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1 – 10 of 29Amir Najibi, Morteza Kianifar and Payman Ghazifard
The authors examined the numerical natural frequency analysis of a 2D functionally graded (FG) truncated thick hollow cone using 3D elasticity theory.
Abstract
Purpose
The authors examined the numerical natural frequency analysis of a 2D functionally graded (FG) truncated thick hollow cone using 3D elasticity theory.
Design/methodology/approach
The material properties of the 2D-FGM (two dimensional-functionally graded materials) cone are graded along the radial and axial axes of the cone using a power–law distribution. The eigenvalue problem was solved using finite element analysis (FEA) employing graded hexahedral elements, and the verification of the finite element approach was assessed by comparing the current solution to earlier experimental studies.
Findings
The effects of semivertex angle, material distribution and the cone configuration on the natural frequencies have been analyzed. For various semivertex angles, thickness, length and power law exponents, many results in the form of natural frequencies and mode shapes are presented for the 2D-FGM cone. As a result, the effects of the given parameters were addressed, and the results were compared, demonstrating the direct efficiency of raising the power–law exponents and cone thickness on the rise of natural frequencies.
Originality/value
For the first time, the numerical natural frequency analysis of a 2D-FG truncated thick hollow truncated cone based on 3D equations of elasticity has been investigated. The material properties of the truncated cone have been distributed along two directions, which has not been considered before in any research for the truncated thick cone. The reason for using these innovative volume fraction functions is the lack of accurate coverage by functions that are available in the literature (Asemi et al., 2011; Babaei et al. 2021).
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Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma and Xiaolin Chang
Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial…
Abstract
Purpose
Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems.
Design/methodology/approach
An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation.
Findings
The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method..
Originality/value
Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.
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In plane elasticity, a general expression for a mutual work difference integral (MWDI) derived from two stress fields is introduced. Once two physical stress fields are known…
Abstract
In plane elasticity, a general expression for a mutual work difference integral (MWDI) derived from two stress fields is introduced. Once two physical stress fields are known beforehand, the relevant MWDI can be evaluated exactly from the coefficients in the complex potentials. A biaxial tension model for evaluating defect energy is introduced. A particular MWDI from two fields, one is for the damaged medium under remote biaxial tension and other is for an infinite perfect plate under the same remote biaxial tension, can be defined as a suitable measure of stiffness for the damaged medium, which is called the defect energy ( E (a) ). The suggested model can deal with the cracks, holes, and elastic inclusions in a unique way. The model can also evaluate the defect energies for different damages exactly without dependence on the orientation of damages. Physically, the higher is the defect energy achieved, the more are the involved damages in the medium. The defect energy may be negative, which means a more rigid inclusion is included in the medium. For 3D‐elasticity, a triaxial tension model is introduced for evaluating the defect energy for the damaged medium. For some particular cases, for example, the dissimilar elastic spherical inclusion, or the elliptic flat crack, the relevant defect energies are evaluated.
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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics…
Abstract
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.
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Based on the recent advances of hybrid stress finite elements, a seriesof alternative stress assumptions for these elements are investigated.Several new element models are…
Abstract
Based on the recent advances of hybrid stress finite elements, a series of alternative stress assumptions for these elements are investigated. Several new element models are proposed by using different concepts for the stress interpolation. Under a unified formulation presented in this paper for Hellinger—Reissner principle based hybrid stress element models, the element series 5β‐family for plane stress and 18β‐family for three‐dimensional problems are discussed. The extra incompatible displacements sometimes also added are not introduced in this unified formulation. A number of popular benchmark elastic problems are examined for both two element families. In each family, the element model presented in this paper using normalized transformed higher order stress trials usually gives better predictions than the others.
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C. Benoit, P. Coorevits and J.‐P. Pelle
A method for controlling the quality of finite element analyses for plate structures is proposed herein. It is based on the concept of error in the constitutive relation as well…
Abstract
A method for controlling the quality of finite element analyses for plate structures is proposed herein. It is based on the concept of error in the constitutive relation as well as on associated techniques for constructing admissible displacement‐stress fields with respect to a reference model. In this study, the chosen model is either Reissner‐Mindlin’s or Kirchhoff‐Love’s model. The finite element used is the DKT element; these error estimators allow us to determine that this element converges for Kirchhoff‐Love’s model. Once these error estimators have been identified, techniques of adaptive meshing developed in 2D are applied and several examples are presented.
