Volume 7, number 1 (2013)
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Item A numerical study of wave dispersion curves in cylindrical rods with circular cross-section(University of West Bohemia, 2013) Valsamos, Georgios; Casadei, Folco; Solomos, GeorgeThis work presents a finite element approach for modeling longitudinal wave propagation in thick cylindrical rods with circular cross-section. The formulation is based on simple time domain response of the structure to a properly chosen excitation, and is calculated with an explicit finite element solver. The proposed post-treatment procedure identifies the wavenumber for each mode of wa ve propagation at the desired frequency. The procedure is implemented and integrated in an efficient way in the explicit finite element code Europlexus. The numerical results are compared to the analytical ones obtaine d from the solution of the Pochhammer — Chree equation, which provides the dispersion curves for wavetrains in solid cylinders of infinite length.
Item Three-body segment musculoskeletal model of the upper limb(University of West Bohemia, 2013) Valdmanová, Linda; Čechová, HanaThe main aim is to create a computational three-body segment model of an upper limb of a human body for determination of muscle forces generated to keep a giv en loaded upper limb position. The model consists of three segments representing arm, forearm, hand and of all majo r muscles connected to the segments. Muscle origins and insertions determination corresponds to a real anatom y. Muscle behaviour is defined according to the Hill-type muscle model consisting of contractile and viscoelastic element. The upper limb is presented by a system of three rigid bars connected by rotational joints. The whole limb is fixed to the frame in the shoulder joint. A static balance problem is solved by principle of virtual work. The system of equation describing the musculoskeletal system is overdetermined because more muscles than necessary cont ribute to get the concrete upper limb position. Hence the mathematical problem is solved by an optimization method s earching the least energetically-consuming solution. The upper limb computational model is verified by electromyography of the biceps brachii muscle.Item Semi-analytic solution to planar Helmholtz equation(University of West Bohemia, 2013) Tukač, Martin; Vampola, TomášAcoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costsItem Application of patch test in meshless analysis of continuously non-homogeneous piezoelectric circular plate(University of West Bohemia, 2013) Staňák, Peter; Sládek, Vladimír; Sládek, Ján; Krahulec, Slavomír; Sátor, LadislavProposed paper presents application of the patch test for meshless analysis of piezoelectric circular plate with functionally graded material properties. Functionally graded materials (FGM) are the special class of composite materials with continuous variation of volume fraction of constituents in predominant direction. Patch test analysis is an important tool in numerical methods for addressing the convergence. Meshless local Petrov-Galerkin (MLPG) method together with moving least-squares (MLS) approximation scheme is applied in the analysis. No finite elements are required for approximation or integration of unknown quantities. Circular plate is considered as a 3-D axisymmetric piezoelectric solid. Considering the axial symmetry, the problem is reduced to a 2-dimensinal one. Displacement and electric potential fields are prescribed on the outer boundaries in order to reach the state of constant stress field inside the considered plate as required by the patch test and the governing equations. Values of prescribed mechanical and electrical fields must be determined in order to comply with applied FGM gradation rule. Convergence study is performed to assess the considered meshless approach and several conclusions are finally presented.Item Experimental and numerical analysis of in- and out- of plane constraint effects on fracture parameters: Aluminium alloy 2024(University of West Bohemia, 2013) Seitl, Stanislav; Hutař, Pavel; García, Tomas Eduardo; Fernández-Canteli, AlfonsoThe influence of in- and out- of plane constraints on the behaviour of a crack under mode I loading conditions is studied. The independence of the stress intensity tensor, with respect to the specimen thickness B shows that under loss of constraint conditions higher order members of the Williams’ tensor expansion must be considered if the experimental results for increasing apparent fracture toughness resulting from decreasing specimen thickness are to be explained. This is achieved using the constraint curves that define the intensity field tensor along the crack propagation direction and can be alternative to the T-stress approach. This approach is then applied to crack instability assessment for program compact tension (CT — positive values of T-stress) and three point bending (3PB— from negative to positive values of T-stress) specimens with different thicknesses. The theoretical results are compared with experimental ones obtained from the research program on aluminium alloy 2024.Item Influence of delayed excitation on vibrations of turbine blades couple(University of West Bohemia, 2013) Půst, Ladislav; Pešek, LuděkIn the presented paper, the computational model of the turbine blade couple is investigated with the main attention to the influence two harmonic excitation forces, having the same frequency and amplitude but with moderate delay in time. Time delay between the exciting harmonic forces depends on the revolutions of bladed disk, on the number of blades on a rotating disk and on the number of stator blades. The reduction of resonance vibrations realized by means of dry friction between the shroud blade-heads increases roughly proportional to the difference of stator and rotor blade-numbers and also to the magnitude of dry friction force. From the analysis of blade couple with direct contact it was proved that the increase of friction forces causes decrease of resonance peaks, but the influence of elastic micro-deformations in the contact surfaces (modeled e.g. by the modified Coulomb dry friction law) is rather small. Analysis of a blade couple with a friction element shows that the lower number of stator blades has negligible influence on the amplitudes of both blades, but decreases amplitudes of the friction element oscillations. Similarly the increase of friction forces causes a decrease of resonance peaks, but an increase of friction element amplitudes.Item The mean stress influence on lifetime under high-cycle fatigue combined loading(University of West Bohemia, 2013) Janoušek, Jaromír; Balda, Miroslav; Svoboda, JaroslavThis paper summarizes the results from the field of combined loading. This study builds on experiments that have been performed during the last ten years and provides information on sinusoidal in-phase stress components and tenseness distribution. Unfortunately, there is no exact method for estimating the damage caused by already known stress history. The main aim of experimental works was to determine the analytical form of Haigh diagrams and analytical expression of terminal lines equations. This article deals with different combinations of tension and torsion pre-stresses and contains results of experiments carried out in the laboratory of Institute of Thermomechanics in Pilsen. The lifetime curves (S-N curves) for combined pre-stress for different damage effect of normal and shear stress components have been obtained. The final results have been compiled and displayed at the threedimensional Haigh diagram with normalized coordinates. The terminal lines equations are solved by non-linear regression by Fletcher’s version of the Levenberg-Maquardt algorithm for the minimization of a sum of squares of equation residuals.Item Stress wave radiation from brittle crack extension by molecular dynamics and FEM(University of West Bohemia, 2013) Hora, Petr; Červená, Olga; Uhnáková, Alena; Machová, Anna; Pelikán, VladimírWe present results for molecular dynamic (MD) and finite element (FEM) simulations in 3D bcc iron crystals, with embedded central through crack (001)[110] of Griffith type, loaded in mode I. The sample geometry and border conditions in MD were chosen in such a way as to invoke a cleavage crack extension. Acoustic emission (AE) sources caused by the crack were analysed on both the atomistic and continuum level with FEM.Item Linearization of friction effects in vibration of two rotating blades(University of West Bohemia, 2013) Byrtus, Miroslav; Hajžman, Michal; Zeman, VladimírThis paper is aimed at modelling of friction effects in blade shrouding which are realized by means of friction elements placed between blades. In order to develop a methodology of modelling, two blades with one friction element in between are considered only. Flexible blades fixed to a rotating disc are discretized by FEM using 1D Rayleigh beam elements derived in rotating space as well as the friction element modelled as a rigid body. The blades and the friction element are connected through two concurrent friction planes, where the friction forces arise on the basis of centrifugal force acting on the friction element. The linearization of friction is performed using the harmonic balance method to determine equivalent damping coefficients in dependence on the amplitudes of relative slip motion between the blades and the friction element. The methodology is applied to a model of two real blades and will be extended for the whole bladed disc with shrouding.
