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20 pages, 917 KB

Open AccessArticle

Numerical Investigation of Buckling Behavior of MWCNT-Reinforced Composite Plates

by Jitendra Singh, Ajay Kumar, Barbara Sadowska-Buraczewska, Wojciech Andrzejuk and Danuta Barnat-Hunek

Materials 2025, 18(14), 3304; https://doi.org/10.3390/ma18143304 - 14 Jul 2025

Viewed by 363

Abstract

The current study demonstrates the buckling properties of composite laminates reinforced with MWCNT fillers using a novel higher-order shear and normal deformation theory (HSNDT), which considers the effect of thickness in its mathematical formulation. The hybrid HSNDT combines polynomial and hyperbolic functions that [...] Read more.

The current study demonstrates the buckling properties of composite laminates reinforced with MWCNT fillers using a novel higher-order shear and normal deformation theory (HSNDT), which considers the effect of thickness in its mathematical formulation. The hybrid HSNDT combines polynomial and hyperbolic functions that ensure the parabolic shear stress profile and zero shear stress boundary condition at the upper and lower surface of the plate, hence removing the need for a shear correction factor. The plate is made up of carbon fiber bounded together with polymer resin matrix reinforced with MWCNT fibers. The mechanical properties are homogenized by a Halpin–Tsai scheme. The MATLAB R2019a code was developed in-house for a finite element model using C⁰ continuity nine-node Lagrangian isoparametric shape functions. The geometric nonlinear and linear stiffness matrices are derived using the principle of virtual work. The solution of the eigenvalue problem enables estimation of the critical buckling loads. A convergence study was carried out and model efficiency was corroborated with the existing literature. The model contains only seven degrees of freedom, which significantly reduces computation time, facilitating the comprehensive parametric studies for the buckling stability of the plate. Full article

(This article belongs to the Special Issue Mechanical Behavior of Advanced Composite Materials and Structures)

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12 pages, 1920 KB

Open AccessArticle

Timelike Surface Couple with Bertrand Couple as Joint Geodesic Curves in Minkowski 3-Space

by Fatemah Mofarreh

Symmetry 2024, 16(6), 732; https://doi.org/10.3390/sym16060732 - 12 Jun 2024

Cited by 1 | Viewed by 1119

Abstract

A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned with the surface normal. Using the Serret–Frenet frame, a timelike surface couple (

TLSC)

with the symmetry of a Bertrand couple (

BC

) can [...] Read more.

A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned with the surface normal. Using the Serret–Frenet frame, a timelike surface couple (

TLSC)

with the symmetry of a Bertrand couple (

BC

) can be specified in terms of linear combinations of the components of the local frames in Minkowski 3-space

E_{1}^{3}

. With these parametric representations, the necessary and sufficient conditions for the specified

BC

are derived to be the geodesic curves defining these surfaces. Afterward, the definition of a

TL

ruled surface (

RS

) is also provided. Furthermore, the application of the method to some significant models is given. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry: Differential Geometry and Its Applications)

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11 pages, 1667 KB

Open AccessArticle

Equiareal Parameterization of Triangular Bézier Surfaces

by Jun Chen, Xiang Kong and Huixia Xu

Mathematics 2022, 10(23), 4620; https://doi.org/10.3390/math10234620 - 6 Dec 2022

Cited by 2 | Viewed by 1779

Abstract

Parameterization is the key property of a parametric surface and significantly affects many kinds of applications. To improve the quality of parameterization, equiareal parameterization minimizes the equiareal energy, which is presented as a measure to describe the uniformity of iso-parametric curves. With the [...] Read more.

Parameterization is the key property of a parametric surface and significantly affects many kinds of applications. To improve the quality of parameterization, equiareal parameterization minimizes the equiareal energy, which is presented as a measure to describe the uniformity of iso-parametric curves. With the help of the binary Möbius transformation, the equiareal parameterization is extended to the triangular Bézier surface on the triangular domain for the first time. The solution of the corresponding nonlinear minimization problem can be equivalently converted into solving a system of bivariate polynomial equations with an order of three. All the exact solutions of the equations can be obtained, and one of them is chosen as the global optimal solution of the minimization problem. Particularly, the coefficients in the system of equations can be explicitly formulated from the control points. Equiareal parameterization keeps the degree, control points, and shape of the triangular Bézier surface unchanged. It improves the distribution of iso-parametric curves only. The iso-parametric curves from the new expression are more uniform than the original one, which is displayed by numerical examples. Full article

(This article belongs to the Special Issue Computer-Aided Geometric Design)

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8 pages, 258 KB

Open AccessArticle

Spheres and Tori as Elliptic Linear Weingarten Surfaces

by Dong-Soo Kim, Young Ho Kim and Jinhua Qian

Mathematics 2022, 10(21), 4065; https://doi.org/10.3390/math10214065 - 1 Nov 2022

Cited by 2 | Viewed by 1405

Abstract

The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric. We established some local characterizations of the round spheres [...] Read more.

