Techno Press


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CONTENTS
Volume 36, Number 5, November30 2010
 

Abstract
Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko\'s equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

Key Words
equilibrium path; limit point; snap-through; snap-back; Davidenko

Address
Tabatabaei, R.: Islamic Azad University, Kerman Branch, Civil Engineering Department, PO Box 76175-6114, Kerman, Iran
Saffari, H.: Shahid Bahonar University, Civil Engineering Department, Kerman, Iran

Abstract
Two or more distinct materials are combined into a single functionally graded material (FGM) where the microstructural composition and properties change gradually. Thermal post-buckling behavior of uniform slender FGM beams is investigated independently using the classical Rayleigh-Ritz (RR) formulation and the versatile Finite Element Analysis (FEA) formulation developed in this paper. The von-Karman strain-displacement relations are used to account for moderately large deflections of FGM beams. Bending-extension coupling arising due to heterogeneity of material through the thickness is included. Simply supported and clamped beams with axially immovable ends are considered in the present study. Post-buckling load versus deflection curves and buckled mode shapes obtained from both the RR and FEA formulations for different volume fraction exponents show an excellent agreement with the available literature results for simply supported ends. Response of the FGM beam with clamped ends is studied for the first time and the results from both the RR and FEA formulations show a very good agreement. Though the response of the FGM beam could have been studied more accurately by FEA formulation alone, the authors aim to apply the RR formulation is to find an approximate closed form post-buckling solutions for the FGM beams. Further, the use of the RR formulation clearly demonstrates the effect of bending-extension coupling on the post-buckling response of the FGM beams.

Key Words
Rayleigh-Ritz; finite element analysis; post-buckling; functionally graded materials; loaddeflection curves; geometric non-linearity; closed form solution.

Address
K. Sanjay Anandrao: Advanced Systems Laboratory, Kanchanbagh, Hyderabad - 500 058, India
R.K. Gupta1a: Advanced Systems Laboratory, Kanchanbagh, Hyderabad - 500 058, India
P. Ramchandran: Defense Research and Development Laboratory, Kanchanbagh, Hyderabad - 500 058, India
G. Venkateswara Rao: School of Mechanical Engineering, Sreenidhi Institute of Science and Technology, Hyderabad - 501 301, India

Abstract
The potential of the liquid column vibration absorber (LCVA) as a seismic vibration control device for structures has been explored in this paper. In this work, the structure has been modeled as a linear, viscously damped single-degree-of-freedom (SDOF) system. The governing differential equations of motion for the damper liquid and for the coupled structure-LCVA system have been derived from dynamic equilibrium. The nonlinear orifice damping in the LCVA has been linearized by a stochastic equivalent linearization technique. A transfer function formulation for the structure-LCVA system has been presented. The design parameters of the LCVA have been identified and by applying the transfer function formulation the optimum combination of these parameters has been determined to obtain the most efficient control performance of the LCVA in terms of the reduction in the root-mean-square (r.m.s.) displacement response of the structure. The study has been carried out for an example structure subjected to base input characterized by a white noise power spectral density function (PSDF). The sensitivity of the performance of the LCVA to the coefficient of head loss and to the tuning ratio have also been examined and compared with that of the liquid column damper (LCD). Finally, a simulation study has been carried out with a recorded accelerogram, to demonstrate the effectiveness of the LCVA.

Key Words
liquid column vibration absorber; seismic vibration control; power spectral density function; simulation.

Address
Tanmoy Konara: Department of Civil Engineering, Bengal Engineering and Science University, Shibpur, Howrah, India
Aparna (Dey) Ghosh: Department of Civil Engineering, Bengal Engineering and Science University, Shibpur, Howrah, India

Abstract
The shape and size of the plastic zone around the crack tip are analyzed under pure mode I, pure mode II and mixed mode (I+II) loading for small scale yielding and for both plane stress and plane strain conditions. A new analytical formulation is presented to determine the radius of the plastic zone in a non-dimensional form. In particular, the effect of T-stress on the plastic zone around the crack tip is studied. The results of this investigation indicate that the stress field with a T-stress always yields a larger plastic zone than the field without a T-stress. It is found that under predominantly mode I loading, the effect of a negative T-stress on the size of the plastic zone is more dramatic than a positive T-stress. However, when mode II portion of loading is dominating the effect of both positive and negative Tstresses on the size of the plastic zone is almost equal. For validating the analytical results, several finite element analyses were performed. It is shown that the results obtained by the proposed analytical formulation are in very good agreements with those obtained from the finite element analyses.

