ORCID Profile
0000-0003-1782-3380
Current Organisation
University of Queensland
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Publisher: Elsevier BV
Date: 03-2000
Publisher: Elsevier BV
Date: 2011
Publisher: Elsevier BV
Date: 09-1992
Publisher: Elsevier BV
Date: 10-2018
Publisher: Elsevier BV
Date: 09-2009
Publisher: Elsevier BV
Date: 2002
Publisher: Elsevier BV
Date: 08-2003
Publisher: American Society of Civil Engineers (ASCE)
Date: 12-1986
Publisher: Informa UK Limited
Date: 12-05-2009
Publisher: Elsevier BV
Date: 07-2009
Publisher: Elsevier BV
Date: 2006
Publisher: Elsevier BV
Date: 05-1994
Publisher: ASME International
Date: 09-1998
DOI: 10.1115/1.2789115
Abstract: Interfacial damage is incorporated in the proposed nonlinear theory. for composite laminated shells. A spring-layer model is employed to characterize damaged interfaces spanning from perfect bonding to different degrees of imperfect bonding in shear. By enforcing compatibility conditions for transverse shear stresses both at interfaces and on two bounding surfaces of a laminated shell, only five unknowns are needed for modeling its behavior. The principle of virtual work is used to derive the governing equations, which are of 14th order in lines of curvature coordinates, variationally self-consistent with seven prescribed boundary conditions. This theory includes the conventional higher-order zigzag model for a perfectly bonded shell as a special case. Numerical results provide a physical understanding of the effect of interracial damage on bending and buckling responses of composite laminated shells.
Publisher: Elsevier BV
Date: 03-2020
Publisher: American Society of Civil Engineers (ASCE)
Date: 1992
Publisher: American Society of Civil Engineers (ASCE)
Date: 03-1993
Publisher: Elsevier BV
Date: 12-1994
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-2009
Publisher: Elsevier BV
Date: 06-2005
Publisher: Elsevier BV
Date: 12-1993
Publisher: Elsevier BV
Date: 06-1996
Publisher: Springer Science and Business Media LLC
Date: 22-03-2011
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1987
Publisher: Informa UK Limited
Date: 03-08-2009
Publisher: Wiley
Date: 28-11-2005
DOI: 10.1002/NME.1417
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2003
DOI: 10.1142/S021945540300080X
Abstract: This paper treats the axisymmetric vibration of thin circular cylindrical shells with intermediate ring supports based on the Goldenveizer–Novozhilov thin shell theory. An analytical method is proposed, and new exact solutions are presented to study the axisymmetric vibration characteristics of the ring supported cylindrical shells. In the proposed method, the state-space technique is employed to derive a homogenous differential equation system for a shell segment, and a domain decomposition approach is developed to cater for the continuity requirements between shell segments. Exact frequency parameters are presented for circular cylindrical shells that have multiple intermediate ring supports and various combinations of end support conditions. These exact vibration frequencies may serve as important benchmarks against which researchers can validate their numerical methods for such circular cylindrical shell problems.
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 09-2001
DOI: 10.2514/2.4803
Publisher: Elsevier BV
Date: 04-2000
Publisher: Springer Science and Business Media LLC
Date: 10-2018
Publisher: Elsevier BV
Date: 11-2006
Publisher: Elsevier BV
Date: 12-2018
Publisher: MDPI AG
Date: 20-10-2017
DOI: 10.3390/POLYM9100532
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-1994
Publisher: Elsevier BV
Date: 06-2011
Publisher: Elsevier BV
Date: 02-1995
Publisher: Springer Science and Business Media LLC
Date: 23-11-2018
Publisher: Springer Science and Business Media LLC
Date: 08-2014
Publisher: Elsevier BV
Date: 12-2013
Publisher: Elsevier BV
Date: 08-2014
Publisher: Elsevier BV
Date: 07-2014
Publisher: Springer Science and Business Media LLC
Date: 15-12-2018
Publisher: Elsevier BV
Date: 02-1999
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 07-1997
DOI: 10.2514/2.234
Publisher: Elsevier BV
Date: 05-2012
Publisher: ASME International
Date: 10-2000
DOI: 10.1115/1.568438
Abstract: This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As ex les, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. [S0739-3717(00)01601-9]
Publisher: Wiley
Date: 26-02-2006
DOI: 10.1002/NME.1505
Publisher: Elsevier BV
Date: 10-1994
Publisher: ASME International
Date: 1994
DOI: 10.1115/1.2930397
Abstract: The influence of isotropic in-plane stresses on the fundamental vibration frequencies of thick triangular plates is investigated. Some critical buckling factors are also presented in the paper. Due to the lack of results and importance of this topic, the Rayleigh-Ritz method is applied to solve the governing eigenvalue function based on the Mindlin plate theory. The fundamental frequency parameters for triangular Mindlin plates subject to uniform tensile and compressive stresses with different combinations of free, simply supported, and cl ed boundary conditions are determined. The solutions are presented in the form of design charts where the fundamental frequency parameters can easily be read for particular thickness to width ratios (t/b) and in-plane stresses. Since no other vibration solution for thick triangular plate is available, the thin triangular plate solutions obtained by setting the thickness to width ratio to be very small (say t/b = 0.001), where possible, are verified with known solutions from the open literature.
