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CONTENTS
Volume 43, Number 3, August10 2012
 

Abstract
Structural reanalysis is frequently used to reduce the computational cost during the process of design or optimization. The supports can be regarded as the design variables in various types of structural optimization problems. The location, number, and type of supports may be varied in order to yield a more effective design. The paper is focused on structural static reanalysis problem with added supports where some node displacements along axes of the global coordinate system are specified. A new approach is proposed and exact solutions can be provided by the approach. Thus, it belongs to the direct reanalysis methods. The information from the initial analysis has been fully exploited. Numerical examples show that the exact results can be achieved and the computational time can be significantly reduced by the proposed method.

Key Words
structural static reanalysis; Cholesky factorization; increase of support constraints; stiffness matrix; computational cost

Address
Haifeng Liu: Department of Mathematics, School of Mathematics and Statistics, Xi\'an Jiaotong University,
Xi\'an 710049, P.R. China
Baisheng Wu: Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, Changchun 130012, P.R. China
Zhengguang Li: Department of Mathematics, School of Mathematics and Statistics, Xi\'an Jiaotong University,
Xi\'an 710049, P.R. China


Abstract
Precast segmental bridge columns (PSBC) are alternatives for monolithic cast-in-situ concrete columns in bridge substructures, with fast construction speed and structural durability. The analytical tool for common use is demonstrated applicable for seismic performance prediction of PSBCs through experiment conducted earlier. Then the analytical program was used for parameter optimization of PSBC configurations under reversal cyclic loading. Shear strength by pushover analysis was compared with theoretical prediction. Moreover, seismic response of PSBC with energy dissipation (ED) bars was compared with its no ED bar counterpart under three history ground acceleration records. The investigation shows that appropriate ED bar and post-tensioned tendon arrangement is important for higher lateral bearing capacity and good ductility performance of PSBCs.

Key Words
bridge construction; concrete precast; pier; shear strength; seismic response; hollow sections; finite element method

Address
Z.Y. Bu, Y. Ding: Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Zhejiang Ningbo 315211, China
J. Chen: Architectural Design and Research Institute of Ningbo University Co. Ltd., Zhejiang Ningbo 315211, China
Y.S. Li: Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Zhejiang Ningbo 315211, China

Abstract
The higher-order asymptotic C(t) − A2(t) approach was employed to investigate the crack-tip stress of two collinear cracks in a power-law creeping material under the plane strain conditions. A comprehensive calculation was made of the single crack, collinear crack model with S/a = 0.4 and 0.8, by using the C(t) − A2(t) approach, HRR-type field and the finite element analysis; the latter two methods were used to check the constraint significance and the calculation accuracy of the C(t) − A2(t) approach, respectively. With increasing the creep time, the constraint A2 was exponentially increased in the smallscale creep stage, while no discernible dependency of the constraint A2 on the creep time was found at the extensive creep state. In addition, the creep time and the mechanical loads have no distinct influence on accuracy of the results obtained from the higher-order asymptotic C(t) − A2(t) approach. In comparison with the HRR-type field, the higher-order asymptotic C(t) − A2(t) solution matches well with the finite element results for the collinear crack model.

Key Words
constraint; creep; plane strain; interacting cracks; C(t) − A2(t) approach

Address
Guang-Chen Jiao: Key Lab of Education Ministry of China for Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
Wei-Zhe Wang: Key Lab of Education Ministry of China for Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China; Stat Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
Pu-Ning Jiang: Key Lab of Education Ministry of China for Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China

Abstract
As an improvement on the isoparametric element method, the derivation presented in this paper is close to that done by Wang (1990) for the 2-D finite element. We extend this idea to solve 3-D crack problems in this paper. A new displacement modelling is constructed with local solutions of threedimensional cracks and a quasi-compatible isoparametric element for three-dimensional fracture mechanics analysis is presented. The stress intensity factors can be solved directly by means of the present method without any post-processing. A new method for calculating the stress intensity factors of three-dimensional cracks with complex geometries and loads is obtained. Numerical examples are given to demonstrate the validity of the present method. The accuracy of the results obtained by the proposed element is demonstrated by solving several crack problems. The results illustrate that this method not only saves much calculating time but also increases the accuracy of solutions. Because this quasi-compatible finite element of 3-D cracks contains any singularities and easily meets the requirement of compatibility, it can be easily implemented and incorporated into existing finite element codes.

