SMR's know-how in computational solid mechanics is based on wide experience with the B2000 finite element analysis code as well as with several other systems. B2000 is SMR's in-house analysis tool for solving solid mechanics problems, like vibration problems, dynamic problems, stability problems, and for solving coupled problems.
Fatigue investigations and damage assessment of structures are becoming increasingly important in many fields like aerospace engineering. Engineers at SMR have long experience, both in developing computer simulation (FEM) based fatigue analysis tools as well as performing analysis. Calculations of fatigue effects in structures range from the linear and non-linear estimations of the propagation of cracks in structures to estimations of the safe life of structures. Linear fracture mechanics comprise standard methods, like the virtual crack extension method, which allows for determining stress intensity factors. The method works well for mode I stress intensity factors. The figure shows a solution of a CT test specimen (aluminum alloy).
Often non-linear phenomena occur, like cracks in aircraft fuselages, where the prediction of the crack propagation allows for estimating the remaining strength. In such cases the method outlined above is not sufficient anymore (see Riks and Rankin).
Modeling of damage in materials is an active field of research. SMR implements damage models for composites within the B2000 code, while research partners are developing stochastic models for more accurate analysis of the loads during the lifetime of an aircraft.
Simulation of high-velocity impact on composite and metal structures is one of the problems urgently required by industry, specifically the aerospace industry. Composite materials are increasingly being used in primary aircraft structures such as wing leading edges, nacelles, propellers and engine fan blades. These parts are susceptible to high velocity impacts from bird strike or foreign objects that can pose a serious risk to aircraft safety.
The B2000 explicit finite element simulation code developed by SMR is continuously being improved by SMR and its research partners from European aerospace industry. Enhanced during SMR's participation in a European Research project, state-of-the-art material damage models can be employed to assess damage caused by impacts, from bumps to punching holes in the structure due to high speeds (up to 400 m/s). The figure illustrates the damaging of composite shell structures due to impact: The upper figure shows the finite element mesh after damage and the lower the experiment.
The analysis of vibrations and the dynamical behaviour due to excitation forces have been applied routinely to cable-stayed bridges using SMR devised analysis tools. Note that similar techniques have been used to analyse the resonance behaviour of large floating bridge structures.
The example shows an eigenmode of a large cable-stayed bridge (model and analysis with B2000 by The Dutch National Aerospace Research Institute (NLR)). The figure displays a vibration mode, the shape being artificially amplified to emphasize the deformation. An animation produced with baspl++ can be executed by clicking here.
Coupled problems are encountered in all fields of engineering, like solid mechanics, heat transfer, or fluid dynamics. Often conceptually different solution techniques, like FEM or finite volume methods and particle methods must be combined.
Coupling is illustrated with an example from solid state physics: The numerical simulation of the thermo-mechanical and optical behaviour of diode end and side pumped solid state laser rods (see figures), where the thermal, thermo-elastic, and optical response of cylindrical and prismatic laser resonators are modeled with B2000 modules. The optical behaviour is simulated by integrated special purpose modules. This project has been carried out with the Institute of Applied Physics of the University of Bern, see (1).
Minimum weight designs of structures are obtained by optimizing with respect to various criteria, such as displacement and stress constraints, buckling, eigenfrequencies, etc. With B2000, SMR is able to offer a gradient-based FEM model optimization system. Non-coupled optimization problems are relatively easily formulated and solved. Coupled problems are harder to tackle with. B2000 allows for aero-elastic coupled shape optimization by combining the FEM optimization system with a classical double-lattice flow solver. The double lattice flow solver is certainly not as accurate as modern Euler or Navier-Stokes solvers but is has the advantage of giving very quick answers - a feature which is very important when performing many design cycles. Thus, the double lattice flow solver based optimization procedure is particularly advantageous during pre-design phases. The figure illustrates the process: It shows an optimized structural model of a F50 design study.
(1) C. Pfistner, R. Weber, H.P. Weber, S. Merazzi, R. Gruber; Thermal Beam Distortions in Longitudinally Pumped Solid State Lasers; IEEE Journal of Quantum Electronics, Vol. 30, No. 7, July 1994.