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  • 1.
    Atashipour, Seyed Abdolrahim
    et al.
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Sburlati, R.
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Elastic analysis of thick-walled pressurized spherical vessels coated with functionally graded materials2014In: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648, Vol. 49, no 12, p. 2965-2978Article in journal (Refereed)
    Abstract [en]

    In recent years, functionally graded material (FGM) has been widely explored in coating technology amongst both academic and industry communities. FGM coatings are suitable substitutes for many typical conventional coatings which are susceptible to cracking, debonding and eventual functional failure due to the mismatch of material properties at the coating/substrate interface. In this study, a thick spherical pressure vessel with an inner FGM coating subjected to internal and external hydrostatic pressure is analyzed within the context of three-dimensional elasticity theory. Young’s modulus of the coating is assumed to vary linearly or exponentially through the thickness, while Poisson’s ratio is considered as constant. A comparative numerical study of FGM versus homogeneous coating is conducted for the case of vessel under internal pressure, and the dependence of stress and displacement fields on the type of coating is examined and discussed.

  • 2.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Structural Analysis of Deep Composite Box-Type Components with application to a proprietary stabilising timber wall element2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The stabilising wall element of the Trä8-system is a deep box-type beam/column element which is made of different types of timber composites including framing members of gluedlaminated timber (glulam) and sheathings of laminated veneer lumber (LVL). This element is used as a ―shear wall‖ in multi-storey buildings up to four storeys. To be able to optimise thecomposite stabilising element and use its maximum potential and efficiency, it is necessary to have sufficient fundamental knowledge and information about the structural behaviour and influences of different mechanical properties and geometrical parameters and dimensions of the sub-elements.In this thesis, structural analysis and design principles of the Trä8 stabilising wall element are discussed, including the early stage of erection during assembly to the final usage and residence. A list of required fundamental basic analyses are presented, including accurate deflection analysis for the serviceability limit state, local pre- and post-buckling of the LVL sheathings, global buckling as well as the lateral-torsional buckling of the stabilising element in different design situations. This thesis is then focused on deformations and local instability. For each type of structural problem, accurate, but simple and general methodology is employed to incorporate a large number of effective geometric and property parameters. In this way, a fast evaluation of the influence of different parameters is possible for a wide range of values without needing several time-consuming 3-D finite element (FE) simulations. In several cases, the accuracy and validity of the obtained solutions and formulae are examined and confirmed by comparing their results to those based on the 3-D FE simulations. First, different composite beam theories including shear effects are employed for deflection analysis of the stabilising timber element. Next, an accurate energy-based methodology isdeveloped rendering an explicit formula that gives accurate predictions for the deflection of the stabilising element within a medium range of sheathing or web thicknesses and/or stiffnesses. For weak shear webs, however, this model is not sufficient. Therefore, another new model based on the partial composite interaction theory is developed for accurate deflection predictions of the element having weak shear webs. This model contains simple but accurate formulae for deflection analysis of any similar composite box-type of element with an arbitrary range of geometry and property parameters.Next, shear buckling of the rectangular LVL-panel between the framing members are analysed using differential quadrature (DQ) numerical technique as well as an explicit analytical solution and a formula is established for accurate and fast prediction of the shear pre-buckling of the LVL. This study is extended by considering the effect of each individual lamina of the LVL as well as general orthotropic material properties using a laminated theoryand the DQ solution approach. Further, the post-buckling of the LVL panel is studied based on a simple analytical method with rotating stress fields together with the accurate 3-D FE simulations. A simple formula is then proposed for accurate prediction of the shear post-buckling resistance of the LVL-panel in the stabilising element. As a result of the thesis concerning the two main focus areas, deformations and local instability, explicit analytical formulae are presented for the design of the box-type stabilisingelement with respect to deflections including shear effects in the serviceability limit state and with respect to local shear buckling of the sheathings of the stabilising element including the post-critical area in the ultimate limit state.

  • 3.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering. Department of Civil and Environmental Engineering, Division of Structural Engineering, Chalmers University of Technology.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Influence of Grain Inclination Angle on Shear Buckling of Laminated Timber Sheathing Products2018In: Structures, ISSN 2352-0124, Vol. 13, p. 36-46Article in journal (Refereed)
    Abstract [en]

    Recent advances in timber production industries have enabled production of new innovative laminated timber products having layers with grain inclination angle. This paper is aimed to study influence of grain inclination angle in the laminated veneer lumber (LVL) and plywood sheathings on their shear buckling loads. Two extreme edge conditions of simply supported and clamped edges are considered. First, an accurate differential quadrature (DQ) computational code is developed using MAPLE programming software to obtain eigen buckling values and their corresponding eigen mode shapes. Next, for convenience of engineering calculations, approximate algebraic formulae are presented to predict critical shear buckling loads and mode shapes of LVL and plywood panels having layers with grain inclination angle, with adequate accuracy. Furthermore, finite element (FE) modelling is conducted for several cases using ANSYS software to show validity and accuracy of the predicted results for the problem. It is shown that the highest shear buckling loads of LVL sheathings is achievable when the inclination angle of about 30° with respect to the shorter edges is considered for production of LVL panels, whereas the same angle with respect to the long edges of the LVL sheathings results in a relatively lower buckling load. Considering similar inclination angle with respect to any edges of a plywood sheathings will also results in its highest pre-buckling capacity. It is also demonstrated that, under optimal design and certain loading circumstances, LVL shows a higher shear buckling capacity compared to a similar plywood sheathing.

