This thesis focused on the mechanisms involved in negative thermal expansion of 2D/3D lattice structures. The effects of varying the constituent materials and geometry were explored. The lattices had geometries similar to those found in light-weight structures in many transport applications, including aerospace and spacecraft. One specific case was to determine how to reduce the coefficient of thermal expansivity (CTE) of such structures to near zero, by using two constituent materials with contrasting CTEs, without incurring penalties in terms of other elastic and failure properties, mass and manufacturability. The lattice geometries able to exhibit altered CTE were explored, and penalties in terms of other elastic properties were quantified. The results were scale-independent and so were generic to all such lattices. Analytical prediction and generic relationships between the geometries of the lattices and their performance were proposed. Experimental validation of the model predictions was undertaken using physical samples. The thermomechanical properties were simulated by commercial finite element method (FEM) codes (Ansys 11, Ansys, Inc.). Ansys parametric design language was adopted to generate large sets of solutions to be evaluated against chosen criteria. Results show small or, in some cases, no penalties to be paid in terms of stiffness and mass for implementing dual-material lattices with near-zero CTE. Such lattices may compete favourably with high-cost and high-density materials (e.g. Invar) and the manufacture of dual-material lattices can be by standard processes or alternative new process such as Additive Layer Manufacturing (ALM). An example of truss core sandwich application for aerospace application was modelled by FEM. Applications as cores in sandwich panels might be the first route by which the ALM manufacturing process is required to develop dual-material capability.

Aim of this work is a systematic investigation of the modes of thermal convection (onset of convection, stationary solutions, periodic solutions, chaotic states) in a material whose properties vary with depth like the material of Earth mantle; the problem was solved in Cartesian geometry. The Stokes equation set was consistently formulated in the spectral region not only horizontally but also vertically, and thus in the model consisting of layers with a constant viscosity but with general course of velocity and temperature in each layer. This equation set was solved with matrix method for each wave vector. Thermal equation was solved in the spatial domain and the transition of velocity and temperature between spectral and spatial domains was performed using the fast Fourier transform. This procedure allows a straightforward parallelization, thereby opening the possibility of not only two-dimensional but also three-dimensional modeling and modeling of chaotic regimes. On the basis of the numerical difficulties of method presented here an model investigated in finite elemens was used. The basic modes of thermal convection were then investigated using model assembled in the software Comsol. Powered by TCPDF (www.tcpdf.org)

Title: Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics Author: Hana Šustková Department: Department of Geophysics Supervisor: doc. RNDr. Ctirad Matyska, DrSc. Abstract: This thesis concerns the study of convection in Cartesian models in two and three dimensions. Specifically, it deals with the systematic monitoring of critical Rayleigh numbers based on the geometry model, on the functional dependence of the viscosity or of other parameters. Models has been created with layered viscosity and constant or temperature- and depth- dependent parameters (thermal expansion and conductivity). The system has been described by conventional dimensionless Boussinesq approximation. Part of the work is devoted to the application of matrix method for solving the appropriate Stokes flow and use of Euler's method for solving the thermal equation. The actual calculations were then performed in an environment of commercial software Comsol and thus by using the finite element method. It was shown that the dominant influence on the critical Rayleigh numbers has a viscosity model (with increasing viscosity the critical Rayleigh numbers increase), other important parameter is system's geometry (larger size and dimension of the geometry reduce the critical Rayleigh number). The...

The diploma thesis deals with a mechanical and thermal analysis of 3-cylinder petrol engine piston with capacity of 1,2 l and maximal output 47 kW. The computation analysis was created with the use of finite element method in the Ansys application. The strain solution was created using several techniques. The 3D model was made according to a real piston in the Pro/Engineer and was partly simplified for computation. Crank mechanism forces and the load stresses were solved using Mathcad. Calculations are done for three positions of power cycle engine, where the maximal loads of the piston are expected. Last part of the thesis is calculation of safety factor highcyclical fatigue made using Femfat application.

