Alexandre Kawano

A mixed continuous and discrete nonlinear constrained algorithm for optimizing ship hull structural design

A nonlinear search algorithm for optimizing constrained design of ship structures is presented. The decision variables can be continuous or discrete and the constraints can be homogeneous or inequality nonlinear functions of those variables. The algorithm does not use gradients; therefore, it can work with non-systematized functions such as tables or another class of design routine. It was tested in the structural design of a Patrol Boat and has proved to be a powerful tool decreasing the time expended in preliminary design when it is done by the conventional spiral approach.

Uniqueness in the determination of vibration sources in rectangular Germain–Lagrange plates using displacement measurements over line segments with arbitrary small length

The theme of this work is related to the field of vibration and source detection, which is important in naval, aerospace and civil engineering industries. The detection of unexpected vibration sources, in general, signals malfunctioning, or even an undesired presence in the case of defense systems. The focus will be on thin plates, which are among the basic building blocks of large complex structures. Here, we consider loads acting on a rectangular plate R of the product form g(t)Q(x), where the function of time g has a continuous first derivative and the spatial load distribution Q is a square-integrable function over R. We prove that the observation of the displacement of a line segment with arbitrary length parallel to one of the sides of the plate is enough for the determination of Q, provided that the interval of time is long enough. We also prove that the normal derivative along a side of the rectangle measured for an arbitrarily small interval of time is sufficient to determine the spatial load distribution Q. The method used to obtain the results is based on the series decomposition of the dynamic response and an analysis of the almost periodic distribution that arises from it.

Identification of unknown spatial load distributions in a vibrating Euler–Bernoulli beam from limited measured data

Two types of inverse source problems of identifying asynchronously distributed spatial loads governed by the Euler–Bernoulli beam equation , with hinged–clamped ends ( ), are studied. Here are linearly independent functions, describing an asynchronous temporal loading, and are the spatial load distributions. In the first identification problem the values , of the deflection , are assumed to be known, as measured output data, in a neighbourhood of the finite set of points , corresponding to the internal points of a continuous beam, for all . In the second identification problem the values , of the slope , are assumed to be known, as measured output data in a neighbourhood of the same set of points P for all . These inverse source problems will be defined subsequently as the problems ISP1 and ISP2. The general purpose of this study is to develop mathematical concepts and tools that are capable of providing effective numerical algorithms for the numerical solution of the considered class of inverse problems. Note that both measured output data and contain random noise. In the first part of the study we prove that each measured output data and can uniquely determine the unknown functions . In the second part of the study we will introduce the input–output operators , and , , corresponding to the problems ISP1 and ISP2, and then reformulate these problems as the operator equations: and , where and . Since both measured output data contain random noise, we use the most prominent regularisation method, Tikhonov regularisation, introducing the regularised cost functionals and . Using a priori estimates for the weak solution of the direct problem and the Tikhonov regularisation method combined with the adjoint problem approach, we prove that the Frechet gradients and of both cost functionals can explicitly be derived via the corresponding weak solutions of adjoint problems and the known temporal loads . Moreover, we show that these gradients are Lipschitz continuous, which allows the use of gradient type iteration convergent algorithms. Two applications of the proposed theory are presented. It is shown that solvability results for inverse source problems related to the synchronous loading case, with a single interior measured data, are special cases of the obtained results for asynchronously distributed spatial load cases.

A uniqueness result for the recovery of a coefficient of the heat conduction equation

There are industrial applications where the recovery of the coefficients of the heat conduction equation from measurements of the temperature over an open set ?* is crucial. We analyse the inverse problem of identifying the conductivity coefficient of the heat equation when a zero initial condition is set and single measurements are made. We prove a uniqueness result for a linearized version of this problem in for n odd that does not depend on a hypothesis about the relative position of the support of the unknown function with respect to ?*. It is an extension, for n odd, of a theorem proved by Elayyan and Isakov.

Bayesian Updating in the Determination of Forces in Euler-Bernoulli Beams

The beam is among the most important structural elements, and it can fail by different causes. In many cases it is important to access the loading acting on them. The determination of loading on beams is important, for example, for model calibration purposes and or to estimate remaining fatigue life. In this article we first prove that identification of the loading is theoretically possible from the observation of the displacement of small portion of it for an arbitrary small interval of time and then propose a method to infer the spatial distribution of forces acting upon a beam from the measurement of the displacement of one of its points. The Bayesian method is used to combine measurements taken from different points at different times. This method enables an effective way of reducing the practical amount of time for obtaining meaningful loading estimates.