  • 4.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    On the Shear Buckling of Clamped Narrow Rectangular Orthotropic Plates2015In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2015, article id 569356Article in journal (Refereed)
    Abstract [en]

    This paper deals with stability analysis of clamped rectangular orthotropic thin plates subjected to uniformly distributed shear load around the edges. Due to the nature of this problem, it is impossible to present mathematically exact analytical solution for the governing differential equations. Consequently, all existing studies in the literature have been performed by means of different numerical approaches. Here, a closed-form approach is presented for simple and fast prediction of the critical buckling load of clamped narrow rectangular orthotropic thin plates. Next, a practical modification factor is proposed to extend the validity of the obtained results for a wide range of plate aspect ratios. To demonstrate the efficiency and reliability of the proposed closed-form formulas, an accurate computational code is developed based on the classical plate theory (CPT) by means of differential quadrature method (DQM) for comparison purposes. Moreover, several finite element (FE) simulations are performed via ANSYS software. It is shown that simplicity, high accuracy, and rapid prediction of the critical load for different values of the plate aspect ratio and for a wide range of effective geometric and mechanical parameters are the main advantages of the proposed closed-form formulas over other existing studies in the literature for the same problem.

  • 5.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Al-Emrani, Mohammad
    Chalmers tekniska högskola .
    Exact Lévy-type solutions for bending of thick laminated orthotropic plates based on 3-D elasticity and shear deformation theories2017In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 163, p. 129-151Article in journal (Refereed)
    Abstract [en]

    Exact solutions for static bending of symmetric laminated orthotropic plates with different Lévy-type boundary conditions are developed. The shear deformation plate theories of Mindlin-Reissner and Reddy as well as the three-dimensional elasticity theory are employed. Using the minimum total potential energy principle, governing equilibrium equations of laminated orthotropic plates and pertaining boundary conditions are derived. Closed-form Lévy-type solutions are obtained for the governing equations of both theories using separation of variables method and different types of classical boundary conditions, namely simply-supported, clamped and free edge, are exactly satisfied. Thereafter, 3-D elasto-static equations for orthotropic materials are solved for bending analysis of laminated plates using two different approaches. First, the method of separation of variables is utilized and an exact closed-from solution is achieved for simply-supported laminated orthotropic plates. Next, a combined Fourier-Differential Quadrature (DQ) approach is employed to present a semi-numerical solution for bending of laminated orthotropic plates with Lévy-type boundary conditions based on the three-dimensional elasticity theory. High accuracy of the presented solutions are proven and comprehensive comparative numerical results are provided and discussed. Presented comparative numerical results can serve as benchmark for investigating the correctness of new solution methods which may be established in the future.

  • 6.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering. Department of Architecture and Civil Engineering, Division of Structural Engineering, Chalmers University of Technology.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Challamel, Noël
    Université de Bretagne Sud, UBS – Institut Dupuy de Lôme, Centre de Recherche.
    A weak shear web model for deflection analysis of deep composite box-type beams2018In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 155, p. 36-49Article in journal (Refereed)
    Abstract [en]

    Deep box-type beams, consisting of framing members and sheathings, are sensitive to shear deformations and hence appropriate refined theories or complicated magnification factors are needed to be used to obtain accurate results. For sheathings or webs between the framing members that are weak in shear, additional shear deformations occur corresponding to the relative axial displacement between the framing members. These sandwich-type or partial interaction-type of in-plane shear behaviour between the framing members, needs to be taken into account, especially when the web shear stiffness is very low. The composite box-type beam treated here is composed of three framing members with sheathings on both sides. To incorporate effects of the sheathings shear deformations between the framing members on the deflection, the sheathings, here called web interlayers, are modelled as shear media with equivalent slip moduli corresponding to a partially interacting composite beam model. Governing equilibrium equations of the model are obtained using the minimum total potential energy principle and solved explicitly. The obtained results are compared with those based on different conventional beam theories and 3-D finite element (FE) simulations. It is shown that the model is capable of predicting accurately the deflection for a wide range of geometry and property parameters. It is demonstrated that the deflection of such deep box-type beams can be expressed as the summation of three different effects, namely bending deformations, conventional shear deformations in the framing members and sheathings, and additional in-plane shear deformations or shear slips of the weak web causing relative axial displacements between the framing members.