<p>Combination of the Calphad method and theoretical calculations provides new possibilities for the study of materials science. This work is a part of the efforts within the CCT project (Centre of Computational Thermodynamics) to combine these methods to facilitate modeling and to extend the thermodynamic databases with critically assessed volume data. In this work, the theoretical calculations refer to first-principles and Debye-Grüneisen calculations. The first-principles (i.e. ab initio) electronic structure calculations, based on the Density- Functional Theory (DFT), are capable of predicting various physical properties at 0 K, such as formation energy, volume and bulk modulus. The ab initio simulation software, VASP, was used to calculate the binding curves (i.e. equation of state at 0 K) of metallic elements, cubic carbides and nitrides. From the binding curves, the equilibrium volumes at 0 K were calculated for several metastable structures as well as stable structures. The vibrational contribution to the free energy was calculated using the Debye-Grüneisen model combined with first-principles calculations. Two different approximations for the Grüneisen parameter, γ, were used in the Debye-Grüneisen model, i.e. Slater’s and Dugdale-MacDonald’s expressions. The thermal electronic contribution was evaluated from the calculated electronic density of states. The calculated thermal expansivities for metallic elements, cubic carbides and nitrides were compared with Calphad assessments. It was found that the experimental data are within the limits of the calculations using the two approximations for γ. By fitting experimental heat capacity and thermal expansivity around Debye temperatures, we obtained optimal Poisson’s ratio values and used them to evaluate Young’s and Shear moduli. In order to reach a reasonable agreement with the experiments, it is necessary to use the logarithmic averaged mass of the constitutional atoms. The agreements between the calculations and experiments are generally better for bulk modulus and Young’s modulus than that for shear modulus. A new model describing thermodynamic properties at high pressures was implemented in Thermo-Calc. The model is based on an empirical relation between volume and isothermal bulk modulus. Pure Fe and solid MgO were assessed using this model. Solution phases will be considered in a future work to check the model for compositional dependence.</p>

Combination of the Calphad method and theoretical calculations provides new possibilities for the study of materials science. This work is a part of the efforts within the CCT project (Centre of Computational Thermodynamics) to combine these methods to facilitate modeling and to extend the thermodynamic databases with critically assessed volume data. In this work, the theoretical calculations refer to first-principles and Debye-Grüneisen calculations. The first-principles (i.e. ab initio) electronic structure calculations, based on the Density- Functional Theory (DFT), are capable of predicting various physical properties at 0 K, such as formation energy, volume and bulk modulus. The ab initio simulation software, VASP, was used to calculate the binding curves (i.e. equation of state at 0 K) of metallic elements, cubic carbides and nitrides. From the binding curves, the equilibrium volumes at 0 K were calculated for several metastable structures as well as stable structures. The vibrational contribution to the free energy was calculated using the Debye-Grüneisen model combined with first-principles calculations. Two different approximations for the Grüneisen parameter, γ, were used in the Debye-Grüneisen model, i.e. Slater’s and Dugdale-MacDonald’s expressions. The thermal electronic contribution was evaluated from the calculated electronic density of states. The calculated thermal expansivities for metallic elements, cubic carbides and nitrides were compared with Calphad assessments. It was found that the experimental data are within the limits of the calculations using the two approximations for γ. By fitting experimental heat capacity and thermal expansivity around Debye temperatures, we obtained optimal Poisson’s ratio values and used them to evaluate Young’s and Shear moduli. In order to reach a reasonable agreement with the experiments, it is necessary to use the logarithmic averaged mass of the constitutional atoms. The agreements between the calculations and experiments are generally better for bulk modulus and Young’s modulus than that for shear modulus. A new model describing thermodynamic properties at high pressures was implemented in Thermo-Calc. The model is based on an empirical relation between volume and isothermal bulk modulus. Pure Fe and solid MgO were assessed using this model. Solution phases will be considered in a future work to check the model for compositional dependence.