A fast and effective method for transient thermoelastic displacement analyses

Frictional heating due to the relative motion of contacting surfaces causes temperature rise and thermal distortion, which in turn affects the contact geometry and pressure distribution. A fast and effective method is present ed for the calculation of the normal surface displacement of an elastic hal fspace due to arbitrary transient surface heating. The method uses Fourier- transformed Green's functions (frequency response functions), found in the closed form by using the approach of Seo and Mura and the heat conduction a nalyses of Carslaw and Jaeger. The frequency response functions are shown a nalytically to be the frequency domain representations of the Green's funct ions given by Barber. The formulation for the surface normal displacement i s in the form of three-dimensional convolution integrals (over surface and rime) of the arbitrary transient heat flux and the Green's functions. Fouri er transforms of these convolution integrals are taken, avoiding the Green' s-function singularities and giving a simple multiplication bmt een the tra nsformed heat flux and the (known) frequency response functions. The discre te convolution-fast Fourier transform (DC-FFT) algorithm is applied for acc urate and efficient calculations of the normal surface displacement from th e frequency response functions for an arbitrary transient heat input. The c ombination of the frequency-domain formulation and the DC-FFT algorithm mak es the solution of transient thermoelastic deformation extremely fast and c onvenient.