The Experts below are selected from a list of 201 Experts worldwide ranked by ideXlab platform
M. Rahman - One of the best experts on this subject based on the ideXlab platform.
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The reciprocal theorem and rigid spherical inclusion vis-à-vis certain point singularities
Philosophical Magazine, 2007Co-Authors: M. Rahman, T. MichelitschAbstract:The elastic interaction of certain point singularities with a rigid spherical inclusion embedded into an otherwise infinite elastic medium is investigated. The particular singularities considered are point force, force-dipole (with and without Moment), centre of dilatation and Concentrated Moment. In each case, simple, closed form expressions are deduced by application of Betti's reciprocal theorem for the net force and net torque acting on the inclusion.
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A general procedure for solving boundary-value problems of elastostatics for a spherical geometry based on Love's approach
The Quarterly Journal of Mechanics and Applied Mathematics, 2007Co-Authors: M. Rahman, Thomas M. MichelitschAbstract:We develop a general procedure for solving the first and second fundamental problems of the theory of elasticity for cases where boundary conditions are prescribed on a spherical surface, using Love's general solution of the elastostatic equilibrium equations in terms of three scalar harmonic functions. It is shown that this general solution combined with a methodology by Brenner paves an elegant way to determine the three harmonic functions in terms of the boundary data. Thus, with this general scheme, solution of any such boundary-value problem is reducible to a routine exercise thereby providing some 'economy of effort'. Furthermore, we develop a similar general scheme for thermoelastic problems for cases when temperature type boundary conditions are prescribed on a spherical surface. We then illustrate the application of the procedure by solving a number of problems concerning rigid spherical inclusions and spherical cavities. In particular, apart from furnishing alternative solutions to the known problems, we demonstrate the use of this general procedure in solving the problem of interaction of a rigid spherical inclusion with a Concentrated Moment and that of a Concentrated heat source situated at an arbitrary point outside the inclusion. We also derive closed-form expressions for the net force and the net torque acting on a rigid spherical inclusion embedded into an infinite elastic solid under an ambient displacement field characterized by an arbitrary-order polynomial in the Cartesian coordinates. To the best of our knowledge, these results are new.
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Point singularities and the singularity method in classical elastodynamics
Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 2000Co-Authors: M. RahmanAbstract:The object of the article is to elucidate the application of the singularity method in classical elastodynamics. To this end, solutions for higher–order point singularities, e.g. time–harmonic Concentrated Moment, centre of dilatation, centre of rotation and force tensor, are derived from the influence tensor by a method usually employed in the theory of electrostatics for the study of potential of a system of charged particles. Solutions of some elastodynamic problems concerning spherical cavities and rigid spherical inclusions are then derived by combining these point singularities.
Yasser Sharifi - One of the best experts on this subject based on the ideXlab platform.
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A simple mathematical model for approximate analysis of tall buildings
Applied Mathematical Modelling, 2010Co-Authors: Reza Rahgozar, A. R. Ahmadi, Yasser SharifiAbstract:The focus of this article is to present a new and simple mathematical model that may be used to determine the optimum location of a belt truss reinforcing system on tall buildings such that the displacements due to lateral loadings would generate the least amounts of stress and strain in building’s structural members. The effect of belt truss and shear core on framed tube is modeled as a Concentrated Moment applied at belt truss location, this Moment acts in a direction opposite to rotation created by lateral loads. The axial deformation functions for flange and web of the frames are considered to be cubic and quadratic functions respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection, rotation of the plane section, and unknown coefficients of shear lag, the mathematical model is developed. The proposed model shows a good understanding of structural behavior; easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stage which requires less time. Numerical examples are given to demonstrate the ease of application and accuracy of the proposed modeled.
