Iskanje po repozitoriju

A+ | A- | | SLO | ENG

Povzetek: This paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems. The boundary value test involves a rectangle with Dirichlet, Neuman, and Robin boundary conditions, and the initial value test is associated with the Dirichlet jump problem on a square. The spectra of the free parameters of the method, i.e., node density, timestep, shape parameter, etc., are analyzed in terms of the average error. It is found that the use of MQs is less stable compared to PHSs for irregular node arrangements. For MQs, the most suitable shape parameter is determined for multiple cases. The relationship of the shape parameter with the total number of nodes, average error, node scattering factor, and the number of nodes in the local subdomain is also provided. For regular node arrangements, MQs produce slightly more accurate results, while for irregular node arrangements, PHSs provide higher accuracy than MQs. PHSs are recommended for use in diffusion problems that require irregular node spacing.
Ključne besede: meshless method, polyharmonic splines, multiquadrics, augmentation, heat diffusion equation
Objavljeno v DiRROS: 04.04.2024; Ogledov: 73; Prenosov: 32
Celotno besedilo (2,79 MB)
Gradivo ima več datotek! Več...

Povzetek: A typical retaining structure built with large-diameter bored piles in soft clastic rock, and sup-ported by pre-stressed permanent ground anchors, is discussed. Step-by-step back analyses were performed. A simplified geological structure was first used in the analyses, together with a simple Mohr-Coulomb model. The results were compared with more complex analyses using a Hardening Soil model and a more detailed geological structure. Much better results were obtained with the use of the HS model, which is more suitable for the modelling of rock of such a type, but even with the use of the MC model the final results were quite good, making the use of the observational method attractive for engineers.
Ključne besede: geotechnics, gretaining structures, bored piles, numerical modelling, finite element method, observational method
Objavljeno v DiRROS: 27.03.2024; Ogledov: 114; Prenosov: 55
Celotno besedilo (1,67 MB)
Gradivo ima več datotek! Več...

Povzetek: After the continuous hot-rolling process, steel bars are immediately placed on the cooling bed. At the beginning of the cooling, the material is at high temperatures, and the yield strength is low. Due to thermal load, yield strength can be exceeded, and permanent plastic strains start accumulating, resulting in possible unwanted shape changes and residual stresses. The present paper aims to develop a thermo-mechanical model for studying and eliminating undesirable phenomena before the products leave the cooling bed. The governing equations are solved for the two-dimensional slice in a strong form, and a modified version of the radial basis function generated finite difference (RBF-FD) method [1]. The initial bar geometry is obtained from the existing meshless hot-rolling simulation system [2]. The thermal and mechanical models are one-way coupled, i.e. the temperature solution represents a driving force for the stress and strain solution. The temperature field is obtained with explicit propagation in time. The convective and radiative heat fluxes on the boundary are updated at each time step using the ray tracing procedure to determine the radiative heat flux. The mechanical part is solved by considering the small strain elasto-plasticity, where the isotropic von Mises temperature-dependent hardening is employed. The global system of nonlinear equations of the mechanical part is solved by the Newton-Raphson method. The closest point projection method is used to solve the constitutive relations. A sensitivity study is performed on the influence of cooling intensity on a rectangular steel bar’s temperature, stress and strain field. We defined the most influential factors for defect formation. For the first time, a novel meshless RBF-FD method is successfully used for solving such a complex industrial problem. The model will be perspectively upgraded from the slice to the three-dimensional model to enable also bending.
Ključne besede: cooling bed, steel bars, thermo-mechanics, strong form, meshless method
Objavljeno v DiRROS: 21.03.2024; Ogledov: 83; Prenosov: 47
Celotno besedilo (1,62 MB)
Gradivo ima več datotek! Več...

Povzetek: Background. Numerous experiments have to be performed before a biomedical application is put to practical use in clinical environment. As a complementary work to in vitro, in vivo and medical experiments, we can use analytical and numerical models to represent, as realistically as possible, real biological phenomena of, in our case, electroporation. In this way we canevaluate different electrical parameters in advance, such as pulse amplitude, duration, number of pulses, or different electrode geometries. Suchnumerical models can contribute significantly to the understanding of an experiment and treatment planning as well as to the design of new electroporation devices and electrodes. Methods. We used commercially available modeling software, based on finite element method. We constructed a model of a subcutaneous tumor during electrochemotherapy (EMAS) and a model ofskin during gene electrotransfer (COMSOL Multiphysics). Tissue-electrode geometries, pulse parameters and currentvoltage measurements from in vivo experiments were used to develop and validate the models. Results. To describeadequately our in vivo observations, a tissue conductivity increase during electroporation was included in our numerical models. The output currents of the models were compared to the currents and the voltages measuredduring in vivo experiments and a good agreement was obtained. Also, when comparing the voltages needed for a successful electropermeabilization assuggested by the models, to voltages applied in experiments and achieving a successful electrochemotherapy or in vivo gene electrotransfer, good agreementcan be observed. Conclusions. Modeling of electric current and electric field distribution during cell and tissue electroporation proves to be helpful in describing different aspects of the process and allowing us to design electrodes and electroporation protocols as a part of treatment planning.
Ključne besede: electroporation, gene electrotransfer, electrochemotherapy, subcutaneous tumor, finite-element method
Objavljeno v DiRROS: 07.03.2024; Ogledov: 121; Prenosov: 35
Celotno besedilo (549,62 KB)

Povzetek: We consider the following convective Neumann systems: $\begin{equation*}\left(\mathrm{S}\right)\qquad\left\{\begin{array}{ll}-\Delta_{p_1}u_1+\frac{|\nabla u_1|^{p_1}}{u_1+\delta_1}=f_1(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega,\\ -\Delta _{p_2}u_2+\frac{|\nabla u_2|^{p_2}}{u_2+\delta_2}=f_2(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega, \\ |\nabla u_1|^{p_1-2}\frac{\partial u_1}{\partial \eta }=0=|\nabla u_2|^{p_2-2}\frac{\partial u_2}{\partial \eta} \text{on}\;\partial\,\Omega,\end{array}\right.\end{equation*}$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ ($N\geq 2$) with a smooth boundary $\partial\,\Omega, \delta_1, \delta_2 > 0$ are small parameters, $\eta$ is the outward unit vector normal to $\partial\,\Omega, f_1, f_2: \Omega \times \mathbb{R}^2 \times \mathbb{R}^{2N} \rightarrow \mathbb{R}$ are Carathéodory functions that satisfy certain growth conditions, and $\Delta _{p_i}$ ($1< p_i < N,$ for $i=1,2$) are the $p$-Laplace operators $\Delta _{p_i}u_i=\mathrm{div}(|\nabla u_i|^{p_i-2}\nabla u_i)$, for $u_i \in W^{1,p_i}(\Omega).$ In order to prove the existence of solutions to such systems, we use a sub-supersolution method. We also obtain nodal solutions by constructing appropriate sub-solution and super-solution pairs. To the best of our knowledge, such systems have not been studied yet.
Ključne besede: Neumann elliptic systems, gradient dependence, subsolution method, supersolution method, nodal solutions
Objavljeno v DiRROS: 16.02.2024; Ogledov: 152; Prenosov: 46
Celotno besedilo (1,48 MB)
Gradivo ima več datotek! Več...