Publisher: Elsevier BV
Date: 10-2017
Publisher: Elsevier BV
Date: 10-2002
Publisher: Springer Science and Business Media LLC
Date: 03-2004
Publisher: American Society of Civil Engineers (ASCE)
Date: 06-1989
Publisher: Elsevier BV
Date: 11-2005
Publisher: Elsevier BV
Date: 11-2016
Publisher: Elsevier BV
Date: 10-2013
Publisher: Springer Science and Business Media LLC
Date: 12-05-1998
Publisher: American Society of Civil Engineers (ASCE)
Date: 04-1993
Publisher: Springer Science and Business Media LLC
Date: 04-05-2006
Publisher: American Society of Civil Engineers (ASCE)
Date: 05-2018
Publisher: Elsevier BV
Date: 09-1999
Publisher: Springer Science and Business Media LLC
Date: 03-1995
DOI: 10.1007/BF01177475
Publisher: Informa UK Limited
Date: 05-2008
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1991
Publisher: Wiley
Date: 2007
DOI: 10.1002/NME.1984
Publisher: Elsevier BV
Date: 09-2002
Publisher: Elsevier BV
Date: 10-2005
Publisher: American Society of Civil Engineers (ASCE)
Date: 07-2003
Publisher: Elsevier BV
Date: 11-2012
Publisher: Elsevier BV
Date: 03-2007
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-2010
Publisher: Elsevier BV
Date: 1993
Publisher: Elsevier BV
Date: 09-2009
Publisher: American Society of Civil Engineers (ASCE)
Date: 03-1994
Publisher: The Royal Society
Date: 23-09-2005
Abstract: An analytical algorithm is proposed to describe the buckling behaviour of multi-walled carbon nanotubes (CNTs) that are embedded in a matrix with consideration of the van der Waals (vdW) interaction. The in idual tube is treated as a cylindrical shell, but the tube deflections are coupled with each other due to the vdW interaction. The interaction between the matrix and the outermost tube is modelled as a Pasternak foundation. Based on the proposed model, an accurate expression and a simple approximate expression are derived for the buckling load of double-walled CNTs that are embedded in a matrix. The approximate expression clearly indicates that the vdW force is coupled with the matrix parameters. A numerical simulation is carried out, and the results reveal that the increase in the number of layers leads to a decrease in the critical buckling load for multi-walled CNTs with a fixed innermost radius. In contrast, when the outermost radius is fixed, the critical buckling load increases with the increase in the number of layers for multi-walled CNTs without a matrix. However, for multi-walled CNTs that are embedded in a matrix, the critical buckling load decreases first and then increases with the increase in the number of layers. This implies that there is a given number of layers for a multi-walled CNT at which the critical buckling load is the lowest, and that this number depends on the matrix parameters.
Publisher: Elsevier BV
Date: 2012
Publisher: IOP Publishing
Date: 18-07-2001
Publisher: Springer Science and Business Media LLC
Date: 18-12-2009
Publisher: Elsevier BV
Date: 1990
Publisher: Elsevier BV
Date: 1992
Publisher: Wiley
Date: 2007
DOI: 10.1002/NME.1870
Publisher: Elsevier BV
Date: 02-2019
Publisher: Springer Science and Business Media LLC
Date: 30-05-2009
Publisher: Wiley
Date: 02-03-2004
DOI: 10.1002/NME.932
Publisher: American Society of Civil Engineers (ASCE)
Date: 02-1998
Publisher: Elsevier BV
Date: 06-2008
Publisher: Elsevier BV
Date: 12-2013
Publisher: Elsevier BV
Date: 07-2013
Publisher: Elsevier BV
Date: 08-2006
Publisher: Elsevier BV
Date: 08-2019
Publisher: Elsevier BV
Date: 11-1993
Publisher: Elsevier BV
Date: 02-2005
Publisher: American Society of Civil Engineers (ASCE)
Date: 1993
Publisher: Elsevier BV
Date: 11-2016
Publisher: Acoustical Society of America (ASA)
Date: 09-1997
DOI: 10.1121/1.420072
Abstract: The free vibration analysis of symmetrically laminated thick rectangular plates is examined. The p-Ritz method is employed in which sets of uniquely defined polynomials are used as the admissible trial displacement and rotation functions. The energy integral expressions of the laminates are derived by incorporating the shear deformation using Reddy’s higher-order plate theory [J. Appl. Mech. ASME 51, 745–752 (1984)]. The formulation is basically applicable to rectangular laminates with any combination of free, simply supported, and cl ed boundary conditions. To evaluate the validity and to demonstrate the applicability of the proposed method, a series of free vibration analyses of laminated composite plates is reported. Wherever possible, the accuracy of this analysis is validated through comparison with available results. Efforts are made to interpret the results to provide physical insight to the problem.
Publisher: Acoustical Society of America (ASA)
Date: 07-1995
DOI: 10.1121/1.413657
Abstract: An approximate method based on the wave-function expansion procedure has been used to solve the problem of reflection of time harmonic plane strain waves normally incident upon the fixed edge of a semi-infinite, uniaxially fiber-reinforced, composite plate of linearly elastic materials. Both symmetric and antisymmetric incident waves have been considered. The dispersion relation of the infinite plate has been solved through an approximate technique to obtain wave functions. The litudes of reflected waves have been determined by satisfying the fixed edge condition through the application of a variational principle. It is shown that the results agree well with known solutions for homogeneous isotropic plates. Numerical results are presented for a graphite/epoxy composite plate. The accuracy of the results is demonstrated through satisfaction of the principle of energy conservation and the reciprocity relations. The influence of fiber-direction elastic stiffness on reflection coefficients has also been studied.
Publisher: Elsevier BV
Date: 12-2015
Publisher: ASME International
Date: 03-1999
DOI: 10.1115/1.2789156
Publisher: Elsevier BV
Date: 07-2003
Publisher: Elsevier BV
Date: 1992
Publisher: Elsevier
Date: 1996
Publisher: Elsevier BV
Date: 1987
Publisher: Springer Science and Business Media LLC
Date: 03-2019
Publisher: Elsevier BV
Date: 10-2019
Publisher: American Society of Civil Engineers (ASCE)
Date: 2012
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2012
DOI: 10.1142/S0219455412500058
Abstract: Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.