The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric. We established some local characterizations of the round spheres and the tori immersed in the 3-dimensional unit sphere, along with the Laplace operator, the spherical Gauss map and the Gauss map associated with the elliptic linear Weingarten metric. Full article

(This article belongs to the Special Issue Geometry of Manifolds and Applications)

20 pages, 4385 KB

Open AccessArticle

Static Analysis of Skew Functionally Graded Plate Using Novel Shear Deformation Theory

by Jitendra Singh, Ajay Kumar, Małgorzata Szafraniec, Danuta Barnat-Hunek and Barbara Sadowska-Buraczewska

Materials 2022, 15(13), 4633; https://doi.org/10.3390/ma15134633 - 1 Jul 2022

Cited by 5 | Viewed by 2495

Abstract

In this article, the static response of a functionally graded material (FGM) plate is studied via hybrid higher-order shear deformation theory which uses hyperbolic and polynomial shape functions and includes the effect of thickness stretching. The composition of the plate comprises metallic and [...] Read more.

In this article, the static response of a functionally graded material (FGM) plate is studied via hybrid higher-order shear deformation theory which uses hyperbolic and polynomial shape functions and includes the effect of thickness stretching. The composition of the plate comprises metallic and ceramic phases. The ceramic volume fraction varies gradually along with the thickness following the power law. The mechanical properties of the FGM plate are determined by the rule of mixtures and the Mori–Tanaka homogenization scheme. The displacement fields are defined to satisfy the requirement of traction-free boundary conditions at the bottom and top surfaces of the plate surface removing the need for determination of shear correction factor. A C⁰ continuity FE model is developed for the present mathematical model. Nine-node isoparametric elements with eight nodal unknowns at each node are developed. The present model comparison with existing literature is completed and found to be coherent. Inhouse MATLAB code is developed for the present work. Sinusoidal and uniformly distributed loading is analyzed in the present work. The parametric study is undertaken to explore the effect of the side-to-thickness ratio, aspect ratio, thickness, and volume fraction index on stresses and transverse displacements. Full article

(This article belongs to the Special Issue Durability and Surface Protection of Porous Materials and External Building Partitions)

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12 pages, 3080 KB

Open AccessArticle

Analysis of Thermoelastic Interaction in a Polymeric Orthotropic Medium Using the Finite Element Method

by Ibrahim Abbas, Aatef Hobiny, Hashim Alshehri, Sorin Vlase and Marin Marin

Polymers 2022, 14(10), 2112; https://doi.org/10.3390/polym14102112 - 22 May 2022

Cited by 23 | Viewed by 2138

Abstract

In this work, the finite element technique is employed to evaluate the effects of thermal relaxation durations on temperature, displacements, and stresses in a two-dimensional, polymeric, orthotropic, elastic medium. The problem is considered in a homogeneous, polymeric, orthotropic medium in the context of [...] Read more.

In this work, the finite element technique is employed to evaluate the effects of thermal relaxation durations on temperature, displacements, and stresses in a two-dimensional, polymeric, orthotropic, elastic medium. The problem is considered in a homogeneous, polymeric, orthotropic medium in the context of the Green and Lindsay model with two thermal relaxation times. The bounding surface of the half-space was subjected to a heat flux with an exponentially decaying pulse. Finite element techniques were used to solve the governing formulations, with eight-node isoparametric rectangular elements with three degrees of freedom (DOF) per node. The developed method was calculated using numerical results applied to the polymeric, orthotropic medium. The findings were implemented and visually shown. Finally, the results were displayed to demonstrate the differences between classical dynamic coupling (CT), the Lord–Shulman (LS) and the Green and Lindsay (GL) models. Full article

(This article belongs to the Special Issue Computational Modeling of Polymers)

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11 pages, 277 KB

Open AccessArticle

Characterization of Clifford Torus in Three-Spheres

by Dong-Soo Kim, Young Ho Kim and Jinhua Qian

Mathematics 2020, 8(5), 718; https://doi.org/10.3390/math8050718 - 3 May 2020

Cited by 3 | Viewed by 3544

Abstract

We characterize spheres and the tori, the product of the two plane circles immersed in the three-dimensional unit sphere, which are associated with the Laplace operator and the Gauss map defined by the elliptic linear Weingarten metric defined on closed surfaces in the [...] Read more.

