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CONTENTS
Volume 42, Number 2, April25 2012
 

Abstract
In-plane free vibrations of circular beams with stepped cross-sections are investigated by using the exact analytical solution. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The stepped arch is divided into a number of arches with constant crosssections. The exact solution of the governing equations is obtained by the initial value method. Several examples of arches with different step ratios, different locations of the steps, boundary conditions, opening angles and slenderness ratios for the first few modes are presented to illustrate the validity and accuracy of the method. The effects of the geometric parameters on the natural frequencies are investigated in details. Several examples in the literature are solved and the results are given in tables. The agreement of the results is good for all examples considered. The mode transition phenomenon is also observed for the stepped arches. Some examples are solved also numerically by using the commercial finite element program ANSYS.

Key Words
curved beam; stepped arch; free vibration; in-plane; exact solution; mode transition

Address
Ekrem Tufekci and Oznur Ozdemirci Yigit: Faculty of Mechanical Engineering, Istanbul Technical University, Gumussuyu, TR34437 Istanbul, Turkey

Abstract
Micromechanical facture models can be used to predict ductile fracture in steel structures. In order to calibrate the parameters in the micromechanical models for the largely used Q345 steel in China, uniaxial tensile tests, smooth notched tensile tests, cyclic notched bar tests, scanning electron microscope tests and finite element analyses were conducted in this paper. The test specimens were made from base metal, deposit metal and heat affected zone of Q345 steel to investigate crack initiation in welded steel connections. The calibrated parameters for the three different locations of Q345 steel were compared with that of the other seven varieties of structural steels. It indicates that the toughness index parameters in the stress modified critical strain (SMCS) model and the void growth model (VGM) are connected with ductility of the material but have no correlation with the yield strength, ultimate strength or the ratio of ultimate strength to yield strength. While the damage degraded parameters in the degraded significant plastic strain (DSPS) model and the cyclic void growth model (CVGM) and the characteristic length parameter are irrelevant with any properties of the material. The results of this paper can be applied to predict ductile fracture in welded steel connections.

Key Words
ductile fracture; micromechanical fracture model; parameter calibration; ultra low cycle fatigue; structural steel

Address
Fangfang Liao: Department of Structural Engineering, Tongji University, Shanghai 200092, China
Wei Wang: Department of Structural Engineering, Tongji University, Shanghai 200092, China; State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, ChinaYiyi Chen: Department of Structural Engineering, Tongji University, Shanghai 200092, China; State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

Abstract
This paper presents an algorithm for structural reliability with the response surface method. For this aim, an approach with three stages is proposed named as improved response surface method. In the algorithm, firstly, a quadratic approximate function is formed and design point is determined with First Order Reliability Method. Secondly, a point close to the exact limit state function is searched using the design point. Lastly, vector projected method is used to generate the sample points and Second Order Reliability Method is performed to obtain reliability index and probability of failure. Five numerical examples are selected to illustrate the proposed algorithm. The limit state functions of three examples (cantilever beam, highly nonlinear limit state function and dynamic response of an oscillator) are defined explicitly and the others (frame and truss structures) are defined implicitly. ANSYS finite element program is utilized to obtain the response of the structures which are needed in the reliability analysis of implicit limit state functions. The results (reliability index, probability of failure and limit state function evaluations) obtained from the improved response surface are compared with those of Monte Carlo Simulation, First Order Reliability Method, Second Order Reliability Method and Classical Response Surface Method. According to the results, proposed algorithm gives better results for both reliability index and limit state function evaluations.

Key Words
response surface method; structural reliability; vector projected method

Address
Hasan Basri Basaga, Alemdar Bayraktar: Department of Civil Engineering, Karadeniz Technical University, 61080, Trabzon, Turkey
Irfan Kaymaz: Department of Mechanical Engineering, Ataturk University, 25240, Erzurum, Turkey

Abstract
The Force Density Method (FDM) is a well known and extremely versatile tool in form finding of cable nets. In its linear formulation such method makes it possible to find all the possible equilibrium configurations of a net of cables having a certain given connectivity and given boundary conditions on the nodes. Each singular configuration corresponds to an assumed force density distribution. Its improvement as Non-Linear Force Density Method (NLFDM) introduces the possibility of imposing assigned relative distances among the nodes, the tensile level in the elements and/or their initial undeformed length. In this paper an Extended Force Density Method (EFDM) is proposed, which makes it possible to set conditions in terms of given fixed nodal reactions or, in other words, to fix the positions of a certain number of nodes and, at the same time, to impose the intensity of the reaction force. Through such extension, the (EFDM) enables us to deal with form findings problems of cable nets subjected to given constraints and, in particular, with mixed structures, made of cables and struts. The efficiency and the robustness of method are assessed through comparisons with other form finding techniques in dealing with characteristic applications to the prestress design of cable systems. As a further extension, the EFDM is applied to structures having some parts not yet geometrically defined, as can happen in designing new creative forms.