Publisher: Elsevier BV
Date: 09-2009
Publisher: Elsevier BV
Date: 10-1995
Publisher: Elsevier BV
Date: 05-2003
Publisher: Informa UK Limited
Date: 31-05-2017
Publisher: Elsevier BV
Date: 2026
Publisher: Elsevier BV
Date: 06-2007
Publisher: World Scientific Pub Co Pte Lt
Date: 22-10-2018
DOI: 10.1142/S0219455418501420
Abstract: This paper proposes a novel functionally graded (FG) concrete slab and investigates its thermal buckling and postbuckling performance using the finite-element (FE) method. The concrete slab consists of three homogeneous thick layers — a fiber-reinforced concrete layer, a geopolymer concrete layer, and a plain Portland cement (PPC) layer — with a thin FG layer between the thick layers. The mechanical properties of the thin FG layers are exponentially graded across the thickness direction. The effects of initial imperfection, the self-weight of the slab, and the friction between the slab and rigid foundation are considered in the analysis. The FE model is validated against the results reported in the literature. A comprehensive parametric study is conducted to examine the effects of the thickness and volume fraction index of the FG layer, initial imperfection, self-weight, friction, and slab slenderness ratio on the thermal buckling and postbuckling behaviors of the concrete slab. The numerical results demonstrate that the proposed FG slab exhibits remarkably better buckling and postbuckling resistance than a conventional PPC concrete slab and that the influences of both self-weight and friction are important and cannot be neglected.
Publisher: Elsevier BV
Date: 1991
Publisher: Elsevier
Date: 2007
Publisher: Elsevier BV
Date: 1993
Publisher: Elsevier BV
Date: 07-2001
Publisher: Elsevier BV
Date: 1983
Publisher: IOP Publishing
Date: 11-01-2008
Publisher: World Scientific Pub Co Pte Lt
Date: 31-08-2015
DOI: 10.1142/S0219455415400155
Abstract: Monomorph and bimorph actuators made of piezoelectric materials are widely used in smart materials and structural control. Recent studies show that their performances can be remarkably improved by the use of functionally graded piezoelectric materials (FGPMs) whose compositional profile and effective material properties are graded along the thickness direction. This paper investigates the linear and nonlinear vibration behaviors of monomorph and bimorph made from a mixture of PZT4 and PZT-5H with material composition following a power law distribution. Theoretical formulations are based on von Kármán kinematic relationships and Timoshenko beam theory to account for the effect of transverse shear deformation. The differential quadrature method (DQM) and the second-order backward difference scheme are employed to obtain the linear and nonlinear vibration frequencies. A parametric study is conducted to investigate the influences of volume fraction index, slenderness ratio, nonlinear deformation and different loading conditions.
Publisher: Elsevier BV
Date: 07-1993
Publisher: IOP Publishing
Date: 06-2010
Publisher: Elsevier BV
Date: 03-1998
Publisher: American Society of Civil Engineers (ASCE)
Date: 03-1984
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1990
Publisher: American Society of Civil Engineers (ASCE)
Date: 03-1988
Publisher: Informa UK Limited
Date: 14-01-2009
Publisher: IOP Publishing
Date: 17-08-2006
Publisher: Elsevier BV
Date: 2001
Publisher: American Society of Civil Engineers (ASCE)
Date: 1990
Publisher: Wiley
Date: 08-01-2009
DOI: 10.1002/NME.2544
Publisher: Acoustical Society of America (ASA)
Date: 12-1996
DOI: 10.1121/1.417230
Abstract: This study forms a generalization of the free vibration analysis of thin composite plates. It extends previous analyses and presents benchmark results for the effects of general lamination and geometric unsymmetry parameters on the natural frequencies of general trapezoidal plates. The Ritz extremum energy principle with kinematically oriented pb-2 shape functions, transformed into efficient numerical procedures, have been further exploited to obtained fast-converging and accurate results. Selected new transverse vibration mode shapes are presented to illustrate the effects of boundary constraints, aspect ratio, and fiber orientation.
Publisher: Springer Science and Business Media LLC
Date: 16-05-2009
Publisher: IOP Publishing
Date: 09-08-2005
DOI: 10.1088/0957-4484/16/10/018
Abstract: A stacked plate model for the vibration of multi-layered graphene sheets (MLGSs), in which the van der Waals (vdW) interaction between layers is described by an explicit formula, is presented. Explicit formulae are derived for predicting the natural frequencies of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the natural frequencies. The natural frequencies are calculated for various numbers of layered graphene sheets, and the results show that the vdW interaction has no influence on the lowest natural frequency (classical frequency) of an MLGS but plays a significant role in all higher natural frequencies (resonant frequencies) for a given combination of m and n. The vibration modes that are associated with the classical frequencies for each sheet of an MLGS are identical. In contrast, the vibration modes that are associated with the resonant frequencies are non-identical and give various vibration patterns, which indicates that MLGSs are highly suited to use as high frequency resonators.
Publisher: Elsevier BV
Date: 10-1993
Publisher: Elsevier BV
Date: 02-2017
Publisher: Elsevier BV
Date: 10-2013
Publisher: Acoustical Society of America (ASA)
Date: 12-1996
DOI: 10.1121/1.417232
Abstract: The first-known investigation is reported for free vibration of circular and annular Mindlin plates with intermediate concentric ring stiffeners. The total potential energy functional is first derived for the stiffened circular and annular plates. The Mindlin first-order shear deformation plate theory is used to account for the effects of plate shear deformation and rotary inertia, while the Engesser theory is used to consider the shear deformation and torsional effects in stiffeners. A set of trial functions is proposed for the displacement fields to satisfy the geometric boundary conditions of the plate at outset. Minimizing the energy functional by applying the Ritz procedure, the governing eigenvalue equation is derived. Solving the eigenvalue equation, first-known sets of vibration solutions are obtained for circular and annular Mindlin plates with concentric ring stiffeners. The accuracy of the results is tested using convergence studies. The significant influences of boundary conditions, plate thickness ratio, cut-out ratio and locations of ring stiffeners are highlighted.
