A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.

Numerical Investigations of the Savonius Turbine with Deformable Blades

Savonius wind turbines are characterized by various advantages such as simple design, independence of wind direction, and low noise emission, but they suffer from low efficiency. Numerous investigations were carried out to face this problem. In the present paper, a new idea of the Savonius turbine with a variable geometry of blades is proposed. Its blades, made of elastic material, were continuously deformed during the rotor revolution to increase a positive torque of the advancing blade and to decrease a negative torque of the returning blade. In order to assess the turbine aerodynamic performance, a two-dimensional numerical model was developed. The fluid-structure interaction (FSI) method was applied where blade deformations were defined by computational solid mechanics (CSM) simulations, whereas computational fluid dynamics (CFD) simulations allowed for transient flow prediction. The influence of the deformation magnitude and the position of maximally deformed blades with respect to the incoming wind direction were studied. The aerodynamic performance increased with an increase in the deformation magnitude. The power coefficient exceeded Cp = 0.30 for the eccentricity magnitude of 10% and reached 0.39 for the highest magnitude under study. It corresponded to 90% improvement in comparison to Cp = 0.21 in the case of the fixed-shape Savonius turbine.

Application of grid convergence index to shock wave validated with LS-DYNA and ProsAir

The discretization error is not always calculated, even though it is essential for the studies of computational solid mechanics. However, it is well known that an error committed by the mesh used can be as large as the measured variable, which greatly invalidates the results obtained. The grid convergence index (GCI) method makes possible to determine on a solid basis, the order of convergence and the asymptotic solution. This method seems to be a suitable estimator despite further research is needed in the context of blast situations and finite element (FE) calculations. For this purpose, field trials were performed consisting in the detonation of a spherical hanging load of homemade explosive. The pressure generated by the shock wave was measured in different positions at two distances. With these data, a TNT equivalent has been obtained and used to calculate the shock propagation with the solvers LS-DYNA and ProsAir. This work aims to verify the GCI method by comparing its results with field data along with the simulations carried out. The comparison also seeks to validate the methodology used to obtain the TNT equivalent.This research shows that the GCI gives good results for both solvers despite the complexity of the physical problem. Besides, LS-DYNA displays better correlation with the experimental data than the ProsAir results, with an error of less than 10% in all values.