Search results for: classical plate theory.

Authors: Jixiao Tao, Xiaoqiao He

Abstract:

The present study deals with the finite element (FE) analysis of thermally-induced bistable plate using various plate elements. The quadrilateral plate elements include the 4-node conforming plate element based on the classical laminate plate theory (CLPT), the 4-node and 9-node Mindlin plate element based on the first-order shear deformation laminated plate theory (FSDT), and a displacement-based 4-node quadrilateral element (RDKQ-NL20). Using the von-Karman’s large deflection theory and the total Lagrangian (TL) approach, the nonlinear FE governing equations for plate under thermal load are derived. Convergence analysis for four elements is first conducted. These elements are then used to predict the stable shapes of thermally-induced bistable plate. Numerical test shows that the plate element based on FSDT, namely the 4-node and 9-node Mindlin, and the RDKQ-NL20 plate element can predict two stable cylindrical shapes while the 4-node conforming plate predicts a saddles shape. Comparing the simulation results with ABAQUS, the RDKQ-NL20 element shows the best accuracy among all the elements.

Keywords: Finite element method, geometrical nonlinearity, bistable, quadrilateral plate elements.

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

Abstract:

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: Biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory.

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Authors: S. Madhu, V. V. Subba Rao

Abstract:

In the implementation of Carbon Nanotube Reinforced Polymer matrix Composites in structural applications, deflection and stress analysis are important considerations. In the present study, a multi scale analysis of deflection and stress analysis of carbon nanotube (CNT) reinforced polymer composite plates is presented. A micromechanics model based on the Mori-Tanaka method is developed by introducing straight CNTs aligned in one direction. The effect of volume fraction and diameter of CNTs on plate deflection and the stresses are investigated using classical laminate plate theory (CLPT). The study is primarily conducted with the intention of observing the suitability of CNT reinforced polymer composite plates under static loading for structural applications.

Keywords: Carbon Nanotube, Micromechanics, Composite plate, Multi-scale analysis, Classical Laminate Plate Theory.

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Authors: V. Piscopo

Abstract:

In the traditional buckling analysis of rectangular plates the classical thin plate theory is generally applied, so neglecting the plating shear deformation. It seems quite clear that this method is not totally appropriate for the analysis of thick plates, so that in the following the two variable refined plate theory proposed by Shimpi (2006), that permits to take into account the transverse shear effects, is applied for the buckling analysis of simply supported isotropic rectangular plates, compressed in one and two orthogonal directions. The relevant results are compared with the classical ones and, for rectangular plates under uniaxial compression, a new direct expression, similar to the classical Bryan-s formula, is proposed for the Euler buckling stress. As the buckling analysis is a widely diffused topic for a variety of structures, such as ship ones, some applications for plates uniformly compressed in one and two orthogonal directions are presented and the relevant theoretical results are compared with those ones obtained by a FEM analysis, carried out by ANSYS, to show the feasibility of the presented method.

Keywords: Buckling analysis, Thick plates, Biaxial stresses

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Authors: Badr Alsulami, Ahmed S. Elamary

Abstract:

This paper summarizes and presents main results of an in-depth numerical analysis dealing with the shear buckling resistance of aluminum plate girders. The studies conducted have permitted the development of a simple design expression to determine the critical shear buckling stress in aluminum web panels. This expression takes into account the effects of reduction of strength in aluminum alloys due to welding process. Ultimate shear resistance (USR) of plate girders can be obtained theoretically using Cardiff theory or Hӧglund’s theory. USR of aluminum alloy plate girders predicted theoretically using BS8118 appear inconsistent when compared with test data. Theoretical predictions based on Hӧglund’s theory, are more realistic. Cardiff theory proposed to predict the USR of steel plate girders only. Welded aluminum alloy plate girders studied experimentally by others; the USR resulted from tests are reviewed. Comparison between the test results with the values obtained from Hӧglund’s theory, BS8118 design method and Cardiff theory performed theoretically. Finally, a new equation based on Cardiff tension-field theory, proposed to predict theoretically the USR of aluminum plate girders.

