Boundary conditions for unit cells from periodic microstructures and their implications

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A variational model for stress analysis in cracked laminates with arbitrary symmetric lay-up under general in-plane loading (2014, background): “…ð88Þ @F @fw0g T f@wg " #x¼a x¼ a ¼ 0 ð89Þ The left-hand side of the above equations, shortly denoted as ½XY x¼þax¼ a, can be manipulated as (Li and Hafeez, 2009), (Li, 2008) and (Li et al., 2009): ½XY x¼þax¼ a ¼ XþaYþa X aY a ¼ 1 2 ðXþa X aÞðYþa þ Y aÞ þ 1 2 ðXþa þ X aÞðYþa Y aÞ ð90Þ (Y+a Y-a) =…”
Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures (2017, methodology): “Periodic boundary conditions are used to obtain the effective properties computationally [58,59].”