Allowable Load Set (ALS) has been introduced as a new concept, which allows an understanding of some unique characteristics of a structure in relation to its integrity under uncertain loading conditions. The ALS helps visualize the relation between a prescribed load and a degree of safety of the structure.
Using the cone property of ALS, however, efficient algorithms for the ALD have been possible without adding slack variables. It is only required to select the active constraint nearest the origin in the load space. For linear structural problems, one finite element analysis is enough to obtain the information on the stress and displacement coefficients that is necessary for checking the constraint equations. During the application of the algorithms, critical or weak areas of the structure can be identified and can be related to the particular load that makes them critical. Examples shown have illustrated the nature of the ALS and the algorithms developed.
A methodology to obtain the ALS of multi-body mechanical systems with a minimum number of finite element analyses is introduced and shown very effective in understanding the safety characteristics of multi-body systems. A new reliability measure based on the concept of the ALS, which is called a relative safety index, is defined as the distance to ALD from the prescribed mean load. This safety index does not require any probability data, but is a good indicator of structural integrity especially when they are not available. As illustrated by examples of excavator, robot arm and Stewart platform, the analysis by ALS reveals important characteristics of the structural integrity of a system.
By maximizing a relative safety index, a robust design can be obtained. This criterion is adopted to obtain a new biomechanical formulation of stable working postures and results are compared with those by previously used force minimization approach. It is also shown that how low back disorders affect working postures and human body reactions. The criterion is also applied to optimize multi-body systems, for examples, a planar Stewart platform and an excavator. A slightly modified global optimization algorithm is utilized for the multi-body system examples based on a multi start method with domain elimination. Although the suggested approach takes more time, it produces more local solutions increasing the probability of finding the global solution.
In summary, it is shown that the ALS is a useful concept not only to show the characteristics of the structural integrity of a system, but also to do a robust design without knowing detailed probability data.