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An approximate analysis of combined system of framed tube, shear core and belt truss in high‐rise buildings
The Structural Design of Tall and Special Buildings, 2009Co-Authors: Reza Rahgozar, Yasser SharifiAbstract:In this paper a mathematical model for the combined system of framed tube, shear core and belt truss is developed with the objective of determining the optimum location of belt truss along the height of the building. The effect of belt truss and shear core on a framed tube is considered as a Concentrated Moment at the belt truss location. This Concentrated Moment acts in a direction opposite to rotation due to lateral loads. The axial deformation functions for web and flange of the frames are considered to be quadratic and cubic functions, respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection (u), rotation of the plane section (ϕ) and unknown coefficients of shear lag (α1, α2, β1 and β2), the mathematical model is developed. This model yields the displacement, axial stress distribution and bending stiffness as a function of the height of the combined system. The range application and validity of the proposed model is demonstrated by several numerical examples (30-, 40- and 50-storey buildings). The effects of belt truss position on lateral displacement and stress distribution are investigated and the optimum location for belt truss is obtained. Copyright © 2009 John Wiley & Sons, Ltd.
Reza Rahgozar - One of the best experts on this subject based on the ideXlab platform.
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An analytical approach to free vibration analysis of multi‐outrigger–belt truss‐reinforced tall buildings
The Structural Design of Tall and Special Buildings, 2011Co-Authors: Mohsen Malekinejad, Reza RahgozarAbstract:SUMMARY This paper deals with a new and simple mathematical model that may be used to determine natural frequencies and mode shapes of a multistory building that consists of a framed tube, a shear core and multi-outrigger–belt trusses. The effect of outrigger–belt truss and shear core on a framed tube was modeled as a Concentrated Moment placed at outrigger–belt truss location, which acted in opposite direction of the rotation created by lateral loads. The analysis is based on a continuum approach, in which a tall building structure may be replaced by an idealized cantilevered beam to model the building's structural characteristics. Energy method and Hamilton's principle have been used to develop the governing equations. After applying separation of variables method to time and space variables, the resulting eigensystem was solved to obtain the building's natural modes and frequencies of vibration. A computer program has been developed in MATLAB (Mathworks Inc., CA, USA) environment, and a numerical example has been solved to demonstrate the accuracy of this method. Results obtained from the proposed mathematical model give a good understanding of a structure's dynamic characteristics. The method is simple to use yet reasonably accurate and hence suitable for quick evaluations during preliminary design stages. Copyright © 2011 John Wiley & Sons, Ltd.
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A simple mathematical model for approximate analysis of tall buildings
Applied Mathematical Modelling, 2010Co-Authors: Reza Rahgozar, A. R. Ahmadi, Yasser SharifiAbstract:The focus of this article is to present a new and simple mathematical model that may be used to determine the optimum location of a belt truss reinforcing system on tall buildings such that the displacements due to lateral loadings would generate the least amounts of stress and strain in building’s structural members. The effect of belt truss and shear core on framed tube is modeled as a Concentrated Moment applied at belt truss location, this Moment acts in a direction opposite to rotation created by lateral loads. The axial deformation functions for flange and web of the frames are considered to be cubic and quadratic functions respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection, rotation of the plane section, and unknown coefficients of shear lag, the mathematical model is developed. The proposed model shows a good understanding of structural behavior; easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stage which requires less time. Numerical examples are given to demonstrate the ease of application and accuracy of the proposed modeled.
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An approximate analysis of combined system of framed tube, shear core and belt truss in high‐rise buildings
The Structural Design of Tall and Special Buildings, 2009Co-Authors: Reza Rahgozar, Yasser SharifiAbstract:In this paper a mathematical model for the combined system of framed tube, shear core and belt truss is developed with the objective of determining the optimum location of belt truss along the height of the building. The effect of belt truss and shear core on a framed tube is considered as a Concentrated Moment at the belt truss location. This Concentrated Moment acts in a direction opposite to rotation due to lateral loads. The axial deformation functions for web and flange of the frames are considered to be quadratic and cubic functions, respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection (u), rotation of the plane section (ϕ) and unknown coefficients of shear lag (α1, α2, β1 and β2), the mathematical model is developed. This model yields the displacement, axial stress distribution and bending stiffness as a function of the height of the combined system. The range application and validity of the proposed model is demonstrated by several numerical examples (30-, 40- and 50-storey buildings). The effects of belt truss position on lateral displacement and stress distribution are investigated and the optimum location for belt truss is obtained. Copyright © 2009 John Wiley & Sons, Ltd.
Turgut Kocatürk - One of the best experts on this subject based on the ideXlab platform.