Keywords: Shear resistance, Aluminum, Cardiff theory, Hӧglund's theory, Plate girder.

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Authors: Khaled. M. Faqih

Abstract:

A model of vortex wake is suggested to determine the induced power during animal hovering flight. The wake is modeled by a series of equi-spaced rigid rectangular vortex plates, positioned horizontally and moving vertically downwards with identical speeds; each plate is generated during powering of the functionally wing stroke. The vortex representation of the wake considered in the current theory allows a considerable loss of momentum to occur. The current approach accords well with the nature of the wingbeat since it considers the unsteadiness in the wake as an important fluid dynamical characteristic. Induced power in hovering is calculated as the aerodynamic power required to generate the vortex wake system. Specific mean induced power to mean wing tip velocity ratio is determined by solely the normal spacing parameter (f) for a given wing stroke amplitude. The current theory gives much higher specific induced power estimate than anticipated by classical methods.

Keywords: vortex theory, hovering flight, induced power, Prandlt's tip theory.

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Authors: F.Ebrahimi, A.Rastgo

Abstract:

Analytical investigation of the free vibration behavior of circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the circular FG plate based on the classical plate theory (CPT) is presented in this paper. The material properties of the functionally graded substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and Numerical investigations are performed for FG plates with two surface-bonded piezoelectric layers. Emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from threedimensional finite element analyses.

Keywords: Circular plate, CPT, Functionally graded, Piezoelectric.

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Authors: Ahmed S. Elamary

Abstract:

Ultimate shear resistance (USR) of slender plate girders can be predicted theoretically using Cardiff theory or Höglund theory. This paper will be concerned with predicting the USR using Höglund theory and EC3. Two main factors can affect the USR, the panel width “b” and the web depth “d”, consequently, the panel aspect ratio (b/d) has to be identified by limits. In most of the previous study, there is no limit for panel aspect ratio indicated. In this paper theoretical analysis has been conducted to study the effect of (b/d) on the USR. The analysis based on ninety six test results of steel plate girders subjected to shear executed and collected by others. New formula proposed to predict the percentage of the distance between the plastic hinges form in the flanges “c” to panel width “b”. Conservative limits of (c/b) have been suggested to get a consistent value of USR.

Keywords: Ultimate shear resistance, Plate Girder, Höglund’s theory, EC3.

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Authors: Rita C. Ramos

Abstract:

Medical Surgical Nursing is one of the major subjects in nursing. This study examined the validity and reliability of the achievement examination utilizing the Classical Test Theory and Item Response Theory. The study answered the following objectives specifically : ( a) To establish the validity and reliability of the achievement examination utilizing Classical Test Theory and Item Response Theory ; ( b ) To determine the dimensionality measure of items and ( c ) to compare the item difficulty and item discrimination of the Medical Surgical Nursing Achievement examination using Classical Test Theory ( CTT ) and Item Response Theory ( IRT ). The developed instrument was administered to fourth year nursing students (N= 136) of a private university in Manila. The findings yielded the following results: The achievement examination is reliable both using CTT and IRT. The findings indicate person and item statistics from two frameworks are quite alike. The achievement examination formed a unidimensional construct.

Keywords: Achievement Examination, Item Response Theory, Medical Surgical, Nursing.

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

Abstract:

On the basis of the theory of nonlinear elasticity, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: Acoustoelasticity, dispersion, finite deformation, lamb waves.

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Authors: Yu T. Tsai, Jin H. Huang

Abstract:

In this paper, the specific sound Transmission Loss (TL) of the Laminated Composite Plate (LCP) with different material properties in each layer is investigated. The numerical method to obtain the TL of the LCP is proposed by using elastic plate theory. The transfer matrix approach is novelty presented for computational efficiency in solving the numerous layers of dynamic stiffness matrix (D-matrix) of the LCP. Besides the numerical simulations for calculating the TL of the LCP, the material properties inverse method is presented for the design of a laminated composite plate analogous to a metallic plate with a specified TL. As a result, it demonstrates that the proposed computational algorithm exhibits high efficiency with a small number of iterations for achieving the goal. This method can be effectively employed to design and develop tailor-made materials for various applications.

