In the present paper, a method is proposed for topology optimization of continuum structures subject to static and plastic admissibility conditions relative to a prescribed load.A key feature of the method is that, using a finite-element discretization, the form of the resulting topology optimization problem is similar to that of the direct static approach of the limit analysis problem. The proposed method is formulated in plane strain using Tresca materials and is illustrated on example problems taken from the literature.

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International audienceA general decomposition approach for the static method of limit analysis is proposed. It is based on piecewise linear stress fields, on a partition into finite element sub-problems and on a specific coordination of the subproblem stress fields through auxiliary interface problems. The final convex optimization problems are solved using nonlinear interior point programming methods. As validated for the compressed bar with Tresca/von Mises materials in plane strain, this method appears rapidly convergent, so that very large problems with millions of constraints and variables can be solved. Then the method is applied to the classical problem of the stability of a Tresca vertical cut: the static bound to the stability factor is improved to 3.7752, a value to be compared with the recent best upper bound 3.7776

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In view of the COVID-19 pandemic, most countries in the world have mandated the use of face masks to limit the spread of this dangerous disease. The billions of face masks that are produced around the world to date generate millions of tonnes of plastic waste that is thrown into the environment. The present work aims to valorise single-use masks or surgical masks in mortar. In this work, the effect of substituting 1–5% of the volume of the mortar with pieces of masks of 2 cm 2 section and 4 cm 2 section is explored. Mechanically, an increase in compressive strength of between 10 and 20% is noted, as well as an improvement in flexural strength of 19–30%. Physically, the thermal resistance of the mortars formulated from waste mask improved by up to 23%, and there was a clear improvement in the acoustic reflection coefficient for all frequencies. The capillary rise test conducted on the mortar samples shows that the amount of the absorbed water increases. However, although in most cases the presence of mask pieces increases the sorptivity of the mortar, this is not associated with a higher capillary rise. The results found are encouraging, allowing on the one hand to improve the physical and mechanical characteristics of the mortar and on the other hand to solve a dangerous environmental problem.