scholarly journals 3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

2022 ◽  
Vol 12 (1) ◽  
pp. 512
Author(s):  
Salvatore Brischetto ◽  
Roberto Torre
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Stress Analysis ◽  
Numerical Models ◽  
Functionally Graded ◽  
Analytical Models ◽  
Direct Result ◽  
Equilibrium Equations ◽  
Plates And Shells ◽  
Moisture Conditions

This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

Closed-form expressions for the steady-state response of damped transmission line conductors considering their bending stiffness

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1319-1329
Author(s):  
Marcelo A Ceballos ◽  
José E Stuardi
Keyword(s):  
Steady State ◽  
Transmission Line ◽  
Numerical Models ◽  
Mechanical Impedance ◽  
Steady State Solution ◽  
Bending Stiffness ◽  
Analytical Models ◽  
Dispersive Media ◽  
Overhead Transmission Line ◽  
Damper Design

This paper begins with a brief compilation of analytical models typically used to calculate the dynamic response of a conductor span belonging to an overhead transmission line, with a Stockbridge-type damper located near one of its ends. In most of analyses found in the literature, the calculation of the response is done through the superposition of waves that propagate in both longitudinal directions impinging and reflecting at the span ends and at the damper attachment points. The approach proposed in this paper allows obtaining the response as the steady-state solution of the governing differential equations providing suitable analytical expressions for conductors with bending stiffness, which are dispersive media for propagating waves. Using these analytical solutions, the influence of bending stiffness on the efficiency and on the optimal mechanical impedance of the damper, which are of great importance in damper design, can be described explicitly. At the same time, the proposed methodology avoids the need of numerical models or approximate formulas to calculate the bending strains in critical points of the conductor with a single damper.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Gaining a better understanding of the extrusion process in fused filament fabrication 3D printing: a review

2021 ◽  
Author(s):  
Bahaa Shaqour ◽  
Mohammad Abuabiah ◽  
Salameh Abdel-Fattah ◽  
Adel Juaidi ◽  
Ramez Abdallah ◽  
...  
Keyword(s):  
3D Printing ◽  
Numerical Models ◽  
Extrusion Process ◽  
Analytical Models ◽  
Limiting Factor ◽  
Fused Filament Fabrication ◽  
Promising Tool ◽  
Relevant Work ◽  
3D Printing Technique ◽  
Required Quality

AbstractAdditive manufacturing is a promising tool that has proved its value in various applications. Among its technologies, the fused filament fabrication 3D printing technique stands out with its potential to serve a wide variety of applications, ranging from simple educational purposes to industrial and medical applications. However, as many materials and composites can be utilized for this technique, the processability of these materials can be a limiting factor for producing products with the required quality and properties. Over the past few years, many researchers have attempted to better understand the melt extrusion process during 3D printing. Moreover, other research groups have focused on optimizing the process by adjusting the process parameters. These attempts were conducted using different methods, including proposing analytical models, establishing numerical models, or experimental techniques. This review highlights the most relevant work from recent years on fused filament fabrication 3D printing and discusses the future perspectives of this 3D printing technology.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

Modelling of interactions between dykes, inclined sheets and faults at Santorini volcano

2021 ◽  
Author(s):  
Kyriaki Drymoni ◽  
John Browning ◽  
Agust Gudmundsson
Keyword(s):  
Tensile Strength ◽  
Fault Zone ◽  
Numerical Models ◽  
Damage Zone ◽  
Sheet Thickness ◽  
Analytical Models ◽  
Energy Conditions ◽  
Dyke Swarm ◽  
Normal Faults ◽  
Santorini Volcano

<p>Dykes and inclined sheets are known occasionally to exploit faults as parts of their paths, but the conditions that allow this to happen are still not fully understood. Here we report field observations from a well-exposed dyke swarm of the Santorini volcano, Greece, that show dykes and inclined sheets deflected into faults and the results of analytical and numerical models to explain the conditions for deflection. The deflected dykes and sheets belong to a local swarm of 91 dyke/sheet segments that was emplaced in a highly heterogeneous and anisotropic host rock and partially cut by some regional faults and a series of historic caldera collapses, the caldera walls providing, excellent exposures of the structures. The numerical models focus on a normal-fault dipping 65° with a damage zone composed of parallel layers or zones of progressively more compliant rocks with increasing distance from the fault rupture plane. We model sheet-intrusions dipping from 0˚ to 90˚ and with overpressures of alternatively 1 MPa and 5 MPa, approaching the fault. We further tested the effects of changing (1) the sheet thickness, (2) the fault-zone thickness, (3) the fault-zone dip-dimension (height), and (4) the loading by, alternatively, regional extension and compression. We find that the stiffness of the fault core, where a compliant core characterises recently active fault zones, has pronounced effects on the orientation and magnitudes of the local stresses and, thereby, on the likelihood of dyke/sheet deflection into the fault zone. Similarly, the analytical models, focusing on the fault-zone tensile strength and energy conditions for dyke/sheet deflection, indicate that dykes/sheets are most likely to be deflected into and use steeply dipping recently active (zero tensile-strength) normal faults as parts of their paths.</p>

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