  • 7.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Challamel, Noël
    Université de Bretagne Sud, UBS – Institut Dupuy de Lôme, Centre de Recherche.
    Stability analysis of three-layer shear deformable partial composite columns2017In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 106-107, p. 213-228Article in journal (Refereed)
    Abstract [en]

    This paper is focused on the effect of imperfect bonding and partial composite interaction between the sub-elements of a box-type column on the critical buckling loads. The box column is modelled as a symmetric three-layer composite structure with interlayer slips at the interfaces, based on the Engesser-Timoshenko theory with uniform shear deformation assumptions. Linear shear springs or slip modulus is considered at the interfaces to model the partial interaction between the sub-elements of the structure. The minimum total potential energy principle is utilized to obtain governing equations and boundary conditions. A direct analytical solution of the original governing equations is presented for obtaining exact buckling characteristic equation of the three-layer partial composite column with different end conditions including clamped-pinned end conditions. Also, the coupled equations are recast into an efficient uncoupled form and shown that there is a strong similarity with those for the two layer element. It is shown that the obtained formulae are converted to the known Euler column formulae when the slip modulus approaches infinity (i.e. perfect bonding) and no shear deformations in the sub-elements are considered. A differential shear Engesser-Timoshenko partial composite model is also employed and critical buckling loads, obtained from an inverse solution method, are compared to examine the validity and accuracy level of the uniform shear model. Comprehensive dimensionless numerical results are presented and discussed

  • 8.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Challamel, Noël
    University of Europeenne Bretagne, Laboratory Genie Civil & Genie Mecan, Université Européenne de Bretagne, Mechanics Division, Department of Mathematics, University of Oslo, LIMATB, Université Européenne de Bretagne, University of South Brittany, Lorient.
    The effect of weak shear webs on the deformations of timber box type beams2015In: Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing / [ed] J. Kruis; Y. Tsompanakis; B.H.V. Topping, Stirlingshire: Civil-Comp Press , 2015, article id 259Conference paper (Refereed)
    Abstract [en]

    This paper deals with deflection analysis of a deep composite box beam due to inplane shear deformations, especially the modelling of the shear deformations in the webs is considered. The beam is composed of three framing members with sheathings on both sides. The sheathings or webs between the framing members are modelled as shear media with equivalent slip moduli corresponding to the partially composite beam model with three separated layers and two interlayer slip areas. The minimum total potential energy principle is employed to obtain the governing equilibrium equations and corresponding boundary conditions. The coupled set of governing equations is recast into an uncoupled form and solved explicitly together with the corresponding boundary conditions. The closed-form solutions obtained are compared to those based on the conventional beam theories. It is shown that the model is capable of predicting accurately the deflections for a wide range of geometry and property parameters, especially for small shear stiffness (slip modulus) values for the webs. The formula for the deflection is reduced to the Timoshenko formula for full composite interaction when the shear slip modulus of the web approaches infinity. Comparative numerical results are presented to show the influence of bending deformations, shear deformations in the framing layers and the in-plane shear deformations in the sheathings

  • 9. Atashipour, Seyed Rasoul
    et al.
    Saidi, A.R.
    Jomehzadeh, E.
    On the boundary layer phenomenon in bending of thick annular sector plates using third-order shear deformation theory2010In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 211, no 1-2, p. 89-99Article in journal (Refereed)
    Abstract [en]

    In this article, the bending equations of thick annular sector plates are extracted based on the third-order shear deformation theory. Using a function, called boundary layer function, the coupled system of equations is converted into two decoupled equations. These equations are used to find a closed form solution for bending of thick transversely isotropic annular sector plates. It is shown that the solution of one of the decoupled equations has a boundary layer behavior like that of Mindlin plate theory. It is seen that the value of the boundary layer function for third order shear deformation theory is higher than that of the Mindlin theory. Thus, variations of stress components in the edge zone of the plate are more significant. Also, as in the Mindlin plate theory, there exist no boundary layer, a weak boundary layer, and a strong boundary layer effect for simply supported, clamped, and free edges, respectively.

  • 10.
    Girhammar, Ulf Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    A study on shear deformations of deep composite box-Type beams used in timber building structures2013In: Proceedings of the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, 3-6 September 2013, Cagliari, Sardinia, Italy / [ed] Barry H.V. Topping; Peter Ivaniy, Stirlingshire: Civil-Comp Press , 2013Conference paper (Refereed)
    Abstract [en]

    The higher-order shear deformation beam theory of Reddy-Bickford predicts accurately the shear deflection without the need of a shear correction factor. However, for more complicated cross-sections, e.g. including holes, it is shown that this theory is not adequate. To be able to predict accurately the shear deflections of deep composite box-type cross-sectional beams, a simple engineering approach is used to derive a closed-form expression for the shear correction factor for those types of beams. The high accuracy and reliability of the developed procedure is demonstrated by comparing those results with accurate three-dimensional finite element results and with Timoshenko and Reddy-Bickford theories. A comprehensive parametric study is presented to investigate the effects of various mechanical properties and geometric dimensions of the box-type of beams for the various models. There is very good agreement between the proposed engineering method and the three-dimensional finite element model

