Load-bearing mechanical structures like trusses face uncertainty in loading along with uncertainty in stress and strength, which are due to uncertainty in their development, production, and usage. According to the working hypothesis of the German Collaborative Research Center SFB 805, uncertainty occurs in processes that are not or only partial deterministic and can only be controlled in processes. The authors classify, compare, and evaluate four different direct methods to describe and evaluate the uncertainty of normal stress distribution in simple truss structures with one column, two columns, and three columns. The four methods are the direct Monte Carlo (DMC) simulation, the direct quasi-Monte Carlo (DQMC) simulation, the direct interval, and the direct fuzzy analysis with α-cuts, which are common methods for data uncertainty analysis. The DMC simulation and the DQMC simulation are categorized as probabilistic methods to evaluate the stochastic uncertainty. On the contrary, the direct interval and the direct fuzzy analysis with α-cuts are categorized as possibilistic methods to evaluate the nonstochastic uncertainty. Three different truss structures with increasing model complexity, a single-column, a two-column, and a three-column systems are chosen as reference systems in this study. Each truss structure is excited with a vertical external point load. The input parameters of the truss structures are the internal system properties such as geometry and material parameters, and the external properties such as magnitude and direction of load. The probabilistic and the possibilistic methods are applied to each truss structure to describe and evaluate its uncertainty in the developing phase. The DMC simulation and DQMC simulation are carried out with full or “direct” sample sets of model parameters such as geometry parameters and state parameters such as forces, and a sensitivity analysis is conducted to identify the influence of every model and state input parameter on the normal stress, which is the output variable of the truss structures. In parallel, the direct interval and the direct fuzzy analysis with α-cuts are carried out without altering and, therefore, they are direct approaches as well. The four direct methods are then compared based on the simulation results. The criteria of the comparison are the uncertainty in the deviation of the normal stress in one column of each truss structure due to varied model and state input parameters, the computational costs, as well as the implementation complexity of the applied methods.
Solution of the Boussinesq’s problem in evaluating ratio between shear stress and contact pressure