Publisher: IOP Publishing
Date: 14-10-2010
Publisher: Elsevier BV
Date: 09-2019
Publisher: Informa UK Limited
Date: 09-09-2016
Publisher: Elsevier BV
Date: 1988
Publisher: Elsevier
Date: 2002
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1990
Publisher: Elsevier BV
Date: 2011
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 04-1998
DOI: 10.2514/2.416
Publisher: Elsevier BV
Date: 10-2011
Publisher: SAGE Publications
Date: 02-05-2013
Publisher: Elsevier BV
Date: 02-2017
Publisher: Elsevier BV
Date: 1991
Publisher: World Scientific Pub Co Pte Lt
Date: 31-08-2015
DOI: 10.1142/S0219455415400258
Abstract: This paper is concerned with the flexural vibration of an atomic force microscope (AFM) cantilever. The cantilever problem is formulated on the basis of the modified couple stress theory and the Timoshenko beam theory. The modified couple stress theory is a nonclassical continuum theory that includes one additional material parameter to describe the size effect. By using the Hamilton's principle, the governing equation of motion and the boundary conditions are derived for the AFM cantilevers. The equation is solved using the differential quadrature method for the natural frequencies and mode shapes. The effects of the s le surface contact stiffness, length scale parameter and location of the sensor tip on the flexural vibration characteristics of AFM cantilevers are discussed. Results show that the size effect on the frequency is significant when the thickness of the microcantilever has a similar value to the material length scale parameter.
Publisher: American Physical Society (APS)
Date: 29-08-2005
Publisher: Elsevier BV
Date: 1986
Publisher: Elsevier BV
Date: 07-1997
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-1994
Publisher: Elsevier BV
Date: 06-1994
Publisher: Elsevier BV
Date: 1994
Publisher: IOP Publishing
Date: 09-08-2016
Publisher: Elsevier BV
Date: 05-1997
Publisher: Elsevier BV
Date: 09-2014
Publisher: Elsevier BV
Date: 07-2012
Publisher: Acoustical Society of America (ASA)
Date: 03-1999
DOI: 10.1121/1.426706
Abstract: The problem of free vibration of arbitrary quadrilateral unsymmetrically laminated plates subject to arbitrary boundary conditions is considered. The Ritz procedures supplemented by the simple polynomial shape functions are employed to derive the governing eigenvalue equation. The displacements are approximated by a set of polynomials which consist of a basic boundary function that impose the various boundary constraints. A first-order shear deformable plate theory is employed to account for the effects of the transverse shear deformation. The numerical accuracy of the solution is verified by studying the convergence characteristics of the vibration frequencies and also by comparison with existing results. The new results of this study include the sensitivity of the vibration responses to variations in the lamination, boundary constraints and thickness effects, and also their interactions. These numerical values are presented for a typical graphite/epoxy material, in tabular and graphical forms.
Publisher: Springer Science and Business Media LLC
Date: 03-1994
DOI: 10.1007/BF01178522
Publisher: Elsevier BV
Date: 05-1998
Publisher: Elsevier BV
Date: 04-2012
Publisher: AIP Publishing
Date: 31-05-2005
DOI: 10.1063/1.1925334
Abstract: Explicit formulas are obtained to describe the buckling behavior of triple-walled carbon nanotubes (CNTs) that are embedded in an elastic matrix, with van der Waals (vdW) interaction taken into consideration. The investigation is based on the continuum shell theory in which the in idual tube is treated as a cylindrical shell. The elastic matrix surrounding the outermost tube is modeled as a Pasternak foundation to account for not only the normal stress, but also the shear stress between the outermost tube and the surrounding matrix. Numerical analyses are carried out to estimate the critical buckling load of triple-walled CNTs, and the results indicate that the critical buckling loads approach a constant of around 0.26N∕m with the increase of the innermost radii regardless of whether or not the triple-walled CNT is embedded in an elastic matrix. The effects of vdW interactions before and after buckling on the critical buckling load are also examined for triple-walled CNTs with various innermost radii.
Publisher: Elsevier BV
Date: 06-2005
Publisher: Springer Science and Business Media LLC
Date: 17-08-2000
Publisher: Wiley
Date: 2006
DOI: 10.1002/NME.1786
Publisher: Elsevier BV
Date: 1987
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-1983
Publisher: Elsevier BV
Date: 2006
Publisher: Elsevier BV
Date: 09-2018
Publisher: Elsevier BV
Date: 2018
Publisher: Elsevier BV
Date: 10-1996
Publisher: Elsevier BV
Date: 06-1995
Publisher: Elsevier BV
Date: 12-2009
Publisher: American Society of Civil Engineers (ASCE)
Date: 04-1987
Publisher: Springer Science and Business Media LLC
Date: 17-04-2018
Publisher: Acoustical Society of America (ASA)
Date: 2000
DOI: 10.1121/1.428348
Abstract: In view of the various novel quantitative ultrasonic evaluation techniques developed using Lamb wave propagation, the influence of an important related phenomenon, backward transmission, is investigated in this paper. Using the discrete layer theory and a multiple integral transform method, the surface displacement and velocity responses of isotropic plates and cross-ply laminated composite plates due to the Lamb waves excited by parabolic- and piston-type transmitting transducers are evaluated. Analytical expressions for the surface displacement and velocity frequency response functions are developed. Based on this a large volume of calculations is carried out. Through examining the characteristics of the surface displacement and velocity frequency response functions and, especially, the different propagation modes’ contributions to them, the influence of the backward wave transmission related to quantitative ultrasonic nondestructive evaluation applications is discussed and some important conclusions are drawn.
Publisher: Acoustical Society of America (ASA)
Date: 06-1999
DOI: 10.1121/1.424660
Abstract: For the purpose of understanding and improving the acousto-ultrasonic (AU) technique, the AU characteristics for an isotropic plate is investigated in this paper. Unlike the previous wave tracing method, a spectral analysis approach is presented, which can take into account the effects of the transducers’ characteristics. Using this approach and introducing the point source oint receiver assumption, the input–output frequency spectrum relationships for the cases of one transmitter/one receiver and one transmitter/multiple receivers coupled to an isotropic thin plate are expressed in explicit forms. Based on this, a wave scattering parameter to bridge two different sensing types of the receiving transducers is presented, and a new type stress wave parameter for the AU technique is developed, which eliminates the influence of the complex mechanic-electron transduction characteristics of the receivers and also separates to some extent the effects of some other external factors such as transducer masses and locations. Finally, some numerical simulations are carried out and conclusions drawn concerning the AU technique.
