A numerical method is presented for determining the limit loads of periodically heterogeneous structures subjected to variable loads. The Melan’s lower-bound shakedown theorem was applied to representative volume elements. Combined with the homogenization technique, the homogenized material properties were determined through transformation from the mesoscopic to macroscopic admissible loading domains. For the numerical applications, solid non-conforming finite element discretization and large-scale nonlinear optimization, based on an interior-point-algorithm were used. The methodology is illustrated by the application to pipes models. This way, the proposed method provides a direct numerical approach to evaluate the macroscopic strength of heterogeneous structures with periodic micro- or meso-structure as a useful tool for the design of structures.

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