A simplified approach to the window gasket modeling for window strength calculation

Introduction. The study of the influence of window deformations on their performance characteristics is an urgent task. This problem is related to the issues of window elements static operation under the combined action of wind and temperature loads. It is proposed to use the capabilities of modern finite element modeling programs to analyze the window static operation. One of the problems is the modeling of an elastic window gaskets. Materials and methods. Computation of a gasket structural behavior in the direct formulation is associated with significant computational costs. In this article it is proposed a simplified method which allows taking into account the gasket mechanical work when creating window fine element model in the COMSOL Multiphysics software. For this purpose, the dependence of the gasket reaction force on the degree of its compression was obtained; this dependence was used to create a special boundary condition that imitates the force transfer from one window element to another through the gasket. Results. Two test computations were carried out with the same loads and grip conditions: in one, the gasket was modeled directly, in the other, it was replaced by the boundary condition described above. The results showed good agreement between the computations, moreover the second one needed much less time. Conclusions. Scientific foundations of window design should be based on modern research methods including computer modeling. Creating a computer model of the window static operation will allow us to consider in detail its deformed state and operational characteristics under various boundary conditions. The method proposed in this article for modeling the gasket structural behavior will be useful in achieving this aim.

Discrete-to-continuum limits of planar disclinations

In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a nearest-neighbor-type energy for the atomic bonds with an additional term to penalize change in volume. We enforce the appearance of disclinations by means of a special boundary condition. Our main result is the discrete-to-continuum limit of this energy as the lattice size tends to zero. Our proof relies on energy relaxation methods. The main mathematical novelty of our proof is a density theorem for the special boundary condition. In addition to our limit theorem, we construct examples of planar disclinations as solutions to numerical minimization of the model and show that classical results for wedge disclinations are recovered by our analysis.

FEATURES OF STRESSES AT THE APEX OF AN ELASTIC WEDGE, SUPPORTED BY A THIN FLEXIBLE COATING ON THE SIDES

Objectives To study the problem of determining the degree of stress at the apex of a wedge-shaped area in cases where the sides (or one of them) are covered with a thin flexible coating.Method It is assumed that the coating is not stretchable. On the other side of the wedge-shaped area, the same coating is assumed to be present; it is either fixed, stress-free or in smooth contact with a rigid base. Mathematically, the problem is reduced to the task of determining the roots of characteristic transcendental equations arising from the existence of a nontrivial solution to the system of linear homogeneous equations.Results Values for the specific characteristics of the radial component of a stress tensor are determined for different combinations of boundary conditions and solution angles. In particular, the angles at which the singular behaviour of stresses occurs are determined. The case is considered when a special boundary condition is given on the edge surface, simulating the overlay. Characteristic equations are obtained to determine the index of the degree dependency of the asymptotic solution in its vicinity for four variants of boundary conditions. In two cases, transcendental equations are obtained, which are solved numerically.Conclusion Calculations of the first positive roots of the equations depending on the angle of the edge solution and Poisson's ratio are presented. The values of the angles, at which the singular behaviour of stresses occurs, are determined. In the case of a combination of boundary conditions (III – IV), the singular stress behaviour is observed for the angle ???? = ????/8, while in the case of (III – III) this value is equal to ????/4.

Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Currently, the photovoltaic (PV) panels widely manufactured on market are composed of stiff front and back layers and the solar cells embedded in a soft polymeric interlayer. The wind and snow pressure are the usual loads to which working PV panels need to face, and it needs the panels keep undamaged under those pressure when they generate electricity. Therefore, an accurate and systematic research on bending behavior of PV panels is important and necessary. In this paper, classical lamination theory (CLT) considering soft interlayer is applied to build governing equations of the solar panel. A Rayleigh–Rita method is modified to solve the governing equations and calculate the static deformation of the PV panel. Different from many previous researches only analyzing simply supported boundary condition for four edges, a special boundary condition which consists of two opposite edges simply supported and the others two free is studied in this paper. A closed form solution is derived out and used to do the numerical calculation. The corresponding bending experiments of PV panels are completed. Comparing the numerical results with experiment results, the accuracy of the analytical solutions are verified.

The weak solvability of the steady problem modelling the flow of a viscous incompressible heat-conductive fluid through the profile cascade

Purpose The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade. Design/methodology/approach Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used. Findings This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force). Practical implications The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature. Originality/value To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems

Convection-dominated diffusion problems usually develop multiscaled solutions and adaptive mesh is popular to approach high resolution numerical solutions. Most adaptive mesh methods involve complex adaptive operations that not only increase algorithmic complexity but also may introduce numerical dissipation. Hence, it is motivated in this paper to develop an adaptive mesh method which is free from complex adaptive operations. The method is developed based on a range-discrete mesh, which is uniformly distributed in the value domain and has a desirable property of self-adaptivity in the spatial domain. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Moreover, a singular point resulting from a nonlinear diffusive term can be maintained by treating it as a special boundary condition. Serval numerical tests are performed. Residual errors are found to be independent of the magnitude of diffusive term. The proposed method can serve as a fast and accuracy tool for assessment of propagation of steep fronts in various flow problems.

Green Water Loads Determination for FPSO Exposed to Beam Sea Conditions

Considering new offshore frontiers for oil exploration and production, specially the Santos Basin region, FPSOs will be exposed to more severe wave conditions. This scenario requires careful analysis with respect to the green water phenomenon. The complex physics involved in the water-on-deck flow implies on several uncertainties regarding green water loads analysis. Taking into account model tests, CFD simulations and analytical formulations, this paper aims to simplify the green water loads determination, proposing a methodology to estimate these loads considering the water elevation above deck measured from experiments or numerical tools. In order to accomplish this objective, CFD simulations with different solvers were run for a benchmark case, showing that it is a suitable approach for a global result in impact dam break cases. After that, a special boundary condition was calibrated to represent model test results of water propagation in a FPSO deck exposed to beam sea in terms of water elevation. Using this CFD model, the loads on exposed structures was determined and compared against the dam break analytical formulation, which was modified to take into account the gap between each structure and the deck. Finally some vane type protection structures were simulated and their efficiency in partially obstructing the water-on-deck flow was evaluated. As a global result from all these analysis, a more comprehensive strategy for green water loads determination is proposed.

A SECTION APPROACH TO A TRAFFIC FLOW MODEL ON NETWORKS

The development of real time traffic flow models for urban road networks is of paramount importance for the purposes of optimizing and control of traffic flow. Motivated by the modeling of road networks in last decade, this paper proposes a different and simplified approach, known as section approach to model road networks in the framework of macroscopic traffic flow models. For evaluation of the traffic states on a single road, an anisotropic continuum GK-model developed by [Gupta and Katiyar, J. Phys. A38, 4069 (2005)] is used as a single-section model. This model is applied to a two-section single lane road with points of entry and exits. In place of modeling the effect of off- and on-ramps in the continuity equation, a set of special boundary condition is taken into account to treat the points of entry and exit. A four-section road network comprised of two one-lane roads is also modeled using this methodology. The performances of the section approaches are investigated and obtained results are demonstrated over simulated data for different boundary conditions.