Key Words
crack; stress intensity factor; singular element; finite element method

Address
Zongjie Cao and Yongyu Liu: Department of Aviation Mechanical Engineering, Aviation University of Air Force,
Changchun, 130022, China

Abstract
In this study, Hamiltonian Approach (HA) is applied to analysis the nonlinear free vibration of beams. Two well-known examples are illustrated to show the efficiency of this method. One of them deals with the Nonlinear vibration of an electrostatically actuated microbeam and the other is the nonlinear vibrations of tapered beams. This new approach prepares us to achieve the beam\'s natural frequencies and mode shapes easily and a rapidly convergent sequence is obtained during the solution. The effects of the small parameters on the frequency of the beams are discussed. Some comparisons are conducted between the results obtained by the Hamiltonian Approach (HA) and numerical solutions using to illustrate the effectiveness and convenience of the proposed methods.

Key Words
non-linear vibration; hamiltonian approach; electrostatically actuated microbeam; tapered beams

Address
M. Bayat and I. Pakar: Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Abstract
Variable-node finite element families, termed (4 + k + l + m + n)-node elements with an arbitrary number of nodes (k, l, m, and n) on each of their edges, are developed based on the generic point interpolation with special bases having slope discontinuities in two-dimensional domains. They retain the linear interpolation between any two neighboring nodes, and passes the standard patch test when subdomain-wise 2 x 2 Gauss integration is employed. Their shape functions are automatically generated on the master domain of elements although a certain number of nodes are inserted on their edges. The elements can provide a flexibility to resolve nonmatching mesh problems like mesh connection and adaptive mesh refinement. In the case of adaptive mesh refinement problem, so-called \"1-irregular node rule\" working as a constraint in performing mesh adaptation is relaxed by adopting the variable-node elements. Through several examples, we show the performance of the variable-node finite elements in terms of accuracy and efficiency.

Key Words
variable-node finite elements; transition elements; nonmatching meshes; adaptive mesh refinement; 1-irregular node rule; mesh connection

Address
Jae Hyuk Lim: Satellite Structure Department, Korea Aerospace Research Institute (KARI), 169-84 Gwahak-ro, Yuseong-gu, Daejeon 305-806, Korea
Dongwoo Sohn: Division of Mechanical and Energy Systems Engineering, College of Engineering, Korea Maritime University, 727 Taejong-ro, Yeongdo-gu, Busan 606-791, Korea
Seyoung Im: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea

Abstract
Accurate finite element (FE) models are needed in many applications of Civil Engineering such as health monitoring, damage detection, structural control, structural evaluation and assessment. Model accuracy depends on both the model structure (the form of the equations) and the model parameters (the coefficients of the equations), and can be generally improved through that process of experimental reconciliation known as model updating. However, modelling errors, including (i) errors in the model structure and (ii) errors in parameters excluded from adjustment, may bias the solution, leading to an updated model which replicates measurements but lacks physical meaning. In this paper, an application of ambient-vibration-based model updating to a large-scale benchmark prototype of a building structure is reported in which both types of error are met. The error in the model structure, originating from unmodelled secondary structural elements unexpectedly working as resonant appendages, is faced through a reduction of the experimental modal model. The error in the model parameters, due to the inevitable constraints imposed on parameters to avoid ill-conditioning and under-determinacy, is faced through a multi-model parameterization approach consisting in the generation and solution of a multitude of models, each characterized by a different set of updating parameters. Results show that modelling errors may significantly impair updating even in the case of seemingly simple systems and that multimodel reasoning, supported by physical insight, may effectively improve the accuracy and robustness of calibration.

Key Words
model updating; modelling errors; multi-model parameterization; ambient vibration; secondary structural elements; resonant appendages

Address
E. Matta and A. De Stefano: Department of Structural and Geotechnical Engineering, Politecnico di Torino, Italy

Abstract
The visualizing energy flow and control in vibrating stiffened plates with a cutout are studied using finite element method. The vibration intensity, vibration energy and strain energy distribution of stiffened plates with cutout at different excitation frequencies are calculated respectively and visualized for the various cases. The cases of different size and boundaries conditions of cutouts are also investigated. It is found that the cutout or opening completely changes the paths and distributions of the energy flow in stiffened plate. The magnitude of energy flow is significantly larger at the edges near the cutout boundary. The position of maximum strain energy distribution is not corresponding to the position of maximum vibrational energy. Furthermore, the energy-based control using constrained damping layer (CDL) for vibration suppression is also analyzed. According to the energy distribution maps, the CDL patches are applied to the locations that have higher energy distribution at the targeted mode of vibration. The energybased CDL treatments have produced significant attenuation of the vibration energy and strain energy. The present energy visualization technique and energy-based CDL treatments can be extended to the vibration control of vehicles structures.

Key Words
stiffened plates; cutout; visualization; energy control; constrained damping layer; finite element method

Address
Kai Li: China Ship Development and Design Center, Wuhan 430064, P.R. China
Sheng Li and De-you Zhao: State Key Laboratory of Structural Analysis for Industrial Equipment, School of Naval Architecture, Dalian University of Technology, Dalian 116024, P.R. China


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