This paper introduces a variable elements length theory to solve the change of contact area in contact problems. It avoids recalculating the whole coefficient matrix. In this theory, element length is changed instead of element number in contact boundary problem. This measure keeps the contact area unchanged and saves computing time. The iterative process is discussed and the error estimate is given. Fast multipole boundary element method (FM-BEM) is improved by the variable elements length theory. The improved FM-BEM is used to solve the contact problems of cubes and strip cold rolling process. The results of improved FM-BEM are compared with the results of traditional FM-BEM and experimental data. Numerical examples clearly demonstrate that the calculation time and accuracy are improved by the improved FM-BEM. This method is suitable for solving contact problems and precision engineering problems.

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