  • 11.
    Girhammar, Ulf Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Analysis of shear deflections of deep composite box-type of beams using different shear deformation models2015In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 155, p. 42-53Article in journal (Refereed)
    Abstract [en]

    The deflection of deep box-type elements due to shear deformations is treated. A closed-form expression for the shear correction factor is derived by using an energy approach. The high accuracy and reliability of the developed procedure is demonstrated by comparing its results with accurate 3-D finite element results and also with the results of the conventional theories of Timoshenko with constant shear coefficient and of Reddy–Bickford applied to this kind of cross-section. A comprehensive and comparative parametric study is presented to investigate the effects of various mechanical properties and geometric dimensions for the different models. Unlike the higher-order shear deformation theories, which are accurate only for beams with rectangular cross-sections, there is a very good agreement between the results of the proposed method and the 3-D FE model. Clearly, the proposed energy method is applicable to more complicated cross-sections, including those with abrupt changes in the geometry, e.g. due to holes.

  • 12. Hosseini-Hashemi, Sh.
    et al.
    Atashipour, Seyed Rasoul
    Fadaee, M.
    An exact analytical approach for in-plane and out-of-plane free vibration analysis of thick laminated transversely isotropic plates2012In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 82, no 5, p. 677-698Article in journal (Refereed)
    Abstract [en]

    In this article, the governing equations of motion of thick laminated transversely isotropic plates are derived based on Reddy’s third-order shear deformation theory. These equations are exactly converted to four uncoupled equations to study the in-plane and out-of-plane free vibrations of thick laminated plates without any usage of approximate methods. Based on the present analytical approach, exact Levy-type solutions are obtained for thick laminated transversely isotropic plates and, for some boundary conditions, the exact characteristic equations hitherto not reported in the literature are given. Also, the in-plane and out-of-plane deformed mode shapes are plotted for different boundary conditions. The present solutions can accurately predict both the in-plane and out-of-plane natural frequencies and mode shapes of thick laminated transversely isotropic plates.

  • 13. Hosseini-Hashemi, Sh.
    et al.
    Atashipour, Seyed Rasoul
    Fadaee, M.
    On the buckling analysis of isotropic, transversely isotropic and laminated rectangular plates via Reddy plate theory: an exact closed-form procedure2012In: Proceedings of the Institution of mechanical engineers. Part C, journal of mechanical engineering science, ISSN 0954-4062, E-ISSN 2041-2983, Vol. 226, no 5, p. 1210-1224Article in journal (Refereed)
    Abstract [en]

    Based on Reddy's third-order shear deformation theory, an exact closed-form solution is proposed to describe linear buckling of transversely isotropic laminated rectangular plates under either mono- or bi-axial compressive in-plane loads. To this end, the coupled governing equations are exactly converted to two sets of uncoupled equations for in-plane and transverse deformations of symmetric laminated plates. The new uncoupled equations are analytically solved by applying both Navier and Lévy-type solution methods. The validity and high accuracy of the current exact solution are evaluated by comparing the present results with their counterparts reported in literature.

  • 14.
    Hosseini-Hashemi, Sh.
    et al.
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Fadaee, M.
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory2012In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 82, no 7, p. 985-1002Article in journal (Refereed)
    Abstract [en]

    This paper deals with closed-form solutions for in-plane and out-of-plane free vibration of moderately thick laminated transversely isotropic spherical shell panels on the basis of Sanders theory without any usage of approximate methods. The governing equations of motion and the boundary conditions are derived using Hamilton's principle. The highly coupled governing equations are recast to some uncoupled equations by introducing four potential functions. Also, some relations were presented for the unknowns of the original set of equations in terms of the unknowns of the uncoupled equations. According to the proposed analytical approach, both Navier and Lévy-type explicit solutions are developed for moderately thick laminated spherical shell panels. The efficiency and high accuracy of the present approach are investigated by comparing some of the present study with the available results in the literature and the results of 3D finite element method. The effects of various shell parameters like shear modulus ratio of transversely isotropic materials and curvature ratio on the natural frequencies are studied. Clearly, the proposed solutions can accurately predict the in-plane and out-of-plane natural frequencies of moderately thick transversely isotropic spherical shell panels

  • 15. Hosseini-Hashemi, Sh.
    et al.
    Atashipour, Seyed Rasoul
    Karimi, M.
    Es'haghi, M.
    Free vibration analysis of functionally graded elliptical plates2012In: International journal of Maritime Technology, ISSN 2345-6000, Vol. 8, no 15, p. 43-60Article in journal (Refereed)
    Abstract [en]

    This paper deals with a free vibration analysis of functionally graded elliptical plates with different classical boundary conditions on the basis of polynomial-Ritz method and classical plate theory. The proposed admissible function is capable to obtain accurate natural frequencies of various classical boundary conditions namely, clamped, free and simply supported edges. The mechanical properties of the FG plate are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. The convergency of applied polynomial-Ritz method is investigated. In order to verify the accuracy of the present solution, a comprehensive comparison study is performed with the available results in the literature for homogeneous elliptical plate and FG circular plate. Also, the numerical results of the present solution for FG elliptical plate are compared with those of the finite element method (FEM). Finally, the effects of the plate geometry and inhomogeneity on the natural frequencies are investigated and some vibrational mode shapes related to symmetric-symmetric, symmetric-antisymmetric, antisymmetric- symmetric and antisymmetric- antisymmetric states are presented.

