## About

24

Publications

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151

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Introduction

Hassan's research interests include mathematics and mechanics of solids, variational principles in mechanics and the development of computational tools for continuous dynamic optimization problems in engineering.

Additional affiliations

July 2022 - present

Education

November 2018 - November 2021

October 2015 - March 2018

October 2011 - March 2015

## Publications

Publications (24)

The paper is devoted to the optimization of axisymmetric structures made of functionally graded materials and subject to mechanical and thermal loads. The novelty of the results is that the volume fraction distribution is not limited to a power-law variation, as in most of the works available in the literature, but can be any (piecewise continuous)...

The paper deals with an optimization problem related to axisymmetric membrane shells made of homogeneous, linear and isotropic materials and subject to a cyclic internal pressure. The optimization problem considers the possible crack growth in the shell as a structural constraint, which is accounted for by the well-known Paris law, and hence obeys...

In this article, the strain and stress analyses of functionally graded plates with circular holes that are subject to a uniaxial far-field traction load are analytically considered. The Young's modulus is assumed to vary linearly along the radial direction around the hole. The adoption of such a type of inhomogeneity variation can be justified as f...

When in the differential equation describing the behaviour of a dynamical system the time derivative of the input is involved, a naive realization may mislead the application of the Pontryagin Maximum Principle for the solution of optimal control problems. We show that a suitable procedure to eliminate the time derivative of the input leads to a re...

This paper is devoted to the minimization of the stress concentration factor in infinite plates with circular hole made of functionally graded materials and subjected to a far-field uniform uniaxial tension. Despite the vast literature on the versatility of these materials, the novelty of the results is that the material distribution is not limited...

This paper is devoted to the minimization of the stress concentration factor in infinite plates with circular hole made of functionally graded materials and subjected to a far-field uniform uniaxial tension. Despite the vast literature on the versatility of these materials, the novelty of the results is that the optimal material distribution is not...

A state–space integer–order approximation of a commensurate–order systems is obtained using a data–driven interpolation approach based on Loewner matrices. Precisely, given the values of the original fractional–order transfer function at a number of generalised frequencies, a descriptor–form state–space model matching these frequency response value...

In this article, a direct transcription approach to the minimization of the volume of elastic straight beams undergoing plane deformation and subject to buckling loads is presented. In particular, the so-called pseudospectral method is employed, where states are approximated by Lagrange interpolating polynomials and static equations are collocated...

It is well known that fractures in elastic bodies initiate at locations of stress concentrations, which could arise due to geometrical discontinuities. While there are several works available in the literature about fracture mechanics studies for homogeneous bodies (both experimental and analytical), only a few studies analyzed the effects of geome...

This dissertation is focused on the utility of variational principles and the vast possibilities they offer as powerful tools for a suggestive use to solve optimization problems in structural mechanics.
To this purpose, an introduction to the analytical approach to continuous dynamic optimization problems and the development of a dedicated computat...

The direct transcription method that employs global collocation at Legendre-Gauss-Radau points is addressed and applied to infinite-dimensional dynamic optimization problems in engineering. The formulation of these latter is considered referring to a Bolza-type performance index. A reduced unconstrained form of it is particularly studied in the pse...

The thermomechanical stress analysis of thick-walled spherical vessels is considered. The thickness of the vessel is assumed to be constituted of an internal functionally graded (FG) coating and an external homogeneous layer. In the graded internal layer the property variations along the thickness are linked to the constituents volume fractions by...

The feasibility of a pressure vessel shape optimization is here investigated. An analytical procedure based on calculus of variations is used for the shape optimization of a naturally closed pressure vessel aiming at either minimizing the mass or maximizing the volume under structural integrity constraints. The obtained shapes are ellipsoids with v...

One of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material com-positionally grades. In the works available in...

The stiffness maximization of elastic straight Euler-Bernoulli beams under the action of linearly distributed loads is addressed. The goal is achieved by minimizing the average compliance, which is given by the value of internal elastic energy distributed over the length of the beam. Studies in the literature suggest considering this approach since...

This paper is devoted to the discussion of practical applications of a recent paradox in curved beams, according to which it is possible to simultaneously remove material and reduce the bending stresses. This paradox is compared to a similar paradox valid for rectilinear beams. The beam cross section zones from which material may advantageously be...

Functionally graded beams, bars and rods have been gaining a relevant consideration in engineering practice and research, taking into account variations of the material properties either in the transverse or in the longitudinal direction. Yet existing literature dealing with analytical study of structural instability for an arbitrary material longi...

Material property variation in non-homogeneous internally pressurized thick-walled cylinders is investigated within the context of dynamic programming theory. The material is assumed to be linear, elastic, isotropic, and functionally graded in the radial direction. Based on the plane stress hypothesis, a state space formulation is given and the opt...

The paper deals with an arising paradox in curved beams subjected to bending moment and normal force. This paradox consists in the fact that by laterally removing material from section zones close to the neutral axis, not only an obvious reduction of the beam mass can be obtained, but also an unexpected, though technically negligible, reduction of...

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact...

The paper is devoted to the analytic optimization of the thickness distributions of axisymmetric vessels where the cost functional to minimize is the compliance. The goal is achieved by minimizing the strain energy under mass constraint. The theoretical framework of the mechanics of thin walled membrane shells is recalled at the beginning of the pa...

This paper deals with two optimisation problems related to axisymmetric membrane shells made of homogeneous, linear and isotropic materials and subjected to an internal pressure. The design variables are the meridian shape and the thickness distribution (possibly not constant). In the first part of the paper, a general background on the mechanics o...

The longest reach problem of an elastic cantilevered rod subjected to a tip load is here revisited. It has been investigated for the first time recently (Wang C.). In this paper, two extensions of the problem are covered: the case of rods of extensible axis and of variable cross sectional area distribution. The problem is stated and solved numerica...

The logic of the Schrödinger equation may be understood most readily by a consideration of a very important class of problems, i.e. those of the transmission and reflection of electrons through semi-infinite potential barriers. In this paper I revisit this problem by applying an alternative approach via Laplace transforms, demonstrating how effecti...