral Transform

A general integral transform of the function ϕ(x) is defined by:

C.1

where K(ξ, x) is the transformation kernel.

Complex Fourier transform:

C.2

Fourier‐SINUS‐ and Fourier‐COSINUS transforms:

C.3

C.4

The inversion of Fourier transforms:

C.5

C.6

C.7

The transform of the derivative reads

C.8

C.2 Two‐Dimensional Fourier Transform

Two‐dimensional Fourier transform of the function ϕ(x, y):

C.9

C.10

C.11

The ...