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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’.

This paper proposes a new configuration and its control strategy for a modular multilevel converter (MMC)-based photovoltaic (PV)-battery energy storage (BES) system. In the MMC-based PV-BES system, each PV submodule is interfaced from its dc side with multiple PV generators using isolated dual active bridge (DAB) dc-dc converters. One BES system is embedded into each arm of the converter and is connected to the dc port of the associated BES submodule using multiple isolated DAB converters. The embedded BES systems are used to smooth the output power of the PV generators and limit the rate of change of the power delivered to the host grid. Moreover, they enable compensation of power mismatches between the arms and legs of the system by exchanging power with the arms of the converter. This paper then proposes a hybrid power mismatch elimination strategy using a combination of power exchange with the arms of the converter and internal power flow control of the MMC. The proposed hybrid power mismatch elimination strategy employs BES systems and differential currents to compensate power mismatches and transfer power between the arms and legs of the converter, respectively. The effectiveness of the proposed power smoothing technique using the embedded BES systems and hybrid power mismatch elimination strategy is demonstrated using time-domain simulations conducted on a switched model of the PV-BES system in PSCAD/EMTDC software environment.

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In the present work, the discontinuous Galerkin (DG) method is applied to linear elasticity for two-dimensional and three-dimensional settings. A locking-free element formulation based on reduced integration and physically-based hourglass stabilization (Q1SP) is coupled for the first time with the DG framework. The incomplete interior penalty Galerkin method is chosen, being one example of different variations of DG methods. Several 2D and 3D typical benchmark problems of linear elasticity are investigated. A selection of numerical integration schemes for the boundary terms is presented, namely reduced and mixed integration schemes. The treatment of the surface terms by means of different rules of integration shows a significant influence on the performance of the resulting DG method in combination with the standard Q1 element. This intelligent treatment of the surface part leads to a DG variant with very good convergence properties.

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