Keywords: Sound transmission loss, laminated composite plate, transfer matrix approach, inverse problem, elastic plate theory, material properties.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: Non-linear vibrations, Annular plates, Large amplitudes, FGM.

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Authors: Xuguang Leng

Abstract:

The theory of tectonic plate asteroid driver provides that comet and asteroid collisions have ample energy to fracture, move, and deform tectonic plate. The enormous kinetic energy of an asteroid collision is dissipated through the fracture and violent movement of the tectonic plates, and stored in the plate deformations. The stored energy will be released in the future through plate slow movement. The reflection of plate edge upwards upon collision impact causes the plate to sit on top of adjacent plate and creates the subduction plate. Higher probability and higher energy of asteroid collision in the equator area provides the net energy to drive heavier land plates to higher latitudes, offsetting the tidal and self spin forces, creating a more random land plates distribution. The trend of asteroid collisions is less frequency and intensity as loose objects are merging into the planets and Jupiter is taking ever larger shares of collisions. As overall energy input from asteroid collision decreases, plate movement is slowing down and eventually land plates will congregate towards equator area. The current trajectory of plate movements is the cumulative effect of past asteroid collisions, and can be altered, new plates be created, by future collisions.

Keywords: Tectonic plate, Earth, asteroid, comet.

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Authors: M. Rokonuzzaman, Z. Gürdal

Abstract:

This paper describes the design optimization of ferrocement-laminated plate made up of reinforcing steel wire mesh(es) and cement mortar. For the improvement of the designing process, the plate is modeled as a multi-layer medium, dividing the ferrocement plate into layers of mortar and ferrocement. The mortar layers are assumed to be isotropic in nature and the ferrocement layers are assumed to be orthotropic. The ferrocement layers are little stiffer, but much more costlier, than the mortar layers due the presence of steel wire mesh. The optimization is performed for minimum weight design of the laminate using a genetic algorithm. The optimum designs are discussed for different plate configurations and loadings, and it is compared with the worst designs obtained at the final generation. The paper provides a procedure for the designers in decision-making process.

Keywords: Buckling, Ferrocement-Laminated Plate, Genetic Algorithm, Plate Theory.

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

Abstract:

In this paper, an analytical approach for free vibration analysis of four edges simply supported rectangular Kirchhoff plates is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for plate with simply supported boundary condition are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of a simply supported rectangular Kirchhoff plate. Subsequently, the eigenvalue problem for free vibration of plates is formulated and the equation of plate natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Kirchhoff plate, propagation matrix, reflection matrix, vibration analysis.

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Authors: M. R. Haboğlu, A. Kurşun, Ş. Aksoy, H. Aykul, N. B. Bektaş

Abstract:

Athermal elastic stress analysis of steel fiber reinforced aluminum laminated composite plate is investigated. Four sides of the composite plate are clamped and subjected to a uniform temperature load. The analysis is performed both analytically and numerically. Laminated composite is manufactured via hot pressing method. The investigation of the effects of the orientation angle is provided. Different orientation angles are used such as [0°/90°]s, [30°/-30°]s, [45°/-45°]s, and [60/-60]s. The analytical solution is obtained via classical laminated composite theory and the numerical solution is obtained by applying finite element method via ANSYS.

Keywords: Laminated Composites, Thermo Elastic Stress, Finite Element Method.

