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The current paper deals with the proof of a global solution of a viscoelasticity singular one-dimensional system with localized frictional damping and general source terms, taking into consideration nonlocal boundary condition. Moreover, similar to that in Boulaaras’ recent studies by constructing a Lyapunov functional and use it together with the perturbed energy method in order to prove a general decay result.

Purpose Metal additive manufacturing is an inherently thermal process, with intense localised heating and for sparse lattice structures, often rapid uneven cooling. Thermal effects influence manufactured geometry through residual stresses and may also result in non-isotropic material properties. This paper aims to increase understanding of the evolution of the temperature field during fabrication of lattice structures through numerical simulation. Design/methodology/approach This paper uses a reduced order numerical analysis based on “best-practice” compromise found in literature to explore design permutations for lattice structures and provide first-order insight into the effect of these design variables on the temperature field. Findings Instantaneous and peak temperatures are examined to discover trends at select lattice locations. Insights include the presence of vertical struts reduces overall lattice temperatures by providing additional heat transfer paths; at a given layer, the lower surface of an inclined strut experiences higher temperatures than the upper surface throughout the fabrication of the lattice; during fabrication of the lower layers of the lattice, isolated regions of material can experience significantly higher temperatures than adjacent regions. Research limitations/implications Due to the simplifying assumptions and multi-layer material additions, the findings are qualitative in nature. Future research should incorporate additional heat transfer mechanisms. Practical implications These findings point towards thermal differences within the lattice which may manifest as dimensional differences and microstructural changes in the built part. Originality/value The paper provides qualitative insights into the effect of local geometry and topology upon the evolution of temperature within lattice structures fabricated in metal additive manufacturing.