Square principles in ℙ<Subscript>max</Subscript> extensions

By forcing with P_max over strong models of determinacy, we obtain models where different square principles at ω ₂ and ω ₃ fail. In particular, we obtain a model of \({2^{{\aleph _0}}} = {2^{{\aleph _1}}} = {\aleph _2} + {\neg }\square \left( {{\omega _2}} \right) + {\neg }\square \left( {{\omega _3}} \right)\).     

Automatic Geometry Based FE Model Generation for Optimization and Robust Design for Passive Safety of Passenger Vehicles

In this paper the optimization of large scale vehicle structures is addressed. A process strategy based on Latin Hypercube sampling, genetic algorithm optimization, and sensitivity analysis is discussed. This process was implemented on a dedicated Linux Cluster, utilizing various free and commercially available software tools, including SFE Concept, Perl, Matlab, and Radioss. The viability of the method is demonstrated for a large scale vehicle model in an offset deformable barrier crash test at 64 kph impact velocity. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical homogenization of elastic and thermal material properties for metal matrix composites (MMC)

A two-scale material modeling approach is adopted in order to determine macroscopic thermal and elastic constitutive laws and the respective parameters for metal matrix composite (MMC). Since the common homogenization framework violates the thermodynamical consistency for non-constant temperature fields, i.e., the dissipation is not conserved through the scale transition, the respective error is calculated numerically in order to prove the applicability of the homogenization method. The thermomechanical homogenization is applied to compute the macroscopic mass density, thermal expansion, elasticity, heat capacity and thermal conductivity for two specific MMCs, i.e., aluminum alloy Al2024 reinforced with 17 or 30 % silicon carbide particles. The temperature dependency of the material properties has been considered in the range from 0 to \(500{\,}^\circ \mathrm {C}\), the melting temperature of the alloy. The numerically determined material properties are validated with experimental data from the literature as far as possible.     

Simulation of bone modeling around a screw implant in the mandible

On the basis of a biomechanical model for the bone healing process around a dental implant, the attainable degree of ossification in two‐phase implantation is studied for a screw implant and compared with corresponding results for a cylinder implant. It is shown that a screw implant delivers a better ossification of the repair zone than a cylinder implant which is in accordance with clinical observation.     

Joint And Muscle Forces During Clenching

The masticatory system is highly redundant. Therefore, complete knowledge about the activation patterns of the chewing muscles belonging to a specific resultant bite force can only be gained either by simultaneous force- and EMG-measurement or with the help of optimization strategies. In this study, such EMG and force measurements were carried out with 10 test persons and the results compared to those computed with several objective functions. The results show an increase of the joint forces with an increase of the horizontal component of the resultant bite force. The test persons seem to favor energy minimization as control mechanism. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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