  • 16. Hosseini-Hashemi, Sh.
    et al.
    Fadaee, M.
    Atashipour, Seyed Rasoul
    A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates2011In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 53, no 1, p. 11-22Article in journal (Refereed)
    Abstract [en]

    An exact closed-form procedure is presented for freevibration analysis of moderately thick rectangularplates having two opposite edges simply supported (i.e. Lévy-type rectangularplates) based on the Reissner–Mindlinplate theory. The material properties change continuously through the thickness of the plate, which can vary according to a power law distribution of the volume fraction of the constituents. By introducing some new potential and auxiliary functions, the displacement fields are analytically obtained for this plate configuration. Several comparison studies with analytical and numerical techniques reported in literature are carried out to establish the high accuracy and reliability of the solutions. Comprehensive benchmark results for natural frequencies of the functionallygraded (FG) rectangularplates with six different combinations of boundary conditions (i.e. SSSS–SSSC–SCSC–SCSF–SSSF–SFSF) are tabulated in dimensionless form for various values of aspect ratios, thickness to length ratios and the power law index. Due to the inherent features of the present exact closed-form solution, the present results will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.

  • 17. Hosseini-Hashemi, Sh.
    et al.
    Fadaee, M.
    Atashipour, Seyed Rasoul
    Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure2011In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 93, no 2, p. 722-735Article in journal (Refereed)
    Abstract [en]

    In this article, a new exact closed-form procedure is presented to solve freevibration analysis of functionallygradedrectangularthickplates based on the Reddy’s third-order shear deformation plate theory while the plate has two opposite edges simply supported (i.e., Lévy-type rectangularplates). The elasticity modulus and mass density of the plate are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents whereas Poisson’s ratio is constant. Based on the present solution, five governing complicated partial differential equations of motion were exactly solved by introducing the auxiliary and potential functions and using the method of separation of variables. The validity and high accuracy of the present solutions are investigated by comparing some of the present results with their counterparts reported in literature and the 3-D finite element analysis. It is obvious that the present exact solution can accurately predict not only the out of plane, but also the in-plane modes of FG plate. Furthermore, a new eigenfrequency parameter is defined having its special own characteristics. Finally, the effects of boundary conditions, thickness to length ratio, aspect ratio and the power law index on the frequency parameter of the plate are presented

  • 18.
    Hosseini-Hashemi, Sh.
    et al.
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak.
    Rezaee, V.
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Accurate free vibration analysis of thick laminated circular plates with attached rigid core2012In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 331, no 25, p. 5581-5596Article in journal (Refereed)
    Abstract [en]

    This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.

  • 19. Hosseini-Hashemi, Sh.
    et al.
    Salehipour, H.
    Atashipour, Seyed Rasoul
    Exact three-dimensional free vibration analysis of thick homogeneous plates coated by functionally graded layer2012In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 223, no 10, p. 2153-2166Article in journal (Refereed)
    Abstract [en]

    Exact closed-form solutions are carried out for both in-plane and out-of-plane free vibration of thick homogeneous simply supported rectangular plates coated by a functionally graded (FG) layer, based on three-dimensional elasticity theory. The elasticity modulus and mass density of the FG coating are assumed to vary exponentially through the thickness of the coating layer, whereas Poisson’s ratio is remaining constant. The equations of motion are solved using two proposed displacement fields for the in-plane and out-of-plane vibration modes. By inserting the displacement fields in the 3-D elasto-dynamic equations, some independent ordinary equations are obtained and solved analytically. Natural frequencies are extracted by satisfying boundary conditions of interface and surfaces of the structure. The solution procedure is validated by comparing the obtained results with corresponding results of a 3-D finite element analysis. Finally, the influence of the FG coating layer on the natural frequencies of the structure is investigated and discussed. Clearly, the present closed-form solutions can exactly predict both in-plane and out-of-plane vibration modes of thick FG coated plates.

