A fast and accurate method for numerical analysis of elastic layered contacts

Solution of contact problems for layered elastic solids generally requires the use of numerical methods. Recently, the fast Fourier transform (FFT) technique has been applied to such contacts. While very fast, FFT is strictly applicable only to periodic contact problems. When it is applied to essentially non-periodic contacts, an error is introduced in the numerical solution. A new method that overcomes the limitation of the 'straightforward' FFT approach for solving non-periodic layered contact problems is introduced in the present article. A special correction procedure based on the multi-level multi-summation technique is used to compensate the FFT results for the periodicity error. The use of a robust iteration scheme based on the conjugate gradient method ensures that the new method is applicable to contact problems involving real rough surfaces. Numerical examples demonstrate that the new method is both accurate and fast.