Publisher: Elsevier BV
Date: 09-2002
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1988
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-2003
Publisher: Elsevier BV
Date: 03-2005
Publisher: Elsevier BV
Date: 04-1994
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 11-1996
DOI: 10.2514/3.13422
Publisher: Elsevier BV
Date: 03-1997
Publisher: Elsevier BV
Date: 04-2016
Publisher: Elsevier BV
Date: 05-2004
Publisher: American Society of Civil Engineers (ASCE)
Date: 05-1988
Publisher: Acoustical Society of America (ASA)
Date: 1996
DOI: 10.1121/1.414548
Abstract: The vibration of shallow spherical and ellipsoidal dishes with variable thickness along the gradient from the apex is studied. The dishes are point-cl ed at the apex or surface-cl ed over concentric central regions which are modeled as singly and doubly connected domains, respectively. This model simulates domes, tank covers, radar dishes, or the antennas of certain communication satellites which are cl ed over a finite region at the apex. The Ritz method is used to develop an efficient numerical procedure incorporating the boundary support characteristics intrinsically. Comparison with finite element and experimental results shows good consistency. Sets of useful vibration frequencies with additional mode shapes are presented to illustrate the capability of the method.
Publisher: ASME International
Date: 10-1994
DOI: 10.1115/1.2930459
Abstract: A first known investigation into the vibratory characteristics of rectangular Mindlin plates with intermediate stiffeners is presented. The Rayleigh-Ritz method is used, with displacement and rotational functions assumed in the form of mathematically complete algebraic polynomials. Sets of numerical frequency parameters for rectangular plates of various boundary conditions, thicknesses and plate dimensions are presented. In the study, the effects of shear deformation and rotary inertia on the vibrational response of the plate structures are investigated. The influence of torsional rigidity and geometric properties of stiffeners on the natural frequency parameters are included. To validate the proposed formulation, numerical results for some simplified problems have been determined where existing literature for these problems can be found. Finally sets of new vibration frequencies for plates with one or more stiffeners in various directions are presented.
Publisher: Springer Science and Business Media LLC
Date: 06-1996
DOI: 10.1007/BF01197031
Publisher: World Scientific Pub Co Pte Lt
Date: 31-08-2015
DOI: 10.1142/S0219455415400118
Abstract: This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.
Publisher: Acoustical Society of America (ASA)
Date: 09-1998
DOI: 10.1121/1.424354
Abstract: The three-dimensional elastic analysis of the vibration of open cylindrical shells are presented. Transverse normal stress usually neglected in plate and shell higher-order theories has been considered. The natural frequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Excessive requirements for memory and computational effort have been overcome, without sacrificing numerical accuracy, by (i) decoupling the three-dimensional displacements into the product of a set of beam and shell shape functions and (ii) classifying the vibration modes. The effects of subtended angle and aspect ratio have been concluded for shells with various boundary conditions. Typical vibration mode shapes demonstrating the dependence of vibration characteristics on boundary constraints are presented.
Publisher: Elsevier BV
Date: 11-1994
Publisher: ASME International
Date: 08-1997
DOI: 10.1115/1.3101731
Abstract: This review article documents recent developments in the free vibration analysis of thin, moderately thick, and thick shallow shells. An introductory review of the studies in Kirchhoff-Love classical thin shell theory is given. The development of studies in moderately thick shells incorporating the effects of transverse shear deformation and rotary inertia is detailed. This review article mainly focuses on research advances in vibration studies since the 1970s using the classical Kirchhoff-Love, first-order, and higher-order theories. The validity and range of applicability of these theories are examined. There are 163 references listed at the end of the article.
Publisher: Springer Science and Business Media LLC
Date: 21-11-2010
Publisher: American Society of Civil Engineers (ASCE)
Date: 1996
Publisher: Elsevier BV
Date: 08-1995
Publisher: Elsevier BV
Date: 1996
Publisher: Elsevier BV
Date: 1992
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-1997
Publisher: Wiley
Date: 19-02-2006
DOI: 10.1002/NME.1489
Publisher: Elsevier BV
Date: 02-2010
Publisher: Elsevier BV
Date: 2018
Publisher: World Scientific Pub Co Pte Lt
Date: 12-2007
DOI: 10.1142/S0219455407002423
Abstract: This paper is concerned with the vibration problem of initially stressed micro/nano-beams. The vibration problem is formulated on the basis of Eringen's nonlocal elasticity theory and the Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of initial stress, transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. These equations are solved analytically for the vibration frequencies of micro/nano-beams with different initial stress values and boundary conditions. The effect of the initial stress on the fundamental frequency and vibration mode shape of the beam is investigated. The solutions obtained provide a better representation of the vibration behavior of initially stressed micro/nano-beams which are stubby and short, since the effects of small scale, transverse shear deformation and rotary inertia are significant and cannot be neglected.
