The paper discusses the physical basis of the process of filtration of water in a case of very low velocities and presents the mathematical model of the process, based on a new constitutive formula. The existence and uniqueness of a weak solution to the resulting nonhomogeneous initial boundary-value problem is then proven.
Paper presents a numerical method for solving the initial boundary-value problem for a certain quasilinear parabolic equation describing the low velocity filtration problem. The convergence of the method is proven.
The authors developed a calculation module into a commercial finite element analysis (FEA) program, which is capable of calculating foundation rafts quickly, with correct results for the engineering practice. The calculation method is based on the so-called `uncoupled iterative method', wherein the structure and the soil continuum are analysed separately. The results of one analysis form the boundary conditions for the subsequent analysis as part of an iterative process. The connection between the raft and the soil is considered to be represented by the bedding modulus of the raft and by the soil stresses. The method provides the same displacements for the raft as for the soil surface, provided sufficient convergence can be reached if the raft is not elevated from the soil.
Recent advances in reliability methods, optimization as well as design sensitivity analysis have resulted in development of computational systems supporting RBDO processes for medium/large structures. For RBDO the efficiency problems are critical and in order to get the optimum design a number of fast approximate methods have been recently proposed. These methods, tested for rather small problems, show acceptable accuracy and speed up computations considerably. However, when applied in the automated way to medium/large scale problems they may cause severe convergence problems or lead to a poor local minimum after expensive computations. Instead of an automated optimization procedure, an interactive approach is proposed. Implemented in the POLSAP-RBO system it allows to combine effective interactive design methods with visual capabilities to efficiently generate optimum design. Benchmark studies of an offshore jacket structure show efficiency of the interactive approach which employs integration, approximation and reduction techniques for maximizing efficiency of RBDO.
The single-mode equation of motion of a class of buckled beams is considered, and the attention is focused on the phenomena of irregular, unpredictable transient oscillations which are observed in the region of the nonlinear resonance hysteresis. This type of transient motion may be dangerous in engineering dynamics, because it may last very long and is defined neither by the coefficient of damping nor by the magnitude of perturbation. While the steady-state chaotic motion has been studied extensively in the recent literature, little attention was paid to the chaotic transients. In the paper the criteria for transient chaos, i.e. the domain of the system control parameter values, where the chaotic transient motion can occur, are determined. The criteria are based on the theoretical concept of global bifurcations, and are estimated numerically.
The paper is concerned with the mathematical modelling and numerical solution of unilateral problems for viscoelastic-plastic structural systems. A new material model is proposed in which the viscoelastic and plastic strains are governed by different constitutive laws. The model is restricted to isothermal quasistatic deformation processes under conditions of geometric linearity. The mechanical problem is posed in the format of piecewise linear plasticity and the unilateral contact conditions are described by means of the clearance function. The linear viscoelastic laws are integrated by a creep approach method, which allows for jump-discontinuities in the history of stress. For the evolution of plastic strains an implicit method is used. The problem is formulated and solved as a sequence of nested (mixed) linear complementarity problems. The question of existence and uniqueness of a solution to the problem is discussed. A numerical algorithm based on the pivotal transformations is devised and its stability is shown numerically. Results of numerical experiments for several illustrative examples of a beam/foundation system subjected to nonproportional loading histories are presented. The results clearly demonstrate the impact of the history of loading and the unilateral constraints upon the current state of the structural system.
Keywords: viscoelasto-plasticity; creep approach; unilateral constraints; finite element method; linear complementarity problem.
An analytical study of stability is made for a hydromechanical servomechanism used in copying systems. In the framework of a nonlinear system of ODE mathematically modelling the servomechanism, we prove that for a ramp input the steady-state solution bifurcates into a stable limit cycle for a certain value of the underlap spool valve.
An approach for modeling finite-rate chemistry effects such as local extinction and reignition in piloted diffusion fiames of CO/H2/N2 or CH4 and air is presented. A partial equilibrium/two-scalar exponential PDF combustion model is combined with a 2D Large Eddy Simulation procedure employing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of the PDF scalars is avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is accounted for by comparing the local Damkohler number against a `critical' local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is modelled via a Lagrangian transport equation for a reactedness progress variable that follows a linear deterministic relaxation to its mean value (IEM). Comparisons between simulations and measurements suggested the ability of the method to calculate adequately the partial extinction and reignition phenomena observed in the experiments.
Keywords: CO/H2/N2 or CH44 flames, extinction and reignition, partial equilibrium model, Large Eddy Simulations, Lagrangian models.