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Solution of chosen exercises of elasticity by using Airy stress function
Koch, Martin ; Profant, Tomáš (referee) ; Novák, Kamil (advisor)
The Bachelor thesis is concerned with solving selected Mechanics of Material tasks using Airy stress function. First, a description of usage and implementation of the function and methods using the function for solving problems are provided. In the analytical part, there are selected tasks solved by using the Airy stress function and the results are compared with the ones obtained by using the standard approach. A calculation using the Finite Element Method is carried out in the last part and is followed by a final comparison of all the solutions.
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Application of the gradient elasticity in fracture mechanics problems
Klepáč, Jaromír ; Profant, Tomáš (referee) ; Kotoul, Michal (advisor)
The presented master’s thesis deals with the application of the gradient elasticity in fracture mechanics problems. Specifically, the displacement and stress field around the crack tip is a matter of interest. The influence of a material microstructure is considered. Introductory chapters are devoted to a brief historical overview of gradient models and definition of basic equations of dipolar gradient elasticity derived from Mindlin gradient theory form II. For comparison, relations of classical elasticity are introduced. Then a derivation of asymptotic displacement field using the Williams asymptotic technique follows. In the case of gradient elasticity, also the calculation of the J-integral is included. The mathematical formulation is reduced due to the singular nature of the problem to singular integral equations. The methods for solving integral equations in Cauchy principal value and Hadamard finite part sense are briefly introduced. For the evaluation of regular kernel, a Gauss-Chebyshev quadrature is used. There also mentioned approximate methods for solving systems of integral equations such as the weighted residual method, especially the least square method with collocation points. In the main part of the thesis the system of integral equations is derived using the Fourier transform for straight crack in an infinite body. This system is then solved numerically in the software Mathematica and the results are compared with the finite element model of ceramic foam.
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Elasticity problems in Python language
Tichoň, Dušan ; Žák, Stanislav (referee) ; Profant, Tomáš (advisor)
This bachelor thesis deals with the programming language Python. Its aim is acquaintance of NumPy, SymPy and Matplotlib libraries and their later application. Also it shows the great computing potential of programming language in creating exercises which will be used and presented for educational purposes.
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A study of the stress field near the stress concentrator at the bi-material interface
Krepl, Ondřej ; Klusák, Jan (referee) ; Profant, Tomáš (advisor)
The aim of this work is the solution of problems of the stress distribution near bimaterial notch tip or eventually the crack impinging orthogonaly the bimaterial interface, determination of stress singularity exponent. The first part is concerned with basics of linear elastic fracture mechanics, i.e. Irwin's concept of stress intensity factor. The second part is devoted to description of anisotropic materials by complex potencial theory. The final part is focused on calculation of eigenvalues of both isotropic and anisotropic materials and application of LES formalism on the calculation of stress singularities of the bimaterial ortotropic notch or the crack impinging orthogonaly the bimaterial interface.
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Computational modelling of mechanical tests of composites "rubber - steel fibre"
Jarý, Milan ; Profant, Tomáš (referee) ; Burša, Jiří (advisor)
This diploma thesis focuses on realization of a computational model of fibre composite with elastomer matrix and on homogenization of properties of this composite. The work deals with computational modelling of strain-stress states which arise in mechanical tests of composites. The composites investigated by mechanical tests comprise of hyperelastic rubber matrix and steel reinforcing fibres. Computational modelling is carried out at two levels of the model. First, with three-dimensional modelling of fibres and matrix as two different materials and, second, using a homogenized model of composite; this constitutive model describes the composite as a homogeneous anisotropic material. It means that properties of fibres are encompassed into strain energy density by the mathematical formulation of the constitutive model. Further, the work deals with computational modelling of mechanical tests of hyperelastic isotropic materials used for identification of their material parameters and for verification of the selected constitutive model of material. For particular hyperelastic material, simulations of tests were carried out, namely of uniaxial tension, biaxial tension, uniaxial compression, biaxial compression, pure shear and uniaxial tension with constrained transversal strain (planar tension). Parameters of the constitutive model were determined of experimental input data. Verification of the constitutive model was carried out by comparison of the data acquired by experiments with the results of simulations of mechanical tests in FE program system Ansys. Then the authentic constitutive model of material was used for description of matrix behaviour in models of mechanical tests of composite material and results were compared with experimental data. Principal objectives which I want to attain are following: • to acquaint with the constitutive models of hyperelastic isotropic and anisotropic materials and identification of their perameters on base of mechanical tests. • to create computational models of testing specimens of composite “ rubber – steel fibre“ for different fibre arrangements and to use the created computational models in simulations of chosen tests. • to test the possibilities of computational modelling of composites with application of homogenized properties and to compare the results of both approaches. Results which were attained: • the computational models were created with the fibres modelled; the strain – stress characteristics are qualitatively corresponding to experiments, and quantitative difference is 20% - 40% (see (4.3)). • the computational models based on homogenization of properties were tested and gave results corresponding to the models with modelled fibres (see (4.4)) with a good accuracy.
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Stress-strain analysis of the bar system
Pop, Miroslav ; Profant, Tomáš (referee) ; Houfek, Martin (advisor)
This bachelor’s thesis deals with the issue of rod systems, which represent a special type of construction widely used in the building and mechanical industry. In the introductory part is presented a theoretical basis and methods of static solution of rod systems are described, then it is described stress of rod systems and are derived relations that were subsequently used for the calculation of the specific example. In the practical part, the thesis deals with the analytical calculation of the planar rod system in shape of a power line pylon, for which the cross-sections of the members are designed and the magnitude of the stresses and deformation displacements are calculated. For the calculation, the general method of joints was used and cross sections were designed with respect to the elastic limit state and the buckling stability limit state. At the end of the work, the results of the analytical calculation were verified with numerical solution in software ANSYS Workbench.
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An aplication of the mathematical dislocation theory to the problem of the crack in the vicinity of the bi-material interface
Padělek, Petr ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
The presented diploma thesis deals with a problem of the determination of the stress intensity factor of the finite length crack in the vicinity of the bi-material interface solved by the distributed dislocation technique. The work is divided into several parts. The first part is theoretical and includes basic concepts of the fracture mechanics, the crack behaviour at the bi-material interface, the formulation of the singular integral equation by virtue of the distributed dislocation technique, the Bueckner's principle, complex potentials and consequently the determination of the stress intensity factor. The second part is the theory application to the specific configuration of the crack of the finite length with respect to the bi-material interface and in the third part, there is carried out the solution of this problem for various configurations of the bi-material solved by the distributed dislocation technique and its comparison with the results obtained from the FE analysis.
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Crack in prismatic bars
Meňhert, Samuel ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
This thesis deals with summarization of information about fracture mechanics mainly with methods which estimate stress intensity factors. They play an important role in determination of behavior of cracks in engineering process. The main goal of this thesis will be familiarization with Kienzler hypothesis which deals with strain energy release rate and internal effects in a point of disrupted cross section and comparison with classic K-concept, when the stress intensity factors are determined by infinite series.
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