Publisher: Elsevier BV
Date: 05-1996
Publisher: Elsevier BV
Date: 10-2016
Publisher: Elsevier BV
Date: 06-1999
Publisher: American Society of Civil Engineers (ASCE)
Date: 07-1990
Publisher: Mathematical Sciences Publishers
Date: 12-2008
Publisher: Elsevier BV
Date: 06-2016
Publisher: American Society of Civil Engineers (ASCE)
Date: 04-1990
Publisher: Elsevier BV
Date: 09-2006
Publisher: American Society of Civil Engineers (ASCE)
Date: 04-1986
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-1990
Publisher: IOP Publishing
Date: 18-05-2010
Publisher: Elsevier BV
Date: 07-1994
Publisher: Informa UK Limited
Date: 04-2003
DOI: 10.1080/713855900
Publisher: Elsevier BV
Date: 10-1993
Publisher: Acoustical Society of America (ASA)
Date: 05-1995
DOI: 10.1121/1.411852
Abstract: Benchmark vibration solutions for thick polygonal plates of arbitrary boundary conditions are presented. The Mindlin first-order shear deformation theory is used to derive the energy functional while the pb-2 Ritz method is employed for solution. By minimizing the difference between the maximum strain and kinetic energies with respect to unknown coefficients in the pb-2 admissible functions, the governing eigenvalue equation is derived. The vibration frequencies are obtained by solving this governing eigenvalue equation. A convergence study has been carried out to verify the accuracy of these results. In the absence of existing results for thick polygonal plates, the present results where possible are compared with available thin plate solutions by setting the thickness to apothem ratio to be very small (say, t/r=0.001). Sets of first known vibration frequencies for moderately thick regular polygonal plates are presented as an enhancement to existing literature.
Publisher: Elsevier BV
Date: 2004
Publisher: Springer Science and Business Media LLC
Date: 06-09-2012
Publisher: Taylor & Francis
Date: 23-06-2008
Publisher: American Society of Civil Engineers (ASCE)
Date: 03-1993
Publisher: Elsevier BV
Date: 11-1999
Publisher: World Scientific Pub Co Pte Lt
Date: 09-0100
DOI: 10.1142/S1758825112500251
Abstract: This paper is concerned with the bifurcation buckling of nano-rings and nano-arches where the allowance for small scale effect is catered for by using Eringen's nonlocal theory of elasticity. Exact buckling solutions for nano-rings and nano-arches under uniform radial pressure are derived and the influence of small scale effect on the buckling pressures and mode shapes is investigated. The new results presented will be useful to engineers who are designing nano-rings and nano-arches to be used in MEMS and NEMS devices.
Publisher: Elsevier BV
Date: 02-2018
Publisher: Elsevier BV
Date: 06-2017
Publisher: Elsevier BV
Date: 02-2003
Publisher: Elsevier BV
Date: 05-2010
Publisher: Elsevier BV
Date: 04-2007
Publisher: Informa UK Limited
Date: 30-01-2019
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 07-2000
DOI: 10.2514/2.1100
Publisher: Elsevier BV
Date: 07-1986
Publisher: Elsevier BV
Date: 04-1997
Publisher: Elsevier BV
Date: 10-1986
Publisher: Informa UK Limited
Date: 05-2010
Publisher: IOP Publishing
Date: 25-10-2012
Publisher: Elsevier BV
Date: 06-2000
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-1993
Publisher: Elsevier BV
Date: 02-2017
Publisher: Springer Science and Business Media LLC
Date: 02-09-2005
Publisher: Elsevier BV
Date: 12-2015
Publisher: American Society of Civil Engineers (ASCE)
Date: 11-1994
Publisher: Elsevier BV
Date: 02-2017
Publisher: Elsevier BV
Date: 02-1995
Publisher: Elsevier BV
Date: 09-2017
Publisher: Elsevier
Date: 2006
Publisher: Elsevier BV
Date: 02-2000
Publisher: Springer Science and Business Media LLC
Date: 11-10-2018
Publisher: Elsevier BV
Date: 02-2006
Publisher: World Scientific Pub Co Pte Lt
Date: 07-2018
DOI: 10.1142/S1758825118500680
Abstract: In the present paper, the vibration behavior of a buckled functionally graded (FG) microplate lying on a nonlinear elastic foundation is studied. The modified couple stress theory is utilized to capture the size effect of the FG microplate, and the Mindlin plate theory with the von Karman’s geometric nonlinearity is adopted to describe its deflection behavior. Based on these assumptions and Hamilton’s principle, the governing equations and associated boundary conditions are derived for the FG microplate. By linearizing the governing equations around a pre-buckling ost-buckling state, linear perturbation equations are obtained. After substituting the pre-buckling ost-buckling deformation and assumed vibration mode into the linear perturbation equations and applying the Galerkin method, an eigenvalue problem is obtained, from which the free vibration frequency of the FG microplate around its pre-buckling ost-buckling state can be determined analytically. Based on the obtained closed-form solutions, numerical ex les are also presented to investigate the effects of the material length scale parameter to thickness ratio, the power law index, and the stiffness of the elastic foundation on the vibration behavior of the buckled FG microplate.
Publisher: Elsevier BV
Date: 04-1996
Publisher: ASME International
Date: 10-1999
DOI: 10.1115/1.2894003
Abstract: Acousto-ultrasonic input-output characteristics for contact-type transmitting and receiving transducers coupled to a thin orthotropic composite plate are analyzed in this paper. By introducing the point source oint receiver assumption, the governing equations of the problem, which relates to wave generation, wave propagation and wave reception, are first established. Using the multiple integral transform method, contour integration technique and some complex function theories, a spectral analysis method which is completely different from the present wave path tracing method for this problem is developed. From this approach, the spectral response of the normal contact force between the receiving transducer and the plate, due to an arbitrary input interrogation pulse excited by the transmitting transducer, is expressed in explicit form. Based on this, some physical properties involved with the output of the receiver are examined in the frequency domain. Finally, combining the fast Fourier transform (FFT) technique, some time domain numerical results are calculated to show the input-output characteristics of the AU system considered.
