Papers by Keyword: Inverse Problem

Abstract: To produce parts with tailored properties, i.e. parts with high strength in some areas and high ductility on some other areas, one of the most popular method, called the tailored tempering process, is to heat up locally the tools. In the hot areas, the blank follows a different thermal path leading to different microstructure evolutions and thus different final mechanical properties. In this paper, a tool is designed to have a side heated up to 500°C and a water cooled side. The hot side is heated up thanks to heated cartridges. A PID regulation is used to control the temperature of the hot side (from 200°C to 500°C) while the cold side is maintained at a low temperature using a thermostated water circulation. A uniform temperature on the working surface is successfully reached on both sides. Instrumentation by thermocouples is designed to be able to fully characterize the heat transfer: solving 2D heat conduction problems, the temperature fields in the tools and the thermal contact resistances at the blank/tool interfaces are estimated. Hardness measurements are also performed on the blank: the possibility to confer a distribution of mechanical properties is highlighted.

Abstract: We determine the sorption isotherm in the infiltration model of contaminated water into porous media. We assume that the contaminated water infiltrates into the dry porous media, flow through the sample and flows out at the other side of the sample. We suppose that the contaminant dissolved in the water reversibly adsorbs into the porous media. We use the Richards equation with van Genuchten relation between effective saturation and pressure head. Further, we use Fick’s law to model the contaminant transport in the water and arbitrary adsorption isotherm to model the evolution of the adsorption. By running the direct problem simulation, we obtain the “measurements” of the expelled water mass and its concentration. Then we “forget” the adsorption isotherm function. We solve this inverse problem by evaluating the gradient of the distance function (between “measured” and computed bottom contaminant flux) in an iterative way. We construct the gradient (variation) of the distance function by solving the corresponding dual system of partial differential equations.

Abstract: In this article, an analytical dependence of distribution of elasticity modulus across the thickness of the cylinder loaded with internal pressure p, at which the equivalent stresses according the Mohr failure criterion are the same at all points. The problem is solved for the cases of plane strain state and plane stress state in the elastic formulation.

Abstract: Reinforced concrete beams are widely employed in civil engineering structures. To reduce the maintenance financial cost, structure damages have to be detected early. To this end, one needs robust monitoring techniques. The paper deals with the identification of mechanical parameters, useful for Structural Health Monitoring, in a 2D beam using inverse modeling technique. The optimal control theory is employed. As an example, we aim to identify a reduction of the steel bar cross-section and a decrease of the concrete Young modulus in damaged areas. In our strategy, the beam is instrumented with strain sensors, and a known dynamic load is applied. In the inverse technique, two space discretizations are considered: a fine dicretization (h) to solve the structural dynamic problem and a coarse discretization (H) for the beam parameter identification. To get the beam parameters, we minimize a classical data misfit functional using a gradient-like algorithm. A low-cost computation of the functional gradient is performed using the adjoint equation. The inverse problem is solved in a general way using engineer numerical tools: Python scripts and the free finite element software Code_Aster. First results show that a local reduction of the steel bar cross-section and a local decrease of concrete Young modulus can be detected using this inverse technique.

Abstract: In paper describes a method of optimization the stress state of an elastic beam, subjected to the simultaneous action of the central application of concentrated force and bending moment. Optimization method based on solving the inverse problem of the theory of elasticity of inhomogeneous bodies, the essence of which is to determine the law of changing the modulus of elasticity on the beams height for which stress state will be given.

Abstract: The paper has a discussion of forward problem and inverse problem for beams in strength of materials. Known load case of a beam can certainly determine its shearing force diagram and bending moment diagram, but conversely, there may be a variety of statically determinate or statically indeterminate constraint conditions. Furthermore, the solution from statically indeterminate constraint conditions doesnt agree with the given shearing force diagram and bending moment diagram in a general way.

Abstract: Based on a brief review of the developing history of vehicle steering inverse dynamics, and using radial basis function neural network, the nonlinear mapping relation between lateral angular velocity and steering angle input is found. The identification results of step and sine steering angle input show that the proposed identification method is not only practical, but also with high accuracy.

Abstract: Hamiltonian matrices have many applications to design automation and autocontrol, in particular in the linear-quadratic autocontrol problem. This paper studies the inverse problems of generalized Hamiltonian matrices for matrix equations. By real representation of complex matrix, we give the necessary and sufficient conditions for the existence of a Hermitian generalized Hamiltonian solutions to the matrix equations, and then derive the representation of the general solutions.

Abstract: Spontaneous combustion is a complicated process and its control function is a partial differential equation (PDE) of heat conduction. To solve the problem of spontaneous combustion, we should specify some parameters first, such as the heat source, thermal conductivity, convective heat transfer coefficient, and so on. Some parameters can be got easily and accurately, but some are not. So there could be a great gap between the result of numerical simulation and the result of experiment. For this inverse problem, we can estimate these parameters with the MCMC (Markov Chain Monte Carlo) method. Then, we could get more accuracy and reliable numerical result.

Abstract: In this paper, the conditions and method of constructing the stiffness distribution function of various parameters indeterminate beams by the fundamental mode and specified polynomial density distributing function were made up. It is discussed that the constructed stiffness distribution functions are positive functions in case with different density distributing.