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

STATISTICAL MODEL FOR GIGACYCLE S-N FATIGUE CURVES: PARAMETER ESTIMATION

In recent years, experimental tests exploring the gigacycle fatigue properties of materials suggest the introduction of modifications in well known statistical fatigue life models. Usual fatigue life models, characterized by failures due to a single failure mode and by the presence of the fatigue limit, have been integrated by models accounting for two failure modes and the possible presence of a fatigue limit. A unified statistical model which can take into account any number of failure modes and the possible presence of a fatigue limit has already been defined. The paper presents a robust method to estimate the parameters involved in the probabilistic model, by applying the Maximum Likelihood Estimation (MLE) method. The robustness of the method, implemented in a MATLAB® environment, is demonstrated by means of several simulated test cases. As an example, the method is applied to experimental data taken from the literatur