  • 20.
    Hosseini-Hashemi, Sh.
    et al.
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Islamic Azad University, Tehran South Campus, Islamic Azad University, Hamedan University of Technology, School of Mechanical Engineering, Iran University of Science and Technology, Tehran.
    Salehipour, H.
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak.
    Atashipour, Seyed Rasoul
    School of Mechanical Engineering, Iran University of Science and Technology, Narmak.
    Sburlati, Roberta
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: Explicit 3-D elasticity solutions2013In: Composites Part B: Engineering, ISSN 1359-8368, E-ISSN 1879-1069, Vol. 46, p. 108-115Article in journal (Refereed)
    Abstract [en]

    In this paper exact closed-form solutions of 3-D elasticity theory are presented to study both in-plane and out-of-plane free vibrations for thick functionally graded simply supported rectangular plates. The solution procedure of the transverse vibration utilizes Levinson’s representation form to describe the displacement; in this way, the 3-D elasto-dynamic equations are written in terms of some suitable independent functions satisfying ordinary differential equations. A similar procedure is presented for in-plane vibration by introducing an appropriate displacement field. In each case, the obtained ordinary differential equations are analytically solved and boundary conditions are satisfied. The proposed solutions are validated by comparing some of the present results with corresponding results known in the literature as well as with 3-D Finite Element Method. Finally, the influence of inhomogeneity on the natural frequencies for a thick functionally graded rectangular plate is discussed.

  • 21. Jomehzadeh, E.
    et al.
    Saidi, A.R.
    Atashipour, Seyed Rasoul
    An analytical approach for stress analysis of functionally graded annular sector plates2009In: Materials & design, ISSN 0264-1275, E-ISSN 1873-4197, Vol. 30, no 9, p. 3679-3685Article in journal (Refereed)
    Abstract [en]

    In this paper, an exact analytical approach is used for bending analysis of functionally graded (FG) annular sector plates. The governing equilibrium equations are obtained based on the first order shear deformation plate theory. Introducing an analytical method, the coupled governing equilibrium equations are replaced by independent equations in term of transverse deflection and a new function. Using an equivalent flexural rigidity, the solutions of FG annular sector plates can be easily extracted from equation of homogeneous annular plates. Also, it is shown that the present method can provide accurate results. Finally, the effects of power of functionally graded material (FGM), plate thickness, inner to outer radius ratio and boundary conditions on the deflection and stresses of a functionally graded annular sector plate are studied.

  • 22. Nasr, A.
    et al.
    Atashipour, Seyed Rasoul
    Fadaee, M.
    An elasticity solution for static analysis of functionally graded curved beam subjected to a shear force2010In: International Journal of Engineering. Transactions B: Applications, ISSN 1728-144X, Vol. 23, p. 169-178Article in journal (Refereed)
    Abstract [en]

    In this paper, using 2-D theory of elasticity, a closed-form solution is presented for stress distributions and displacements of a FG curved beam under shear force at its free end. The material properties are assumed to vary continuously through the radial direction based on a simple power law model and Poisson’s ratio is supposed to be constant. In order to verify the solution, it is shown that allstress and displacement relations are converted to those of a homogenous curved beam when the inhomogeneity constant approaches zero. The effects of inhomogeneity on stress distributions are investigated. It is shown that specified stress distribution profiles can be obtained by changing the variation of volume fraction of constituents. It is observed that for a specific value of inhomogeneity constant, a proper stress distribution along the radial direction is obtained for designing purposes.

  • 23. Saidi, A.
    et al.
    Atashipour, Seyed Rasoul
    Analytical solution of free vibration of thick transversely isotropic rectangular plates, based on first order shear deformation theory2009In: Aerospace Mechanics Journal, Vol. 4, p. 59-69Article in journal (Refereed)
    Abstract [en]

    In this paper, a reformulation for equations of motion for transversely isotropic plates has been obtained based on first shear deformation theory. Unlike the three coupled original equations, this new reformulation consists of two decoupled partial differential equations which can be solved much easier. For free vibration analysis of transversely isotropic plates, the mentioned equations have been solved for two cases. In the first case, using double Fourier series, closed-form solution has been achieved for natural frequencies of simply supported plates. In the second case, free vibration of a plate with arbitrary boundary conditions in two parallel edges has been considered. In order to satisfy the arbitray boundary conditions, some relations have been presented for unknown functions of the original system of equations in terms of the unknowns of the decoupled equations. Finally, numerical results for six possible cases of classical boundary conditions have been presented. Besides, some important results of the presented analysis have been presented for transversely isotropic plates. The results show that despite of the small differences between the natural frequencies of the thin isotropic and transversely isotropic plates, the differences are more significant for the natural frequencies of the thick plate. Also, effects of increasing thickness on the value of natural frequencies for transversely isotropic plates are more than the isotropic ones.