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Amale Mahi, El Abbas Adda Bedia, Abdelouahed Tounsi and Amina Benkhedda
A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides…
Abstract
Purpose
A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues.
Design/methodology/approach
Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions.
Findings
In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems.
Originality/value
To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.
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Jacek Ptaszny and Marcin Hatłas
The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear…
Abstract
Purpose
The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time.
Design/methodology/approach
The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered.
Findings
FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver.
Research limitations/implications
The present results are limited to linear elasticity.
Originality/value
This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.
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Mohammad Hadi Moradi and Mehdi Ranjbar-Roeintan
The purpose of this research is to extract the natural frequencies of a circular plate containing a central hole reinforced with boron nitride nanotubes (BNNTs) and containing…
Abstract
Purpose
The purpose of this research is to extract the natural frequencies of a circular plate containing a central hole reinforced with boron nitride nanotubes (BNNTs) and containing piezoelectric layers.
Design/methodology/approach
A unit cell shall be taken into account for the simulation of BNNT's volume fraction. A rectangular micromechanical model is used to obtain the mechanical properties of unit cell of piezoelectric fiber-reinforced composite (PFRC). The three-dimensional (3D) elasticity method is presented to provide the relationship between displacements and stresses. The one-dimensional differential quadrature method (1D-DQM) and the state-space methodology are combined to create the semi-analytical technique. The state-space approach is utilized to implement an analytical resolution in the thickness direction, and 1D-DQM is used to implement an approximation solution in the radial direction. The composite consists of a polyvinylidene fluoride (PVDF) matrix and BNNTs as reinforcement.
Findings
A study on the PFRC is carried, likewise, the coefficients of its properties are obtained using a micro-electromechanical model known as the rectangular model. To implement the DQM, the plate was radially divided into sample points, each with eight state variables. The boundary situation and DQM are used to discretize the state-space equations, and the top and bottom application surface conditions are used to determine the natural frequencies of the plate. The model's convergence is assessed. Additionally, the dimensionless frequency is compared to earlier works and ABAQUS simulation in order to validate the model. Finally, the effects of the thickness, lateral wavenumber, boundary conditions and BNNT volume fraction on the annular plate's free vibration are investigated. The important achievements are that increasing the volume fraction of BNNTs increases the natural frequency.
Originality/value
The micromechanical “XY rectangle” model in PFRC along with the three-dimensional elasticity model is used in this literature to assess how the piezoelectric capabilities of BNNTs affect the free vibration of polymer-based composite annular plates under various boundary conditions.
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Uroš Bohinc, Adnan Ibrahimbegovic and Boštjan Brank
The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable…
Abstract
Purpose
The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable plate model (among available hierarchical plate models) for each particular FE of the selected mesh, that is provided as the final output of the mesh adaptivity procedure.
Design/methodology/approach
The model adaptivity procedure can be seen as an appropriate extension to model adaptivity for linear elastic plates of so‐called equilibrated boundary traction approach error estimates, previously proposed for 2D/3D linear elasticity. Model error indicator is based on a posteriori element‐wise computation of improved (continuous) equilibrated boundary stress resultants, and on a set of hierarchical plate models. The paper illustrates the details of proposed model adaptivity procedure for choosing between two most frequently used plate models: the one of Kirchhoff and the other of Reissner‐Mindlin. The implementation details are provided for a particular case of the discrete Kirchhoff quadrilateral four‐node plate FE and the corresponding Reissner‐Mindlin quadrilateral with the same number of nodes. The key feature for those elements that they both provide the same quality of the discretization space (and thus the same discretization error) is the one which justifies uncoupling of the proposed model adaptivity from the mesh adaptivity.
Findings
Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology in guiding the final choice of the optimal model and mesh in analysis of complex plate structures.
Originality/value
The paper confirms that one can make an automatic selection of the most appropriate plate model for thin and thick plates on the basis of proposed model adaptivity procedure.
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