Publisher: Elsevier BV
Date: 1986
Publisher: Elsevier BV
Date: 2011
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 02-1995
DOI: 10.2514/3.12364
Publisher: American Society of Civil Engineers (ASCE)
Date: 07-1991
Publisher: Wiley
Date: 12-1993
Publisher: Elsevier BV
Date: 02-2005
Publisher: American Society of Civil Engineers (ASCE)
Date: 11-1986
Publisher: Informa UK Limited
Date: 04-07-2021
Publisher: American Society of Civil Engineers (ASCE)
Date: 10-1994
Publisher: Elsevier BV
Date: 1993
Publisher: Elsevier BV
Date: 03-1999
Publisher: Elsevier BV
Date: 03-2010
Publisher: Elsevier BV
Date: 05-2004
Publisher: Elsevier BV
Date: 11-2002
Publisher: American Society of Civil Engineers (ASCE)
Date: 06-2008
Publisher: Springer Science and Business Media LLC
Date: 19-11-2016
Publisher: American Society of Mechanical Engineers
Date: 07-2012
Abstract: This paper presents a novel hybrid system for reducing the hydroelastic response of pontoon-type, very large floating structure (VLFS) under wave action. The hybrid system comprises flexible connectors and “gill cells” which are compartments in VLFS with holes or slits at their bottom surfaces for allowing water to enter or leave freely. The gill cells are modeled by eliminating the buoyancy forces at their locations. In the hydroelastic analysis, the water is assumed to be an ideal fluid and its motion is irrotational so that a velocity potential exists. The VLFS is modeled as an isotropic plate according to the Mindlin plate theory. In order to decouple the fluid-structure interaction problem, the modal expansion method is adopted for the hydroelastic analysis which is carried out in the frequency domain. The boundary element method is used to solve the Laplace equation for the velocity potential, whereas the finite element method is employed for solving the equations of motion of the floating plate. It is found that by appropriately positioning the flexible line connector and a suitable distribution of gill cells in the VLFS, the hydroelastic response and stress resultants of the VLFS can be significantly reduced.
Publisher: Elsevier BV
Date: 02-1993
Publisher: Elsevier BV
Date: 10-1993
Publisher: Elsevier BV
Date: 2011
Publisher: Elsevier BV
Date: 02-2000
Publisher: Elsevier BV
Date: 12-2019
Publisher: Elsevier BV
Date: 2012
Publisher: American Society of Civil Engineers (ASCE)
Date: 11-1997
Publisher: Springer Science and Business Media LLC
Date: 03-1996
DOI: 10.1007/BF01181041
Publisher: Elsevier BV
Date: 05-2004
Publisher: Elsevier BV
Date: 12-2018
Publisher: Wiley
Date: 15-03-1995
Publisher: Elsevier BV
Date: 09-1995
Publisher: American Society of Civil Engineers (ASCE)
Date: 04-1987
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1984
Publisher: Elsevier BV
Date: 12-2009
Publisher: ASME International
Date: 11-2004
DOI: 10.1115/1.1795220
Abstract: This paper presents thermal buckling and post-buckling analyses for moderately thick laminated rectangular plates that contain functionally graded materials (FGMs) and subjected to a uniform temperature change. The theoretical formulation employs the first-order shear deformation theory and accounts for the effect of temperature-dependent thermoelastic properties of the constituent materials and initial geometric imperfection. The principle of minimum total potential energy, the differential quadrature method, and iterative algorithms are used to obtain critical buckling temperatures and the post-buckling temperature-deflection curves. The results are presented for both symmetrically and unsymmetrically laminated plates with ceramic/metal functionally graded layers, showing the effects of temperature-dependent properties, layup scheme, material composition, initial imperfection, geometric parameters, and boundary conditions on buckling temperature and thermal post-buckling behavior.
Publisher: American Society of Civil Engineers (ASCE)
Date: 11-1999
Publisher: Elsevier BV
Date: 04-2016
Publisher: Elsevier BV
Date: 05-2003
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 02-1997
DOI: 10.2514/2.96
Publisher: Elsevier BV
Date: 1983
Publisher: American Society of Civil Engineers (ASCE)
Date: 05-1985
Publisher: Springer Science and Business Media LLC
Date: 05-07-2011
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1991
Publisher: Elsevier BV
Date: 2017
Publisher: IOP Publishing
Date: 11-11-2014
Publisher: Elsevier BV
Date: 2017
Publisher: IOP Publishing
Date: 25-09-2003
Publisher: Elsevier BV
Date: 02-2017
Publisher: American Society of Civil Engineers (ASCE)
Date: 12-1983
Publisher: Elsevier BV
Date: 12-2004
Publisher: Elsevier BV
Date: 09-2001
Publisher: Elsevier BV
Date: 09-1995
Publisher: World Scientific Pub Co Pte Lt
Date: 16-02-2014
DOI: 10.1142/S0219455413500673
Abstract: Buckling and post-buckling behaviors of piezoelectric nanobeams are investigated by using the nonlocal Timoshenko beam theory and von Kármán geometric nonlinearity. The piezoelectric nanobeam is subjected to an axial compression force, an applied voltage and a uniform temperature rise. After constructing the energy functionals, the nonlinear governing equations are derived by using the principle of minimum total potential energy and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the buckling and post-buckling responses of piezoelectric nanobeams with hinged–hinged, cl ed–hinged and cl ed–cl ed end conditions. Numerical ex les are presented to study the influences of the nonlocal parameter, temperature rise and external electric voltage on the size-dependent buckling and post-buckling responses of piezoelectric nanobeams.
Publisher: Elsevier BV
Date: 02-2013
Publisher: Elsevier BV
Date: 04-2018
Publisher: Elsevier BV
Date: 07-1994
Publisher: Informa UK Limited
Date: 2013
Publisher: Elsevier BV
Date: 1992
Publisher: Springer Science and Business Media LLC
Date: 25-01-2005
Publisher: Elsevier BV
Date: 1997
Publisher: Elsevier BV
Date: 2017
Publisher: ASME International
Date: 19-08-2010
DOI: 10.1115/1.4001859
Abstract: In this paper, a more refined pressure distribution expression is derived to describe the van der Waals (vdW) interaction between any two tubes of a multiwalled carbon nanotube (MWCNT). Based on this new vdW force expression, a continuum cylindrical shell model is established for the buckling and post-buckling analysis of MWCNTs. The buckling and post-buckling responses are simulated for MWCNTs with various sizes to examine the consequences of ignoring the nonlinear term in the Taylor expansion of vdW force function. By comparing the results furnished by the commonly used linear vdW force model and the present nonlinear vdW force model, it is found that the buckling responses before the critical buckling strain are almost the same. Thus, the simple linear vdW force model suffices for the calculation of buckling loads. However, the post-buckling responses simulated from present nonlinear vdW force model are significantly lower than those given by the linear vdW force model. This indicates that the present nonlinear vdW force model must be used when considering the post-buckling responses.