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Authors: Gulshan Taj M. N. A., Anupam Chakrabarti, Vipul Prakash

Abstract:

In the present investigation, free vibration of functionally graded material (FGM) skew plates under thermal environment is studied. Kinematics equations are based on the Reddy’s higher order shear deformation theory and a nine noded isoparametric Lagrangian element is adopted to mesh the plate geometry. The issue of C₁ continuity requirement related to the assumed displacement field has been circumvented effectively to develop C₀ finite element formulation. Effective mechanical properties of the constituents of the plate are considered to be as position and temperature dependent and assumed to vary in the thickness direction according to a simple power law distribution. The displacement components of a rectangular plate are mapped into skew plate geometry by means of suitable transformation rule. One dimensional Fourier heat conduction equation is used to ascertain the temperature profile of the plate along thickness direction. Influence of different parameters such as volume fraction index, boundary condition, aspect ratio, thickness ratio and temperature field on frequency parameter of the FGM skew plate is demonstrated by performing various examples and the related findings are discussed briefly. New results are generated for vibration of the FGM skew plate under thermal environment, for the first time, which may be implemented in the future research involving similar kind of problems.

Keywords: Functionally graded material, finite element method, higher order shear deformation theory, skew plate, thermal vibration.

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Authors: Junaid Kameran Ahmed

Abstract:

A laminated plate composite of graphite/epoxy has been analyzed dynamically in the present work by using a quadratic element (8-node diso-parametric), and by depending on 1^st order shear deformation theory, every node in this element has 6-degrees of freedom (displacement in x, y, and z axis and twist about x, y, and z axis). The dynamic analysis in the present work covered parametric studies on a composite laminated plate (square plate) to determine its effect on the natural frequency of the plate. The parametric study is represented by set of changes (plate thickness, number of layers, support conditions, layer orientation), and the plates have been simulated by using ANSYS package 12. The boundary conditions considered in this study, at all four edges of the plate, are simply supported and fixed boundary condition. The results obtained from ANSYS program show that the natural frequency for both fixed and simply supported increases with increasing the number of layers, but this increase in the natural frequency for the first five modes will be neglected after 10 layers. And it is observed that the natural frequency of a composite laminated plate will change with the change of ply orientation, the natural frequency increases and it will be at maximum with angle 45 of ply for simply supported laminated plate, and maximum natural frequency will be with cross-ply (0/90) for fixed laminated composite plate. It is also observed that the natural frequency increase is approximately doubled when the thickness is doubled.

Keywords: Laminated plate, orthotropic plate, square plate, natural frequency, graphite/epoxy.

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Authors: Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami

Abstract:

In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed.

Keywords: Displacement fields, finite elements, plate bending, Kirchhoff theory, strain based approach.

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Authors: M. R. Ghasemi, A. Ehsani

Abstract:

In this paper, the optimum weight and cost of a laminated composite plate is seeked, while it undergoes the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill theory is used as the failure criterion. The theory of analysis was based on the Classical Lamination Theory (CLT). A newly type of Genetic Algorithm (GA) as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via GAs is a long process, and the major time is consumed through the analysis, Radial Basis Function Neural Networks (RBFNN) was employed in predicting the output from the analysis. Thus, the process of optimization will be carried out through a hybrid neuro-GA environment, and the procedure will be carried out until a predicted optimum solution is achieved.

Keywords: Composite Laminates, GA, Multi-objectiveOptimisation, Neural Networks, RBFNN.

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Authors: Mohammad Reza Ghasemi, Ali Ehsani

Abstract:

In this paper, the optimum weight and cost of a laminated composite plate is seeked, while it undergoes the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill theory is used as the failure criterion. The theory of analysis was based on the Classical Lamination Theory (CLT). A newly type of Genetic Algorithm (GA) as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via GAs is a long process, and the major time is consumed through the analysis, Radial Basis Function Neural Networks (RBFNN) was employed in predicting the output from the analysis. Thus, the process of optimization will be carried out through a hybrid neuro-GA environment, and the procedure will be carried out until a predicted optimum solution is achieved.

Keywords: Composite Laminates, GA, Multi-objectiveOptimization, Neural Networks, RBFNN.

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Authors: Mostafa Raki, Mahdi Hamzehei

Abstract:

Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.

Keywords: Stability of plate, thermal buckling, rectangularplate, functionally graded material, first order shear deformationtheory.

