Numerical Modelling of Metal Foams with Weaire-Phelan Cell

2013 ◽  
Vol 334-335 ◽  
pp. 122-126 ◽  
Author(s):  
Sid Ali Kaoua ◽  
Haddad Meriem ◽  
Dahmoun Djaffar ◽  
Azzaz Mohammed
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Metal Foam ◽  
Metallic Foam ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Geometrical Characteristics ◽  
Structural Network ◽  
Regular Network

The mechanical properties of open-cell metal foam structures are investigated using the finite element method. The foam structure is modelled by a regular network of anisotropic Weaire-Phelan cells in which the strands are modelled as 3D finite element beams. We consider four types of strand cross sections: (i) circular, (ii) square, (iii) triangular and (iv) Plateau border shape. The numerical results obtained with our proposed mathematical model are checked against the experimental results obtained on real Nickel metallic foam and an excellent agreement is found. In addition, we conducted a parametric analysis to study the effect of some geometrical characteristics on the elasticity of the metal foam. Among these geometrical parameters, the shape, the dimensions of strand cross section, the inertia, the alignment of strands and the structural network irregularities are investigated, discussed and documented.

scholarly journals OPTIMIZATION OF ELASTIC BRIDGE TRUSSES / TAMPRIŲ TILTO SANTVARŲ OPTIMIZAVIMAS

2013 ◽  
Vol 5 (5) ◽  
pp. 506-512
Author(s):  
Ignas Rimkus ◽  
Šarūnas Kisevičius ◽  
Stanislovas Kalanta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Iterative Process ◽  
Branch And Bound Method ◽  
Rolled Steel ◽  
The Finite Element Method ◽  
Section Area ◽  
Steel Sections

The article analyzes the problems of optimizing elastic bridgetrusses, which is a tool for seeking the establishment of theminimum volume (mass) of construction and optimization of thecross-section area and height as well as the structure of the truss.It has been formulated as a nonlinear discrete mathematical programmingproblem. The upper band of the truss works not onlyfor compression but also for bending. The cross-sections of theelements are designed from rolled steel sections. Mathematicalmodels are prepared by using the finite element method and complyingwith requirements for the strength, stiffness and stabilityof the structure. The formulated problems are solved referringto an iterative process and applying the mathematical softwarepackage “MATLAB” along with routine “fmincon”. The ratio ofbuckling is corrected in every case of iteration. Requirementsfor cross-section assortment (discretion) are fulfilled employingthe branch and bound method. Santrauka Darbe nagrinėjami tamprių tilto santvarų optimizavimo uždaviniai, kuriais siekiama nustatyti minimalų konstrukcijos tūrį (masę), optimizuojant strypų skerspjūvius, santvaros aukštį bei tinklelio struktūrą. Jie formuluojami kaip netiesiniai diskrečiojo matematinio programavimo uždaviniai. Santvaros viršutinės juostos elementai ne tik gniuždomieji elementai, bet ir lenkiamieji. Strypų skerspjūviai projektuojami iš plieninių valcuotųjų profiliuočių. Uždavinių matematiniai modeliai sudaromi taikant baigtinių elementų metodą ir atsižvelgiant į konstrukcijos stiprumo, standumo bei pastovumo reikalavimus. Suformuluoti uždaviniai sprendžiamai iteraciniu būdu, naudojant matematinį kompiuterinį paketą MATLAB ir jo paprogramį fmincon. Kiekvienoje iteracijoje koreguojami gniuždomųjų elementų klupumo koeficientai. Skerspjūvių sortimento (diskretiškumo) reikalavimai užtikrinami taikant šakų ir rėžių metodą.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Local Hydrostatic Pressure Test for Cylindrical Vessels

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
H. Al-Gahtani ◽  
A. Khathlan ◽  
M. Sunar ◽  
M. Naffa'a
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Cylindrical Vessel ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Wide Range ◽  
Pressure Test ◽  
Local Test ◽  
Alternative Test

