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CONTENTS
Volume 33, Number 6, December20 2009
 

Abstract
In this paper a 3-D continuum damage mechanics formulation for composite laminates and its implementation into a finite element model that is based on the layer-wise laminate plate theory are described. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle ply composite laminates under quasi-static loading that exhibit the free edge effects are investigated. The effects of various numerical modeling parameters on the progressive damage response are investigated. It will be shown that the dominant damage mechanism in the lay-ups of [+30/-30]s and [+45/-45]s is matrix cracking. However, the lay-up of [+15/-15] may be delaminated in the vicinity of the edges and at +

Key Words
continuum damage mechanic; angle ply laminate; layer-wise; FEM.

Address
B. Mohammadi: School of Mechanical Engineering, Iran University of Science and Technology, University Road, Hengam Street, Resalat Square, Narmak, Tehran, Iran
H. Hosseini-Toudeshky: Aerospace Engineering Department & Center of Excellence in Computational Aerospace Engineering,
Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran
M.H. Sadr-Lahidjani: Aerospace Engineering Department, Amirkabir University of Technology, No. 424,
Hafez Ave., Tehran, Iran

Abstract
In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.

Key Words
differential quadrature; buckling load; natural frequency; boundary conditions; constitutive law; equilibrium.

Address
S. Rajasekaran: Department of Civil Engineering, PSG College of Technology, Coimbatore 641004, Tamilnadu, India
L. Gimena, P. Gonzaga and F.N. Gimena: Department of Projects Engineering, Campus Arrosadia C.P. 31006, Public University of Navarre, Pamplona, Navarra, Spain

Abstract
Stresses are solved for two parallel cracks in an infinite orthotropic plate during passage of incoming shock stress waves normal to their surfaces. Fourier transformations were used to reduce the boundary conditions with respect to the cracks to two pairs of dual integral equations in the Laplace domain. To solve these equations, the differences in the crack surface displacements were expanded to a series of functions that are zero outside the cracks. The unknown coefficients in the series were solved using the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors were defined in the Laplace domain and were inverted numerically to physical space. Dynamic stress intensity factors were calculated numerically for selected crack configurations.

Key Words
orthotropic material; two cracks; dynamic stress intensity factor; composite materials; Fourier transforms; numerical Laplace inversion.

Address
Shouetsu Itou: Department of Mechanical Engineering, Kanagawa University, Rokkakubashi, Kanagawa-ku, Yokohama 221-8686, Japan

Abstract
In this paper a free-free uniform beam with damping effects subjected to follower and transversal forces at its end is considered as a model for a space structure. The effect of damping on the stability of the system is first investigated and the effects of the follower and transversal forces on the vibration of the beam are shown next. Proportional damping model is used in this work, hence, the effects of both internal (material) and external (viscous fluid) damping on the system are noted. In order to derive the frequency of the system, the Ritz method has been used. The mode shapes of the system must therefore be extracted. The Newmark method is utilized in the study of the system vibration. The results show that an increase in the follower and transversal forces leads to an increase of the vibrational motion of the beam which is not desirable.

Key Words
beam instability; non-conservative force; follower force; proportional damping; vibration analysis.

Address
O. Kavianipour: Department of Aerospace Engineering, K. N. T. University of Technology, Tehran, Iran
S.H. Sadati: Department of Mechanical Engineering, K. N. T. University of Technology, Tehran, Iran

Abstract
In this paper, probabilistic seismic performance assessment of a typical non-seismic RC frame building representative of a large inventory of existing buildings in developing countries is conducted. Nonlinear time-history analyses of the sample building are performed with 20 large-magnitude medium distance ground motions scaled to different levels of intensity represented by peak ground acceleration and 5% damped elastic spectral acceleration at the first mode period of the building. The hysteretic model used in the analyses accommodates stiffness degradation, ductility-based strength decay, hysteretic energy-based strength decay and pinching due to gap opening and closing. The maximum inter story drift ratios obtained from the time-history analyses are plotted against the ground motion intensities. A method is defined for obtaining the yielding and collapse capacity of the analyzed structure using these curves. The fragility curves for yielding and collapse damage levels are developed by statistically interpreting the results of the time-history analyses. Hazard-survival curves are generated by changing the horizontal axis of the fragility curves from ground motion intensities to their annual probability of exceedance using the log-log linear ground motion hazard model. The results express at a glance the probabilities of yielding and collapse against various levels of ground motion intensities.

Key Words
non-seismic; RC frames; Incremental Dynamic Analysis (IDA); seismic performance; fragility curves; yielding; collapse; hazard survival.

Address
M.M. Maniyar: Department of Structural Engineering, S.P.C.E., Mumbai - 400058, India
R.K. Khare: Department of Civil Engineering, S.G.S. Institute of Technology & Science, Indore - 452003, India
R.P. Dhakal: Department of Civil and Natural Resources Engineering, University of Canterbury,Private Bag 4800, Christchurch, New Zealand

Abstract
In this work, the linear vibration characteristics of 90o pipe bends and their cylindrical and toroidal shell components are studied. The finite element method, based on shear-deformation shell elements, is used to carry out a vibration analysis of metallic multiple 90o mitred pipe bends. Single, double, and triple mitred bends are considered, as well as a smooth bend. Sample natural frequencies and mode shapes are given. To validate the procedure, comparison of the natural frequencies is made with existing results for cylindrical and toroidal shells. The influence of the multiplicity of the bend, the boundary conditions, and the various geometric parameters on the natural frequency is described. The differential quadrature method, based on classical shell theory, is used to study the vibration of components of these bends. Regression formulas are derived for cylindrical shells (straight pipes) with one or two oblique edges, and for sectorial toroidal shells (curved pipes, pipe elbows). Two types of support are considered for each case. The results given provide information about the vibration characteristics of pipe bends over a wide range of the geometric parameters.

Key Words
finite element method; pipe bend; natural frequencies; mode shapes.

Address
D. Redekop and D. Chang: Department of Mechanical Engineering, University of Ottawa, Canada K1N 6N5

Abstract
Quantitative condition assessment of structures has been traditionally using proof load test leading to an indication of the load-carrying capacity. Alternative approaches using ultrasonic, dynamics etc. are based on the unloaded state of the structure and anomalies may not be fully mobilized in the load resisting path and thus their effects are not fully included in the measured responses. This paper studies the effect of the load carried by a reinforced concrete beam on the assessment result of the crack damage. This assessment can only be performed with an approach based on static measurement. The crack damage is modelled as a crack zone over an area of high tensile stress of the member, and it is represented by a damage function for the simulation study. An existing nonlinear optimization algorithm is adopted. The identified damage extent from a selected high level load and a low load level are compared, and it is concluded that accurate assessment can only be obtained at a load level close to the one that creates the damage.

Key Words
reinforced concrete; beam; damage; assessment; inverse problem; finite element; crack; static load; deflection.

Address
X.Q. Zhu: School of Engineering, The University of Western Sydney, Kingswood Campus, NSW 1797, Australia
S.S. Law: Civil and Structural Engineering Department, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, P. R. China
H. Hao: School of Civil and Resource Engineering, The University of Western Australia, Crawley, WA 6009, Australia

Abstract
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Key Words
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Address
Ren Xiaohui and Chen Wanji: State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China
Institute for Structural Analysis of Aerocraft, Shenyang Institute of Aeronautical Engineering, Shenyang 110136, China

Abstract
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Key Words
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Address
Baizhi Wang, Qingmin Yu, Naixian Hou and Zhufeng Yue:
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi

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