Engineering components inevitably encounter various eigenstrains, such as thermal expansion strains, residual strains, and plastic strains. In this paper, a set of formulas for the analytical solutions to cases of uniform eigenstrains in a cuboidal region-influence coefficients, is presented in terms of derivatives of four key integrals. The linear elastic field caused by arbitrarily distributed eigenstrains in a half-space is thus evaluated by the discrete correlation and fast Fourier transform algorithm, along with the discrete convolution and fast Fourier transform algorithm. By taking advantage of both the convolution and correlation characteristics of the problem, the formulas of influence coefficients and the numerical algorithms are expected to enable efficient and accurate numerical analyses for problems having nonuniform distribution of eigenstrains and for contact problems.

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