Key Words
cable structures; form finding; force finding; force density method; new structural forms

Address
P.G. Malerba: Department of Structural Engineering, Politecnico di Milano, 20133 Milan, Italy
M. Patelli: Studio Malerba, 20133 Milan, Italy
M. Quagliaroli: Department of Structural Engineering, Politecnico di Milano, 20133 Milan, Italy

Abstract
Present study deals with the development of finite element based solution methodology to investigate active control of dynamic response of delaminated composite shells with piezoelectric sensors and actuators. The formulation is based on first order shear deformation theory and an eight-noded isoparametric element is used. A coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. For modeling the delamination, multipoint constraint algorithm is incorporated in the finite element code. A simple negative feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of delaminated composite shells in a closed loop employing Newmark\'s time integration scheme. The validity of the numerical model is demonstrated by comparing the present results with those available in the literature. A number of parametric studies such as the locations of sensor/actuator patches, delamination size and its location, radius of curvature to width ratio, shell types and loading conditions are carried out to understand their effect on the transient response of piezoceramic delaminated composite shells.

Key Words
active control; delamination; composite; shell; finite element; smart material

Address
Namita Nanda and Y. Nath: Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, 110016, India

Abstract
Bridge vibration displacements have been directly measured by LVDTs (Linear Variable Differential Transformers) or laser equipment and have also been indirectly estimated by an algorithm of integrating measured acceleration. However, LVDT measurement cannot be applied for a bridge crossing over a river or channel and the laser technique cannot be applied when the weather condition is poor. Also, double integration of accelerations may cause serious numerical deviation if the initial condition or a regression process is not carefully controlled. This paper presents an algorithm of estimating bridge vibration displacements using vibration strains measured by FBG (Fiber Bragg Grating) sensors and theoretical mode shapes of a simply supported beam. Since theoretically defined mode shapes are applied, even high modes can be used regardless of the quality of the measured data. In the proposed algorithm, the number of theoretical modes is limited by the number of sensors used for a field test to prevent a mathematical rank deficiency from occurring in compu ting vibration displacements.89The proposed algorithm has been applied to various types of bridges and its efficacy has been verified. The closeness of the estimated vibration displacements to measured ones has been evaluated by computing the correlation coefficient and by comparing FRFs (Frequency Response Functions) and the maximum displacements.

Key Words
vibration displacement, FBG sensors, theoretical mode shapes, correlation coefficient, FRF

Address
Soobong Shin, Sun-Ung Lee, Yuhee Kim: Department of Civil Engineering, Inha University, Incheon, Korea
Nam-Sik Kim: Department of Civil and Environmental Engineering, Pusan National University, Busan, Korea

Abstract
Calculating the displacements of retaining walls under seismic loads is a crucial part in optimum design of these structures and unfortunately the techniques based on active seismic pressure are not sufficient alone for an appropriate design of the wall. Using limit analysis concepts, the seismic displacements of retaining walls are studied in present research. In this regard, applying limit analysis method and upper bound theorem, a new procedure is proposed for calculating the yield acceleration, critical angle of failure wedge, and permanent displacements of retaining walls in seismic conditions for two failure mechanisms, namely sliding and sliding-rotational modes. Also, the effect of internal friction angle of soil, the friction angle between wall and soil, maximum acceleration of the earthquake and height of the wall all in the magnitude of seismic displacements has been investigated by the suggested method. Two sets of ground acceleration records related to near-field and far-field domains are employed in analyses and eventually the results obtained from the suggested method are compared with those from other techniques.

Key Words
limit analysis; retaining walls; seismic displacement; yield acceleration

Address
Mohammad Mojallal and Ali Ghanbari: Faculty of Engineering, Tarbiat Moallem University, No. 49 Mofatteh Ave., Tehran, I.R. Iran

Abstract
Free vibration and dynamic responses of piles semi-rigidly connected with the superstructures are investigated. Timoshenko beam theory is employed to characterize the pile partially embedded in a two-parameter elastic foundation. The formulations for the method of reverberation-ray matrix (MRRM) are then derived to investigate the dynamics of the pile with surface cracks, which are modeled as massless rotational springs. Comparison with existent numerical and experimental results indicates the proposed method is very effective and accurate for dynamic analysis, especially in the high frequency range. Finally, the effects of some physical parameters on the natural frequencies, frequency responses and transient responses of the piles are studied.

Key Words
pile; semi-rigid; timoshenko beam theory; reverberation-ray matrix; dynamic analysis

Address
Wei Yan: Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo 315211, P.R. China
W.Q. Chen: Department of Engineering Mechanics, Zhejiang University, Yuquan Campus, Hangzhou 310027, P.R. China


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