The juncture of a small cylindrical nozzle to a large cylindrical vessel is very common in the pressure vessel industry. Upon fabrication, it is required that the whole structure is subjected to pressure testing. The test can be expensive as it necessitates pressurizing the whole structure typically having a large volume. Hence, it is proposed to make a “local test,” which is considerably simpler as it involves capping the small nozzle and testing only a relatively small portion of the structure. This paper investigates the accuracy and reliability of such an alternative test, using the finite-element method. Two different finite-element types are used in the study, specifically a shell-based element and a solid-based element. The verification of the finite-element results for two different cases shows that the models used in the study are valid. It also proves that the two element types yield very similar stress results. In addition, the study includes a numerical investigation of more than 40 different nozzle-to-vessel junctures with a wide range of parameters for the nozzle and vessel. The results indicate that the use of cylindrical caps that are slightly larger than the nozzle is not recommended as it produces stresses that are significantly different from those for the original required pressure test. As such, the study provides an estimate of the smallest size of the cap that may be used in the local test to generate stresses that agree with the full test. For most practical geometries, it is shown that the size of the cap needs to be at least 2–30 times larger than that of the nozzle, depending on the geometrical parameters of the juncture.

The Accepting of Pipe Bends With Ovality and Thinning Using Finite Element Method

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
AR. Veerappan ◽  
S. Shanmugam ◽  
S. Soundrapandian
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Cross Sections ◽  
Pressure Ratio ◽  
Empirical Relationship ◽  
The Finite Element Method ◽  
Element Method

Thinning and ovality are commonly observed irregularities in pipe bends, which induce higher stress than perfectly circular cross sections. In this work, the stresses introduced in pipe bends with different ovalities and thinning for a particular internal pressure are calculated using the finite element method. The constant allowable pressure ratio for different ovalities and thinning is presented at different bend radii. The allowable pressure ratio increases, attains a maximum, and then decreases as the values of ovality and thinning are increased. An empirical relationship to determine the allowable pressure in terms of bend ratio, pipe ratio, percent thinning, and percent ovality is presented. The pipe ratio has a strong effect on the allowable pressure.

LOAD-CARRYING CAPACITIES FOR CIRCULAR METAL FOAM CORE SANDWICH PANELS AT LARGE DEFLECTION

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6218-6223 ◽  
Author(s):  
W. HOU ◽  
Z. WANG ◽  
L. ZHAO ◽  
G. LU ◽  
D. SHU
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Large Deflection ◽  
Metal Foam ◽  
Yield Criterion ◽  
Metallic Foam ◽  
Foam Core ◽  
Element Simulation ◽  
Load Carrying ◽  
Good Agreement

This paper is concerned with the load-carrying capacities of a circular sandwich panel with metallic foam core subjected to quasi-static pressure loading. The analysis is performed with a newly developed yield criterion for the sandwich cross section. The large deflection response is estimated by assuming a velocity field, which is defined based on the initial velocity field and the boundary condition. A finite element simulation has been performed to validate the analytical solution for the simply supported cases. Good agreement is found between the theoretical and finite element predictions for the load-deflection response.

Fatigue damage in bending of reinforced concrete frames using non-destructive tests for dynamic strength of the cylinder

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Dragan D. Milašinović ◽  
Aleksandar Landović ◽  
Danica Goleš
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fatigue Damage ◽  
Cross Section ◽  
Modal Parameters ◽  
The Finite Element Method ◽  
Concrete Frames ◽  
Content Type ◽  
Non Destructive

PurposeThe purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.Design/methodology/approachThe problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.FindingsThe modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.Originality/valueThe paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

Residual stress distribution in built-in beams

2020 ◽  
pp. 146442072095861
Author(s):  
FA de Castro ◽  
Paulo P Kenedi ◽  
LL Vignoli ◽  
I I T Riagusoff
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stress Distribution ◽  
Cross Section ◽  
Cross Sections ◽  
Element Model ◽  
Residual Stress Distribution ◽  
Concentrated Load ◽  
Load Growth ◽  
Final Failure

Metallic hyperstatic structures, like beams, submitted to excessive loads, do not fail completely before fully yielding in more than one cross section. Indeed, for built-in beams, three cross sections must be fully yielded before the final failure can occur. So, modeling the evolution of the cross-section residual stress distribution is an important subject that should be addressed to guarantee the stress analysis modeling correctness. This paper analyses the residual stress distribution evolution, in critical cross sections, of built-in beams during a transversal concentrated load growth, until the final failure through hinges formation. A finite element model is also presented. The results show good matches with the numerical model, used as a reference.

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