  • 24. Saidi, A.R.
    et al.
    Atashipour, Seyed Rasoul
    Vibration of functionally graded rectangular plates2005Conference paper (Refereed)
  • 25. Saidi, A.R.
    et al.
    Atashipour, Seyed Rasoul
    Jomehzadeh, E.
    Exact elasticity solutions for thick-walled functionally graded spherical pressure vessels2009In: International Journal of Engineering, ISSN 1025-2495, E-ISSN 1735-9244, Vol. 22, no 4, p. 405-416Article in journal (Refereed)
    Abstract [en]

    In this paper, exact closed-form solutions for displacement and stress components of thick-walled functionally graded (FG) spherical pressure vessels are presented. To this aim, linear variation of properties, as an important case of the known power-law function model is used to describe the FG material distribution in thickness direction. Unlike the pervious studies, the vessels can have arbitrary inner to outer stiffness ratio without changing the function variation of FGM. After that, a closed-form solution is presented for displacement and stress components based on exponential model for variation of properties in radial direction. The accuracy of the present analyses is verified with known results. Finally, the effects of non-homogeneity and different values of inner to outer stiffness ratios on the displacement and stress distribution are discussed in detail. It can be seen that for FG vessels subjected to internal pressure, the variation of radial stress in radial direction becomes linear as the inner stiffness becomes five times higher than outer one. When the inner stiffness is half of the outer one, the distribution of the circumferential stress becomes uniform. For the case in which the external pressure is applied, as the inner to outer shear modulus becomes lower than 1/5, the value of the maximum radial stress is higher than external pressure.

  • 26. Saidi, A.R.
    et al.
    Atashipour, Seyed Rasoul
    Jomehzadeh, E.
    Reformulation of Navier equations for solving three dimensional elasticity problems with applications to thick plate analysis2009In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 208, no 3-4, p. 227-235Article in journal (Refereed)
    Abstract [en]

    In this paper, a new reformulation of the Navier equations of motion is introduced for solving the known three-dimensional elastostatics and elastodynamics problems. At first, three decoupled equations in terms of displacement components and three decoupled equations in terms of rotation components are obtained. These equations are also invariant with respect to the choice of the coordinate system. In order to solve a three-dimensional elasticity problem based on the presented formulation, one of the three equations in terms of displacement components and the corresponding rotation equation should be solved independently. Using some relations, the other two displacement components can be obtained in terms of the mentioned displacement and rotation component. In order to verify the relations, the closed-form solutions are obtained for deflection and natural frequencies of the thick rectangular plate. The numerical results are compared with available results in the literature and it can be seen that the results of the present study are identical to those of the previous works.

  • 27. Saidi, A.R.
    et al.
    Atashipour, Seyed Rasoul
    Keshavarzi, H.
    Bending analysis of thick laminated rectangular plates using a boundary layer function2010In: Proceedings of the Institution of mechanical engineers. Part C, journal of mechanical engineering science, ISSN 0954-4062, E-ISSN 2041-2983, Vol. 224, no 10, p. 2073-2081Article in journal (Refereed)
    Abstract [en]

    In this article, the governing bending equations of thick laminated transversely isotropic rectangular plates are derived based on third-order shear deformation theory (TSDT). Using a new function, called the boundary layer function, the three coupled governing equations are converted to two decoupled equations. These equations are in terms of the deflection of the plate and the mentioned boundary layer function, which are written in invariant form. By solving the decoupled equations, a Levy-type analytical solution is presented for bending of a transversely isotropic plate. Finally, numerical results are presented for boundary layer phenomenon and its effects in TSDT. It is shown that all of the boundary layer effects in Mindlin—Reissner theory appear in this theory. However, it is shown that the intensity of the boundary layer effects in TSDT exceeds that of the Mindlin—Reissner theory.

  • 28. Saidi, A.R.
    et al.
    Bodaghi, M.
    Atashipour, Seyed Rasoul
    Levy-type solution for bending-stretching of thick functionally graded rectangular plates based on third-order shear deformation theory2012In: Mechanics of Advanced Materials and Structures, ISSN 1537-6494, E-ISSN 1537-6532, Vol. 19, no 8, p. 577-589Article in journal (Refereed)
    Abstract [en]

    In this article, an analytical approach for bending-stretching analysis of thick functionally graded rectangular plates is presented. The governing equilibrium equations are obtained based on the third-order shear deformation plate theory. Introducing four new analytical functions and doing some algebraic operations, five highly coupled governing equilibrium equations are converted into two independent partial differential equations in terms of transverse displacement and a new function, called boundary layer function. Reformulated equations are solved analytically for the functionally graded rectangular plates with two opposite edges simply supported. Some important numerical results for stress components, deflection, and the boundary layer function are presented.

  • 29. Saidi, A.R.
    et al.
    Jomehzadeh, E.
    Atashipour, Seyed Rasoul
    Exact analytical solution for bending analysis of functionally graded annular sector plates2009In: International Journal of Engineering, ISSN 1025-2495, E-ISSN 1735-9244, Vol. 22, no 3, p. 307-316Article in journal (Refereed)
    Abstract [en]

    In this article, an exact levy solution is presented for bending analysis of a functionally graded (FG) annular sector plate. The governing equilibrium equations are obtained based on the classical plate theory. Introducing an analytical method for the first time, the three coupled governing equilibrium equations are replaced by an independent equation in term of transverse deflection. This equation which is a forth-order partial differential equation is similar to the governing equilibrium equation of a homogeneous isotropic annular sector plate. Using an equivalent flexural rigidity, the solutions of FG annular sector plates can be easily extracted from equation of homogeneous annular plates. Finally, the effects of the exponents of the power functions, aspect ratio, inner to outer radius ratio and boundary conditions on the mechanical behavior of a functionally graded annular sector plate are discussed.

