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The paper introduces a powerful method for developing lightweight designs and enhancing the load-bearing capacity of common structures. The method, referred to as the 'method of aggregation', has been derived from reverse engineering of sub-additive and super-additive algebraic inequalities. The essence of the proposed method is consolidating multiple elements loaded in bending into a reduced number of elements with larger cross sections but a smaller total volume of material. This procedure yields a huge reduction in material usage and is the first major contribution of the paper. For instance, when aggregating eight load-carrying beams into two beams supporting the same total load, the material reduction was more than 1.58 times. The second major contribution of the paper is in demonstrating that consolidating multiple elements loaded in bending into a reduced number of elements with larger cross sections but the same total volume of material leads to a big increase in the load-bearing capacity of the structure. For instance, when aggregating eight cantilevered or simply supported beams into two beams with the same volume of material, the load-bearing capacity until a specified tensile stress increased twice. At the same time, the load-bearing capacity until a specified deflection increased four times. [ABSTRACT FROM AUTHOR]

We propose a framework for analysis and optimization of repairable flow networks by (i) stating and proving the maximum flow minimum flow path resistance theorem for networks with merging flows (ii) a discrete-event solver for determining the variation of the output flow from repairable flow networks with complex topology (iii) a procedure for determining the threshold flow rate reliability for repairable networks with complex topology (iv) a method for topology optimization of repairable flow networks and (v) an efficient algorithm for maximizing the flow in non-reconfigurable flow networks with merging flows. Maximizing the flow in a static flow network does not necessarily guarantee that the flow in the corresponding non-reconfigurable repairable network will be maximized. In this respect, we introduce a new concept related to repairable flow networks: ‘a specific resistance of a flow path’ which is essentially the average percentage of losses from component failures for a flow path from the source to the sink. A very efficient algorithm based on adjacency arrays has also been proposed for determining all minimal flow paths in a network with complex topology and cycles. We formulate and prove a fundamental theorem about non-reconfigurable repairable flow networks with merging flows. The flow in a repairable flow network with merging flows can be maximized by preferentially saturating directed flow paths from the sources to the sink, characterized by the largest average availability. The procedure starts with the flow path with the largest average availability (the smallest specific resistance), and continues by saturating the unsaturated directed flow path with the largest average availability until no more flow paths can be saturated. A discrete-event solver for reconfigurable repairable flow networks with complex topology has also been constructed. The proposed discrete-event solver maximizes the flow rate in the network upon each component failure and return from repair. By maximizing the flow rate upon each component failure and return from repair, the discrete-event solver ensures a larger total output flow during a specified time interval. The designed simulation procedure for determining the threshold flow rate reliability is particularly useful for comparing flow network topologies, and selecting the topology characterized by the largest threshold flow rate reliability. It is also very useful in deciding whether the resources allocated for purchasing extra redundancy are justified. Finally, we propose a new optimization method for determining the network topology combining a maximum output flow rate attained within a specified budget for building the network. The optimization method is based on a branch and bound algorithm combined with pruning the full-complexity network as a way of exploring the possible repairable networks embedded in the full-complexity network. [ABSTRACT FROM AUTHOR]

Abstract: A simple, easily reproduced experiment based on artificial flaws has been proposed which demonstrates that the distribution of the minimum failure load does not necessarily follow a Weibull distribution. The experimental result presented in the paper clearly indicates that the Weibull distribution with its strictly increasing function, is incapable of approximating a constant probability of failure over a loading region. New fundamental concepts have been introduced referred to as ‘hazard stress density’ and ‘cumulative hazard stress density’. These concepts helped derive an equation giving the probability of failure without making use of the notions ‘flaws’ and ‘locally initiated failure by flaws’. As a result, the derived equation is more general than earlier models. The cumulative hazard stress density is an important fingerprint of materials and can be used for determining the reliability of loaded components. It leaves materials to ‘speak for themselves’ by not imposing a power law dependence on the variation of the critical flaws which is always the case if the Weibull model is used. An important link with earlier models has also been established. We show that the cumulative hazard stress density is numerically equal to the product of the number density of the flaws with a potential to cause failure and the probability that a flaw will be critical at the specified loading stress. We show that, predictions of the probability of failure from tests related to a small gauge length to a large gauge length are associated with large errors which increase in proportion with the ratio of the gauge lengths. Large gauge length ratios amplify the inevitable errors in the probability of failure associated with the small gauge length to a level which renders the predicted probability for failure of the large gauge length meaningless. Finally, a general integral has been derived, giving the reliability associated with time interval and random loading of a material with flaws. The integral has been validated by a Monte Carlo simulation. [Copyright &y& Elsevier]