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Steady State Response of Viscoelastically Corner Point-Supported Generally Orthotropic Rectangular Plates under the Effect of Sinusoidally Varying Moment
Turkish Journal of Engineering and Environmental Sciences, 2005Co-Authors: Turgut KocatürkAbstract:The vibration of generally orthotropic rectangular elastic plates having viscoelastic point supports at the corners is analyzed. Lagrange's equations are used to examine the free vibration characteristics and steady state response to a sinusoidally varying Moment affecting the center of a viscoelastically point-supported, generally orthotropic elastic plate of rectangular shape. For applying the Lagrange's equations, the trial function denoting the deflection of the plate is expressed in polynomial form. By using the Lagrange's equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the off-axis angle, of the mechanical properties, and of the damping of the supports to the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically for a Concentrated Moment at the center for various values of the mechanical properties characterizing the anisotropy of the plate material, for various off-axis angles and for various damping of supports for a given stiffness of supports. The results are given for the considered frequency range of the external periodical Moment. Convergence studies are performed. The validity of the results obtained is demonstrated by comparing them with the solutions of specially orthotropic plates based on the Kirchhoff-Love plate theory.
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Determination of the steady state response of viscoelastically corner point-supported rectangular specially orthotropic plates under the effect of sinusoidally varying Moment
Journal of Sound and Vibration, 2003Co-Authors: Turgut Kocatürk, Cihan Demir, Semih Sezer, Nihat İlhanAbstract:Abstract Vibration of orthotropic rectangular plates having viscoelastic point supports at the corners under the effect of sinusoidally varying Concentrated Moment is analyzed. The Lagrange equation is used to examine the free vibration characteristics and the steady state response to a sinusoidally varying Concentrated Moment acting at the centre of a viscoelastically point-supported orthotropic elastic plate of rectangular shape. In the study, for applying the Lagrange equation, the trial function denoting the deflection of the plate is expressed in the polynomial form. By using the Lagrange equation, the problem is reduced to the solution of a system of algebraic equations. The influence of the mechanical properties, and of the damping of the supports on the mode shapes and the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically, for a Concentrated Moment at the centre for various values of the mechanical properties which characterize the anisotropy of the plate material and for various damping ratios. The results of the natural frequencies are given for the first three antisymmetrical–symmetrical modes, and the steady state responses to a sinusoidally varying Concentrated Moment are determined for the frequency ranges of the first two antisymmetrical–symmetrical mode types. Convergence studies are made. The validity of the obtained results is demonstrated by comparing them with other solutions for free vibration analysis of point-supported or completely free rectangular plates for the first three antisymmetrical–symmetrical vibration modes based on the Kirchhoff–Love plate theory.
Xia Guiyu - One of the best experts on this subject based on the ideXlab platform.
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Transfer matrix method for the analysis of frame-shear wall structures including shear deformation effects of shear wall
2015Co-Authors: Xia GuiyuAbstract:Considering the shear deformation effect of shear wall and the rigid joint condition of connecting beam, a differential equation was presented for the analysis of frame-shear wall structures based on the variational principle. The initial parameter solutions to the differential equation were derived, and the transfer matrix method was put forward to analyze the frame-shear wall structures with variable stiffness. The additional items of calculations of frame-shear wallstructures subjected to the uniformly distributing load and triangularly distributing load were established using transfer matrix method. The deflection, slope, Moment and totel shear force were derived for frame-shear wall structures under the Concentrated load and Concentrated Moment on the top, the uniformly distributing load and triangularly distributing load along the height. By using two hinged systems of frame-shear wall structure as the examples, the derived formulae were checked. The results show that when the equivalent flexural stiffness of connecting beam is 0 k N·m/m, the fixed system is degenerated into the hinged system, and when the shear stiffness of shear wall tends to be infinite, the flexural-shear type shear wall is transformed into the flexural type shear wall without the shear deformation effects, so the present differential equation can be used to analyze multi models of frame-shear wall structures. For variable stiffness structures, the calculating results obtained by the present transfer matrix method agree with those of the analytical solutions obtained by the equivalent uniform stiffness, so both methods are feasible. To obtain high precision, the transfer matrix method and finite element method are preferred to adapt to the variable stiffness structures. When the shear deformation effect of shear wall is considered, the results obtained by the presented formulae in this paper differ from those obtained by other formulae.