On transmissible load formulations in topology optimization

Transmissible loads are external loads defined by their line of action, with actual points of load application chosen as part of the topology optimization process. Although for problems where the optimal structure is a funicular, transmissible loads can be viewed as surface loads, in other cases such loads are free to be applied to internal parts of the structure. There are two main transmissible load formulations described in the literature: a rigid bar (constrained displacement) formulation or, less commonly, a migrating load (equilibrium) formulation. Here, we employ a simple Mohr’s circle analysis to show that the rigid bar formulation will only produce correct structural forms in certain specific circumstances. Numerical examples are used to demonstrate (and explain) the incorrect topologies produced when the rigid bar formulation is applied in other situations. A new analytical solution is also presented for a uniformly loaded cantilever structure. Finally, we invoke duality principles to elucidate the source of the discrepancy between the two formulations, considering both discrete truss and continuum topology optimization formulations

Effects of Al:Si and (Al+Na):Si Ratios on the Static Corrosion of Sodium-Boroaluminosilicate Glasses

International audienceUnderstanding alteration mechanisms of borosilicate glasses in aqueous media is essential to nuclear waste performance assessments to ensure radioisotopes are contained for extended durations. Aluminum is typically added to glass compositions to reduce the extent of alteration. However, previous work on 7-day durability tests has suggested that Al has a non-linear relationship with extent of alteration. The effects of Al:Si and (Al+Na):Si substitutions on glass durability were evaluated using series of glasses based on the International Simple Glass corroded in static conditions up to 13 months in deionized water at 90 °C. The alteration behavior was determined by measurement of element release in solution. The ⁓7-day alteration trends across the series were consistent with predicted trends. The 13 month results indicated overall alteration decreased as Al:Si ratios increased and was unaffected by changes in (Al+Na):Si except for the glass with the highest (Al+Na):Si ratio (ISG-A23N), which completely altered within 14 days. Frequent sampling and in-situ Raman measurements revealed ISG-A23N experienced several distinguishable alteration rate regimes within 7 days, forming a ⁓100 µm alteration layer and a NaSiAlO4 zeolite