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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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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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A study of the stress distribution around the bimaterial notch tip in the terms of the generalized stress intensity factor
Hrstka, Miroslav ; Kotoul, Michal (referee) ; Profant, Tomáš (advisor)
The presented diploma thesis deals with a problem of a generalized stress intensity factor determination and a consecutive study of stress distribution around the bimaterial notch tip, combining analytical and numerical methods. This task is possible to sectionalize into three parts. The first part is dedicated to the fundamentals of the linear fracture mechanics and the mechanics of composite materials. The second part deals with methods of anisotropic plane elasticity solution. Pursuant to the solution the computational models in the third part are created. The first model makes for determination of a singularity exponent eigenvalue by dint of Lekhnitskii-Eshelby-Stroh formalism. The second model makes for determination of the generalized stress intensity factor using psi-integral method, which is based on the Betti reciprocal theorem. All needed calculation are performed in the software ANSYS 12, Maple 12 and Silverforst FTN95. Results will be compared with the values obtained from a direct method of the generalised stress intensity factor determination.
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An aplication of the boundary element method to the problem of the crack in the vicinity of the bi-material interface
Sedláček, Stanislav ; Vrbka, Jan (referee) ; Profant, Tomáš (advisor)
There are many shape and other changes in the engineering constructions. These changes cause the concentration of the stress. There is a higher probability of the crack initiation in the vicinity of these stress concentrators. The problems of the crack can be solved nowadays only with help of sufficient numeric tools. The Boundary Element Method is one of the many numerical tools which offer the solution of some problems of the mechanics. The goal of this diploma thesis is to formulate boundary element method for the plane problem of the linear elasticity for izotropic material with different types of the stress concentrators.
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Problem of the crack terminating at the bimaterial interface
Svoboda, Miroslav ; Ševeček, Oldřich (referee) ; Profant, Tomáš (advisor)
The objective of this diploma thesis is the stress-strain analysis of the crack terminating at the orthotropic bi-material interface suggested as the plane problem of the linear fracture mechanics. The first part is engaged in basic relations of the linear fracture mechanics. The second part is focused on the singularity exponent evaluation for the crack impinging and generally inclined with respect to the bi-material interface. It follows the determination of the generalized stress intensity factors applying the analytical-numerical approach represented by the finite element analysis. The last part of this work is focused on the testing of algorithms applied to the specific crack and bi-material interface configurations. A conclusion discusses the influence of the bi-material mechanical properties and the angel of the crack inclination to the obtained numerical results.
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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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Computational modelling of stress-strain states in tyres
Lavický, Ondřej ; Profant, Tomáš (referee) ; Burša, Jiří (advisor)
Work occupies computational modelling mechanical behavior elastomers and composits with rubber matrix and their utilization for compute model of tire creation. MATADOR tire 165/65 R13 Axisymetric 2D model was created in two geometric variants. For the computational modeling is applying the Finite element method (FEM). The model was in different variants distinctive grade of modeling material. At first was done inner pressure analyst impact on deformation of each of model. Then was count influence on tire load with angular velocity meanwhile with inner pressure. The impact thickness of tire protector layer on global deformation tyre casing was verified too.
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A torsion of the beam with non-circular cross-section
Kalivoda, Ondřej ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
Bachelor thesis deals with the analytical and numerical methods solving the problems of the torsion of bars with various geometries of cross-sections. The theoretical background of the problem is introduced in the beginning of the thesis. The possibilities of the analytical solution of the partial differential equations in the case of the simplified shapes of the cross-sections are discussed in the following part. These results are compared with the numerical ones received from the finite element analysis via the ANSYS software. The numerical results are extended to the cases of the generalized shapes of the beam cross-sections.
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Stress and deformation analysis of railway bridge over the Odra River
Svoboda, Josef ; Profant, Tomáš (referee) ; Fuis, Vladimír (advisor)
This bachelor thesis deals with strain, stress and deformation analysis of the planar truss bridge construction. The aim is to determined the size of axial forces for statically determinate system and then making construction changes to reduce axial stresses in the individual beams in the structure. This structural modification becomes statically indeterminate structure. To solve this problem we consider different positions of the train at the bridge. The obtained values we can use to assess stress and deformation of the structure and the analytical results will be compared with the results obtained using the finite element method.
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