Publisher: American Society of Civil Engineers (ASCE)
Date: 03-2003
Publisher: World Scientific Pub Co Pte Lt
Date: 06-2009
DOI: 10.1142/S1758825109000150
Abstract: This paper is concerned with the postbuckling problem of cantilevered nano rods/tubes under an end concentrated load. Eringen's nonlocal beam theory is used to account for the small length scale effect. The governing equation is derived from statical and geometrical considerations and Eringen's nonlocal constitutive relation. The nonlinear differential equation is solved using the shooting method for the postbuckling load and the buckled shape. By comparing with the classical postbuckling solutions, the sensitivity of the small length scale effect on the buckling load and buckled shape may be observed. It is found that the small length scale effect decreases the postbuckling load and increases the deflection of the rod.
Publisher: Elsevier BV
Date: 10-1991
Publisher: Wiley
Date: 2002
DOI: 10.1002/NME.519
Publisher: IOP Publishing
Date: 02-2000
Publisher: Elsevier BV
Date: 2017
Publisher: Elsevier BV
Date: 03-1999
Publisher: American Society of Civil Engineers (ASCE)
Date: 1984
Publisher: Elsevier BV
Date: 11-2017
Publisher: CRC Press
Date: 07-07-2006
Publisher: Elsevier BV
Date: 10-2013
Publisher: IOP Publishing
Date: 10-03-2011
DOI: 10.1088/0022-3727/44/13/135401
Abstract: A nonlinear continuum model is developed for the nonlinear vibration analysis of multi-layered graphene sheets (MLGSs), in which the nonlinear van der Waals (vdW) interaction between any two layers is formulated explicitly. The nonlinear equations of motion are studied by the harmonic-balance methods. Based on the present model, the nonlinear stiffened litude–frequency relations of double-layered graphene sheets (DLGSs) are investigated in the spectral neighbourhood of lower frequencies. The influence of the vdW interaction on the vibration properties of DLGSs is well illustrated by plotting the resulting modes' shapes, in which in-phase and anti-phase vibrations of DLGSs are studied. In particular, the large- litude vibration which associates with the anti-phase resonant frequencies, separating DLGS into single-layered GSs, is a promising application that needs to be explored further. In contrast, the vibration modes that are associated with the resonant frequencies are nonidentical and give various vibration patterns, which indicates that MLGSs are highly suited to being used as high-frequency resonators.
Publisher: Elsevier BV
Date: 06-2001
Publisher: Elsevier BV
Date: 10-2004
Publisher: Elsevier BV
Date: 02-2018
Publisher: Elsevier BV
Date: 10-1987
Publisher: Elsevier BV
Date: 10-2019
Publisher: Elsevier BV
Date: 12-2018
Publisher: Elsevier BV
Date: 06-2018
Publisher: Elsevier BV
Date: 03-2011
Publisher: Elsevier BV
Date: 04-1998
Publisher: Springer Science and Business Media LLC
Date: 07-2003
Publisher: American Society of Civil Engineers (ASCE)
Date: 06-1987
Publisher: Wiley
Date: 30-04-1993
Publisher: Elsevier BV
Date: 03-2017
Publisher: IOP Publishing
Date: 28-01-2008
Publisher: AIP Publishing
Date: 18-02-2005
DOI: 10.1063/1.1869543
Abstract: An idea of “spatial periodic strain” is proposed and an equilibrium relationship is established for the mechanics of zigzag single-walled carbon nanotubes (SWCNTs). An efficient approach is presented to investigate mechanical properties of zigzag SWCNT, and its validity is demonstrated by comparing its calculation results with existing results.
Publisher: Elsevier BV
Date: 1987
Publisher: Wiley
Date: 30-05-1994
Publisher: Elsevier BV
Date: 1986
Publisher: Elsevier BV
Date: 04-1998
Publisher: American Society of Civil Engineers (ASCE)
Date: 08-1984
Publisher: Elsevier BV
Date: 04-2016
Publisher: Elsevier BV
Date: 04-2000
Publisher: American Society of Civil Engineers (ASCE)
Date: 06-1986
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1985
Publisher: Springer Science and Business Media LLC
Date: 02-1997
Publisher: AIP
Date: 2010
DOI: 10.1063/1.3452051
Publisher: Elsevier BV
Date: 04-2017
Publisher: SAGE Publications
Date: 1997
DOI: 10.1177/107754639700300109
Abstract: This paper investigates the limits and range of application of the shallow shell theory for vibration of singly curved cylindrical panels. The significance of neglecting tangential displacements in bending and twist in the Donnell-Mushtari-Vlasov shallow shell theory is examined. The Ritz stationary energy principle, with a class of geometrically oriented two-dimensional polynomial functions (p-Ritz method), is employed to determine the frequency parameters. A comparison of numerical results from the shallow and deep shell theories is presented. The paper concludes that the limits of the shallow shell theory are dependent on the aspect ratio and boundary condition. The conclusion regarding limitation for a cantilevered shallow shell available in the literature cannot be directly extended to other types of boundary conditions. For shells with unit aspect ratio, shallow shell solutions are practically accurate even for relatively large subtended angles, but the results could be otherwise for long shells. In general, the shallow shell theory is relatively accurate for shells with a subtended angle of not more than 40°.
Publisher: Elsevier BV
Date: 10-2017
Publisher: Elsevier BV
Date: 10-1993
Publisher: American Society of Civil Engineers (ASCE)
Date: 12-1988
Publisher: Elsevier BV
Date: 12-2017
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Funder: Australian Research Council
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