On stress analysis of load for microperiodic composite half-plane with slant lamination

Abstract

The paper deals with the plane problem of normal and tangential load for microperiodic composite with slant lamination. The boundary condition was considered as a normal and tangential load given on the surface of the composite half-plane. Microperiodic composite consisted of two components, differing in their Young’s modules. The homogenized model with microlocal parameters, which is presented by Woźniak (Int J Eng Sci 25:483–498, 1987. https://doi.org/10.1016/0020-7225(87)90102-9), Jędrysiak (Compos Struct 202:1253–1262, 2018. https://doi.org/10.1016/J.COMPSTRUCT.2018.05.155) was used to solve the considered problem. The problem was formulated and solved using the averaged boundary condition given by Perkowski et al. (Compos Sci Technol 67:2683–2690, 2007. https://doi.org/10.1016/J.COMPSCITECH.2007.02.013). The considered boundary value problem will be solved using the Fourier transform method. An analytical solution was obtained in a general form for any form of the function describing normal and tangential loads on the surface of a half-plane. An analytical solution was determined for the special cases of an elliptical, normal and tangential loads and for the special case of the concentrated force. The results are shown in the form of figures.