  • 30.
    Sburlati, R.
    et al.
    Department of Civil, Chemical and Environmental Engineering, University of Genoa, Italy.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Elastic analysis of circular sandwich plates with FGM face-sheets2013In: Proceedings of the 19th International Conference on Composite Materials: ICCM 2013, Montreal (Canada), ICCM , 2013, p. 9001-9009Conference paper (Refereed)
  • 31.
    Sburlati, Roberta
    et al.
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Atashipour, Seyed Abdolrahim
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Exact elastic analysis of a doubly coated thick circular plate using functionally graded interlayers2015In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 85, no 12, p. 1779-1792Article in journal (Refereed)
    Abstract [en]

    Development of new coating systems has been an important issue over the years with the motivation of extending the effective life of mechanical elements. For this intent, functionally graded materials have been recently used in a variety of applications as promising replacements for conventional coatings. In the present study, a hybrid coating system taking advantage of graded composition concept is proposed to enhance the through-thickness stress distribution within a double-sided coated circular thick homogeneous plate. The coating system is composed of two main layers: an external homogeneous layer and an interlayer between the external layer and the plate, with graded material composition. All layers are modeled within the context of three-dimensional elasticity theory, and an elasto-static solution is obtained by using suitable potential functions. Accuracy and reliability of the proposed analysis is investigated by comparison with results obtained in the literature, as well as with the results of a three-dimensional finite element simulation. Comparative study shows the inherent advantages of the present hybrid coating system over the conventional homogeneous coating or the functionally graded coating layers.

  • 32.
    Sburlati, Roberta
    et al.
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Atashipour, Seyed Rasoul
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Atashipour, Seyed Abdolrahim
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer2014In: Composites Part B: Engineering, ISSN 1359-8368, E-ISSN 1879-1069, Vol. 61, p. 99-109Article in journal (Refereed)
    Abstract [en]

    This work aims at understanding the effect of a radially heterogeneous layer around the hole in a homogeneous plate on the stress concentration factor. The problem concerns a single hole in a plate under different far-field in-plane loading conditions. By assuming a radial power law variation of Young’s modulus and constant value for Poisson’s ratio, the governing differential equations for plane stress conditions, and general in-plane loading conditions are studied. The elastic solutions are obtained in closed form and, in order to describe localized interface damage between the ring and the plate, two different interface conditions (perfectly bonded and frictionless contact) are studied. The formulae for the stress concentration factors are explicitly given for uniaxial, biaxial and shear in-plane loading conditions and comparisons with interface hoop stress values are performed. The solutions are investigated to understand the role played by the geometric and graded constitutive parameters. The results are validated with numerical finite element simulations in which some simplified hypotheses assumed in the analytical model, are relaxed to explore the range of validity of the elastic solution presented. In this way the results obtained are useful in tailoring the parameters for specific applications.

  • 33.
    Sburlati, Roberta
    et al.
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Atashipour, Seyed Rasoul
    Department of Civil, Chemical and Environmental Engineering, Genoa University.
    Hosseini-Hashemi, Sh.
    School of Mechanical Engineering, Iran University of Science and Technology, Tehran.
    Study on the effect of functionally graded coating layers on elastic deformation of thick circular plates: A closed-form elasticity solution2013In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 99, p. 131-140Article in journal (Refereed)
  • 34. Shokrieh, M.M.
    et al.
    Atashipour, Seyed Rasoul
    Analysis of mold filling stage in vacuum assisted resin transfer molding with flexible tools considering resin injection tube2010In: Aerospace Mechanics Journal, Vol. 5, p. 41-54Article in journal (Refereed)
    Abstract [en]

    Resin transfer molding, that is a sub-branch of liquid composite molding, is one of the manufacturing methods of polymeric composites. Various modification has been presented to improve this process and enhance the product quality. One of the most important modified suggestions is the vacuum assisted resin transfer molding process with flexible tools. Because of the flexibility of tools, resin flow in the mold compact the fiber preform and consequently the thickness of the preform is varied. This phenomenon will affect all process parameters. In order to achieve more actual results and a proper modeling of the mold filling stage, in this article, the governing equations of the molding of a large part incorporating flexibility of tools, gravitational effects, and also friction losses have been solved analyticaly. Then, numerical results have been compared with other models and existing experimental results. It has been shown that neglecting injection tube in modeling of resin transfer molding process with flexible tools has more errors in comparison with RIM process, using traditional molds.

  • 35. Shokrieh, M.M.
    et al.
    Atashipour, Seyed Rasoul
    Resin flow in fiber preformed in vacuum assisted resin transfer molding with flexible tools2010In: Iranian Journal of Information Science and Technology, ISSN 1726-8125, Vol. 21, p. 329-338Article in journal (Refereed)
1 - 35 of 35
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