Key Words
plastic zone; crack; mixed mode (I+II); T-stress; analytical method.

Address
M.R. Ayatollahi: Fatigue and Fracture Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics,
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran
Karo Sedighiani: Fatigue and Fracture Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics,
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran

Abstract
Offshore wind turbines are relatively complex structural and mechanical systems located in a highly demanding environment. In the present paper the fundamental aspects and the major issues related to the design of these special structures are outlined. Particularly, a systemic approach is proposed for a global design of such structures, in order to handle coherently their different parts: the decomposition of these structural systems, the required performance and the acting loads are all considered under this philosophy. According to this strategy, a proper numerical modeling requires the adoption of a suitable technique in order to organize the qualitative and quantitative assessments in various sub-problems, which can be solved by means of sub-models at different levels of detail, for both structural behavior and loads simulation. Specifically, numerical models are developed to assess the safety performances under aerodynamic and hydrodynamic actions. In order to face the problems of the actual design of a wind farm in the Mediterranean Sea, in this paper, three schemes of turbines support structures have been considered and compared: the mono pile, the tripod and the jacket support structure typologies.

Key Words
offshore wind turbines; systemic approach; numerical modeling; environmental actions; structural analysis and design.

Address
Francesco Petrini: School of Engineering, University of Rome \"La Sapienza\", Via Eudossiana 18, 00184 Rome, Italy
Hui Li:Harbin Institute of Technology, P.O.B. 2537, 204 Haihe Road, Harbin, 150090, China
Franco Bontempi: School of Engineering, University of Rome \"La Sapienza\", Via Eudossiana 18, 00184 Rome, Italy

Abstract
The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Key Words
displacement fields; stress-resultant fields; Mindlin-Reissner plate theory; Integrated Force Method.

Address
H.R. Dhananjaya: Department of Civil Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur – 50603, Malaysia, (Manipal Institute of Technology, Manipal – 576 104, India)
J. Nagabhushanam: Department of Aerospace Engineering, Indian Institute of Science Bangalore – 560 012, India
P.C. Pandey: Department of Civil Engineering, Indian Institute of Science Bangalore – 560 012, India
Mohd. Zamin Jumaat: Department of Civil Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur – 50603, Malaysia

Abstract
The classical flexibility difference method detects damage by observing the difference of conventional deflection flexibility matrices between pre- and post-damaged states of a structure. This method is not able to identify multiple damage scenarios, and its criteria to identify damage depend upon the boundary conditions of structures. The key point behind the inability and dependence is revealed in this study. A more feasible flexibility for damage detection, the Angle-between-String-and-Horizon (ASH) flexibility, is proposed. The physical meaning of the new flexibility is given, and synthesis of the new flexibility matrix by modal frequencies and translational mode shapes is formulated. The damage indicators are extracted from the difference of ASH flexibility matrices between the pre- and postdamaged structures. One feature of the ASH flexibility is that the components in the ASH flexibility matrix are associated with elements instead of Nodes or DOFs. Therefore, the damage indicators based on the ASH flexibility are mapped to structural elements directly, and thus they can pinpoint the damaged elements, which is appealing to damage detection for complex structures. In addition, the change in the ASH flexibility caused by damage is not affected by boundary conditions, which simplifies the criteria to identify damage. Moreover, the proposed method can determine relatively the damage severity. Because the proposed damage indicator of an element mainly reflects the deflection change within the element itself, which significantly reduces the influence of the damage in one element on the damage indicators of other damaged elements, the proposed method can identify multiple damage locations. The viability of the proposed approach has been demonstrated by numerical examples and experimental tests on a cantilever beam and a simply supported beam.

Key Words
flexibility; angle-between-string-and-horizon flexibility; damage detection.

Address
Guirong Yan: School of Engineering, University of Western Sydney, Penrith, NSW, 1797, Australia
Zhongdong Duan: Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
Jinping Ou: School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian, 116024, China; School of Civil Engineering, Harbin Institute of Technology, Harbin, 150090, China


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