This work focuses on analysis of longfiber unidirectional carbon-epoxy composite using finite element method on a unit cell. A micromechanical model of he unit cell is created in computational system MSC Marc using orthotropic elastic fibers and isotropic elastoplastic matrix. The plasticity of the matrix is prescribed in the model by a hardening function. Material parameters of the
micromodel are identified using gradient optimization method in OptiSLang system. In the optimization, stress-strain relations obtained from the micromodel are compared with the stress-strain relations from a nonlinear macromodel. The macromodel of the composite material was created in author‘s previous work. Parameters of the macromodel were identified from experimental tensile tests also using optimization with MSC Marc and OptiSLang. and Obsahuje seznam literatury
The subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil inserted in a channel (e.g. wind tunnel). A solid airfoil with two degrees of freedom can rotate around the elastic axis and oscillate in the vertical direction. The numerical simulation consists of the finite element soluton of the Navier-Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. High Reynolds numbers up to 106 require the application of a suitable stabilization of the finite element discretization. Numerical results are compared with an experiment. and Obsahuje seznam literatury
Modification of the Finite Element Methode (FEM) based on the different types spline shape function is an up-to-date strategy for numerical solution of partial differential equations (PDEs). This approach has an advantage that the geometry in Computer Graphics framework and approximation of fields of unknown quantities in FEM are described by the same technique. The spline variant of FEM is often called the Isogeometric Analysis (IGA). Another benefit of this numerical solution of PDEs is that the approximation of unknown quantities is smooth. It is an outcome of higher-order continuity of spline basis functions. It was shown, that IGA produces outstanding convergence rate and also appropriate frequency errors. Polynomial spline (Cp-1 continuous piecewise polynomials, p ≥ 2) shape functions produce low dispersion errors and moreover, dispersion spectrum of unbounded domains does not include optical modes unlike FEM based on the higher-order C0 continuous Lagrange interpolation polynomials.In this contribution, the B-spline (NURBS with uniform weights) shape functions in the FEM framework are tested in the numerical solution of free vibration of an elastic block. The main attention is paid to the comparison of convergence rate and accuracy of IGA with the classical Lagrangian FEM, Ritz method and experimental data. and Obsahuje seznam literatury
The growth in the field of construction of shallow underground structures has been associated with construction of new roads, collectors and other structures. This contribution deals with modeling of distribution pattern of the maximum velocity amplitude (blasting vibration field) on surface basement. This basement will be situated within small distance from source of technical seismicity that is used as a part of technological processes. The model represents seismic effect of blasting operati on in shallow tunnel. Plaxis 2D modeling system and its dynamic module based on finite element method are used for this presentation., Martin Stolárik., and Obsahuje bibliografické odkazy
The study presents a modification to conventional finite element method under plane strain conditions to address the problem of successive excavation of linear parts of tunnels. Although the successive excavation is a three-dimensional mechanical problem, the designers often prefer 2D analysis owing to considerably simple and transparent geometric model and fast computations when compared to a 3D solution. The main idea behind the suggested method referred to as, 2D3D model, is to express the influence of excavation of a single stroke of soil not only in the particular cross section but in the entire soil body in front of and behind the examined profile. This is achieved by introducing special finite elements which have common triangular cross-section but are of infinite length in the longitudinal direction. The longitudinal approximations of the displacement field adopt the evolution of convergence measurements, while standard linear shape functions are kept in the element triangular cross-section. A profile corresponding to the city road tunnel Blanka in Prague with available convergence measurements was examined to verify the method. The results show that the method provides reasonably accurate results when compared to the convergence confinement method without the need to subjectively determine the lambda parameter. It also significantly reduces the computational time of a more versatile but complex 3D analysis., Tomáš Janda, Michal Šejnoha and Jiří Šejnoha., and Obsahuje bibliografii
The aim of this study was to analyze the possibilities of various types of stent modeling and to develop some new models. A brief survey of basic properties of stents and a list of basic designs of stents is presented. Two approaches to stent modeling were identified. Structural mechanics is the theoretical background of our analytical model of a spiral stent. The finite element method was also used. The measurement equipment for model evaluation was developed., J. Záhora, A. Bezrouk, J. Hanuš., and Obsahuje bibliografii
In this paper the numerical approximation of a two dimensional aeroelastic problem is addressed, where nonlinear effects are considered. For the flow model we use the Navier-Stokes equations, spatially discretized by the FE method and stabilized with a modification of the Galerkin Least Squares (GLS) method. The motion of the computational domain is treated with the aid of the Arbitraty Lagrangian Eulerian (ALE) method. The structure model is considered as a solid body with two degrees of freedom (bending and torsion). The motion is described with the aid of a system of nonlinear differential equations and coupled with the flow model by the strongly coupled algorithm. and Obsahuje seznam literatury
We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal L2 projection with respect to a weighted L2 inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
The presented study evolved from authors considerations devoted to expected crediabiity of results obtained by finite element methods especially in cases when comparisons with those of experiment are not available. Thus, assessing the validity of numerical results one has to rely on the employed method of the solution itself. Out of many situations which might be of importance, we paid our attention to comparison of results obtaned by different element types, two different time integration operators, mesh refinements and finally to frequency analysis of the loading pulse and that of output signals expressed in displacements and strains obtained by solving a well defined transient task in solid continuum mechanics. Statistical tools for the quantitative assessment of 'close' solutions are discussed as well. and Obsahuje seznam literatury
We consider a family of conforming finite element schemes with piecewise polynomial space of degree k in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is h k + τ 2 in the discrete norms of L∞(0, T ; H1 (Ω)) and W1,∞(0, T ; L 2 (Ω)), where h and τ are the mesh size of the spatial and temporal discretization, respectively. These error estimates are useful since they allow us to get second order time accurate approximations for not only the exact solution of the wave equation but also for its first derivatives (both spatial and temporal). Even though the proof presented in this note is in some sense standard, the stated error estimates seem not to be present in the existing literature on the finite element methods which use the Newmark method for the wave equation (or general second order hyperbolic equations).