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Authors: Behzad Mohammadzadeh, Huyk Chun Noh

Abstract:

Plate is one of the popular structural elements used in a wide range of industries and structures. They may be subjected to blast loads during explosion events, missile attacks or aircraft attacks. This study is to investigate dynamic responses of the rectangular plate subjected to explosive loads. The effects of material properties and plate thickness on responses of the plate are to be investigated. The compressive pressure is applied to the surface of the plate. Different amounts of thickness in the range from 1mm to 30mm are considered for the plate to evaluate the changes in responses of the plate with respect to plate thickness. Two different properties are considered for the steel. First, the analysis is performed by considering only the elastic-plastic properties for the steel plate. Later on damping is considered to investigate its effects on the responses of the plate. To do analysis, numerical method using a finite element based package ABAQUS is applied. Finally, dynamic responses and graphs showing the relation between maximum displacement of the plate and aim parameters are provided.

Keywords: Impulsive loaded plates, dynamic analysis, abaqus, material nonlinearity.

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Authors: A.R.Nezamabadi, M.Mansouri Gavari, S.Mansouri, M.Mansouri Gavari

Abstract:

This article considers the positional buckling of composite thick plates under thermal loading . For this purpose , the complex finite strip method is used . In analysis of complex finite strip, harmonic complex function in longitudinal direction , cubic functions in transversal direction and parabola distribution of transverse shear strain in thickness of thick plate based on higherorder shear deformation theory are used . In given examples , the effect of angles of stratification , number of layers , dimensions ratio and length – to – thick ratio across critical temperature are considered.

Keywords: Thermal buckling , Thick plate , Complex finite strip , Higher – order shear deformation theory.

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: Vibrations, plate, thickness, symmetry, factorization, approximation.

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Authors: Parveen K. Saini, Mayank Kushwaha

Abstract:

The influence of material property variation on stress concentration factor (SCF) due to the presence of a circular hole in a functionally graded material (FGM) plate is studied in this paper. A numerical method based on complex variable theory of elasticity is used to investigate the problem. To achieve the material property, variation plate is decomposed into a number of rings. In this research work, Young’s modulus is assumed to be varying exponentially and it is found that stress concentration factor can be reduced by increasing Young’s modulus progressively away from the hole.

Keywords: Stress Concentration, Circular Hole, FGM Plate, Bending.

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Authors: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

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Authors: A. Khelassi, R. Bendib

Abstract:

The paper considers the effect of feed plate location on the interactions in a seven plate binary distillation column. The mathematical model of the distillation column is deduced based on the equations of mass and energy balances for each stage, detailed model for both reboiler and condenser, and heat transfer equations. The Dynamic Relative Magnitude Criterion, DRMC is used to assess the interactions in different feed plate locations for a seven plate (Benzene-Toluene) binary distillation column ( the feed plate is originally at stage 4). The results show that whenever we go far from the optimum feed plate position, the level of interaction augments.

Keywords: Distillation column, assessment of interactions, feedplate location, DRMC.

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Authors: El Kaak, Rachid, El Bikri, Khalid, Benamar, Rhali

Abstract:

This paper describes a study of geometrically nonlinear free vibration of thin circular functionally graded (CFGP) plates resting on Winkler elastic foundations. The material properties of the functionally graded composites examined here are assumed to be graded smoothly and continuously through the direction of the plate thickness according to a power law and are estimated using the rule of mixture. The theoretical model is based on the classical Plate theory and the Von-Kármán geometrical nonlinearity assumptions. An homogenization procedure (HP) is developed to reduce the problem considered here to that of isotropic homogeneous circular plates resting on Winkler foundation. Hamilton-s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear fundamental frequency has also been analysed.

Keywords: Functionally graded materials, nonlinear vibrations, Winkler foundation.

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Authors: Eda Gök

Abstract:

Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: Flexural loading, non-local continuum mechanics, Peridynamic theory, solid structures, tensile loading.

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