We characterize spheres and the tori, the product of the two plane circles immersed in the three-dimensional unit sphere, which are associated with the Laplace operator and the Gauss map defined by the elliptic linear Weingarten metric defined on closed surfaces in the three-dimensional sphere. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

12 pages, 3102 KB

Open AccessFeature PaperArticle

Certain Algorithms for Modeling Uncertain Data Using Fuzzy Tensor Product Bézier Surfaces

by Musavarah Sarwar and Muhammad Akram

Mathematics 2018, 6(3), 42; https://doi.org/10.3390/math6030042 - 9 Mar 2018

Cited by 2 | Viewed by 5033

Abstract

Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty [...] Read more.

Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty in mathematical interpolation models. In the context of surface modeling, fuzzy tensor product Bézier surfaces are suitable for representing and simplifying both crisp and imprecise surface data with fuzzy numbers. The framework of this research paper is concerned with various properties of fuzzy tensor product surface patches by means of fuzzy numbers including fuzzy parametric curves, affine invariance, fuzzy tangents, convex hull and fuzzy iso-parametric curves. The fuzzification and defuzzification processes are applied to obtain the crisp Beziér curves and surfaces from fuzzy data points. The degree elevation and de Casteljau’s algorithms for fuzzy Bézier curves and fuzzy tensor product Bézier surfaces are studied in detail with numerical examples. Full article

(This article belongs to the Special Issue Fuzzy Mathematics)

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11 pages, 542 KB

Open AccessArticle

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members

by Ki Yong Ann and Chang-Geun Cho

Materials 2013, 6(9), 3978-3988; https://doi.org/10.3390/ma6093978 - 10 Sep 2013

Cited by 7 | Viewed by 6126

Abstract

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an [...] Read more.

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test. Full article

(This article belongs to the Special Issue Constitutive Behavior of Composite Materials)

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9 pages, 2480 KB

Open AccessArticle

Three Dimensional Stress Analysis in Adhesively Bonded Joints with Rivets

by Ali Kaya, Mehmet Tekelioğlu and Muhammet Cerit

Math. Comput. Appl. 1999, 4(3), 195-203; https://doi.org/10.3390/mca4030195 - 1 Dec 1999

Cited by 3 | Viewed by 1517

Abstract

Stress and strain distributions in the adhesively bonded joints subjected to distributed forces are investigated using finite element method. The bonded materials reinforced with rivets are the same. The investigations are conducted on a three dimensional model. The finite element model of the [...] Read more.

Stress and strain distributions in the adhesively bonded joints subjected to distributed forces are investigated using finite element method. The bonded materials reinforced with rivets are the same. The investigations are conducted on a three dimensional model. The finite element model of the joint is obtained using isoparametric three dimensional elements having eight nodes with three degrees of freedom each. The stress components and their distributions both on adhesive surface and on metallic elements are given in dimensionless from using three dimensional graphics. Full article

13 pages, 4228 KB

Open AccessArticle

Boundary Emenet Formulation in Elastoplastic Stress Anaysis

by Halit Gun and A. Adib Becker

Math. Comput. Appl. 1998, 3(3), 139-151; https://doi.org/10.3390/mca3030139 - 1 Dec 1998

Viewed by 1283

Abstract

This paper presents a review of different elasto-plastic Boundary Element (BE) formulations with particular emphasis on two main approaches; the initial strain displaccmcnt- gradient approach with its modeling of the partial or full interior domain, and the particular integral approach which can be [...] Read more.

This paper presents a review of different elasto-plastic Boundary Element (BE) formulations with particular emphasis on two main approaches; the initial strain displaccmcnt- gradient approach with its modeling of the partial or full interior domain, and the particular integral approach which can be applied exclusively to the surface avoiding any modeling interior. The initial strain formulation is implemcntcd in a computer program using two-dimensional isoparametric quatratic elements to discretise either the complete intcrior domain or only the part associated with the plastic region. The BE solutions are shown to bc in good agreement with analytical and Finite Elcment (FE) solutions. Full article

11 pages, 3479 KB

Open AccessArticle

Three Dimensional Stress Anaysis in Adhesively Bonded Joints

by Ali Kaya and Mehmet Tekelioğlu

Math. Comput. Appl. 1998, 3(2), 101-111; https://doi.org/10.3390/mca3020101 - 1 Aug 1998

Cited by 1 | Viewed by 1351

Abstract

Stress and strain distributions in the adhesive bonded joints subjected to distributed forces are investigated using finite element method. Two different cases are considered, the bonded materials are the same, and the bonded materials are different. The investigations are conducted on a three [...] Read more.

Stress and strain distributions in the adhesive bonded joints subjected to distributed forces are investigated using finite element method. Two different cases are considered, the bonded materials are the same, and the bonded materials are different. The investigations are conducted on a three dimensional model. The finite element model of the joint is obtained using isoparametric three dimensional elements having eight nodes with three degrees of freedom each. The stress components and their distributions both on adhesive surface and on metallic elements are given in dimensionless form using three dimensional graphics. Full article

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