A Dynamic Programming Setting for Functionally Graded Thick-Walled Cylinders

Abdalla, Hassan Mohamed Abdelalim; Casagrande, Daniele; Bona, Francesco De

doi:10.3390/ma13183988

Cited by 13 publications

(8 citation statements)

References 24 publications

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“…A first attempt to deal with the aforementioned optimization problem has been done for the first time in [20] for a functionally graded pressurized thick-walled cylinder within the plane stress condition. Nevertheless, the present paper remarkably presents three novelties that can be summarized as follows.…”

Section: Objectives and Resultsmentioning

confidence: 99%

“…• Firstly, different from [20] where only plane stress condition is considered, a unified mathematical approach for both plane stress and plane strain hypotheses is presented. • Secondly, goal functions are expressed in terms of constituents volume fractions and not merely in the property variations, making therefore the present framework suitable for technological aspects associated with the manufacture process.…”

Section: Objectives and Resultsmentioning

confidence: 99%

“…Problem 1 Given the dynamical system (20) and the boundary conditions (21) and 22, find the control function v c :…”

Section: Statementmentioning

confidence: 99%

See 2 more Smart Citations

An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

Abdalla

Casagrande

2021

J Elast

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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 compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

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Section: Objectives and Resultsmentioning

confidence: 99%

Section: Objectives and Resultsmentioning

confidence: 99%

See 1 more Smart Citation

An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

Abdalla

Casagrande

2021

J Elast

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“…As testing is costly and time-consuming modeling of material is essential, the knowledge of it helps not only in finding the material properties of FGM’s produced but also for developing new materials with appreciated properties. The modeling of FGM is important in the study of cylinders, pressure vessels, spheres, plates and disks (Abdalla et al , 2020; Madan et al , 2019c). A mismatch in experimental and theoretical results is owing to many reasons such as porosity, shrinkage, binding, geometrical factors (size, shape and orientation of fibers), environmental conditions and human error (Verma et al , 2019).…”

Section: Introductionmentioning

confidence: 99%

Modeling of functionally graded materials to estimate effective thermo-mechanical properties

Madan

Bhowmick

2021

WJE

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Purpose Functionally graded materials are a special class of composites in which material are graded either continuously or layered wise depending upon its applications. With such variations of materials, the properties of structure vary either lengthwise or thickness wise. This paper aims to investigate models for effective estimation of material properties, as it is necessary for industries to identify the properties of composites or functionally graded materials (FGM’s) before manufacturing and also to develop novel material combinations. Design/methodology/approach Available models were compared for different material combinations and tested with experimental data for properties such as Young’s modulus, density, coefficient of thermal expansion (CTE) and thermal conductivity. Combinations of metal–ceramic and metal–metal were selected such that their ratios cover a wide range of materials. Findings This study reveals different models will be required depending on the material used and properties to be identified. Practical implications The results of the present work will help researchers in the effective modeling of composites or FGM’s for any analysis. Originality/value This paper presents a comparison and review of various analytical methods with experimental data graphically to find out the best suitable method. For the first time, the Halpin-Tsai model was extended in the analysis of the CTE which shows good approximations.

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“…Thick-walled cylinders are widely used in the petrochemical industry, in natural gas, in high-pressure hydraulic systems and in other structures, such as high-pressure oil pipes, petrochemical pressure vessels, heat exchange tubes, storage vessels, nuclear reactor pressure vessels, cannon barrel, steam pipelines and functionally graded materials [1,2]. These internally pressured, thick-walled cylindrical vessels usually operate under hightemperature and high-pressure steam conditions; thus, creep deformation is considered one of the main failure mechanisms of these structures.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Modelling of Creep Deformation of Viscoelastic Thick-Walled Cylinder with Fractional Maxwell Model

et al. 2021

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The deformation of a thick-walled cylinder under pressure is a classic elastic mechanics problem with various engineering applications. In this study, the displacement of a viscoelastic thick-walled cylinder under internal pressure is investigated via analytical as well as numerical modelling. The fractional Maxwell model is initially introduced to describe the creep deformation of high-strength Q460 steel. Subsequently, an analytical solution to the creep deformation of the thick-walled cylinder under both internal and external pressures is deduced with the corresponding principle. The analytical solution is examined with a numerical simulation that incorporates the fractional Maxwell model by a user-defined subroutine. The numerical simulation agrees well with the analytical solution. The limitations of the current study are also discussed.

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A Dynamic Programming Setting for Functionally Graded Thick-Walled Cylinders

Cited by 13 publications

References 24 publications

An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

Modeling of functionally graded materials to estimate effective thermo-mechanical properties

Analytical and Numerical Modelling of Creep Deformation of Viscoelastic Thick-Walled Cylinder with Fractional Maxwell Model

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