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CONTENTS
Volume 2, Number 4, December 2009
 

Abstract
We introduce a radial basis collocation method to solve axially moving beam problems which involve 2nd order differentiation in time and 4th order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, 4th order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

Key Words
radial basis function; collocation method; axially moving beam; strong form.

Address
Lihua Wang: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
Jiun-Shyan Chen: Civil & Environmental Engineering Department, University of California Los Angeles (UCLA),
Los Angeles, CA 90095, USA
Hsin-Yun Hu: Mathematics Department, Tunghai University, Taichung 4011, Taiwan, R.O.C.

Abstract
A new seamless multiscale simulation was developed for coupling the continuum model with its molecular dynamics. Kriging-based Finite Element Method (K-FEM) is employed to model the continuum base of the entire domain, while the molecular dynamics (MD) is confined in a localized domain of interest. In the coupling zone, where the MD domain overlaps the continuum model, the overall Hamiltonian is postulated by contributions from the continuum and the molecular overlays, based on a quartic spline scaling parameter. The displacement compatibility in this coupling zone is then enforced by the Lagrange multiplier technique. A multiple-time-step velocity Verlet algorithm is adopted for its time integration. The validation of the present method is reported through numerical tests of one dimensional atomic lattice. The results reveal that at the continuum/MD interface, the commonly reported spurious waves in the literature are effectively eliminated in this study. In addition, the smoothness of the transition from MD to the continuum can be significantly improved by either increasing the size of the coupling zone or expanding the nodal domain of influence associated with K-FEM.

Key Words
kriging interpolation; multiscale simulation; molecular dynamics.

Address
Wichain Sommanawat: School of Engineering and Technology, Asian Institute of Technology, Pathumthani 12120, Thailand
Worsak Kanok-Nukulchai: School of Engineering and Technology, Asian Institute of Technology, Pathumthani 12120, Thailand

Abstract
In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

Key Words
multiscale modeling; finite deformations; elasto-viscoplastic; polycrystalline materials.

Address
Karel Matou: Department of Aerospace and Mechanical Engineering, University of Notre Dame, 367 Fitzpatrick Hall of Engineering, Notre Dame, IN 46556-5637, USA
Antoinette M. Maniatty: Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, UAS

Abstract
The effect of soil-structure interaction on a simple single storeyed and two bay space frame resting on a pile group embedded in the cohesive soil (clay) with flexible cap is examined in this paper. For this purpose, a more rational approach is resorted to using the three dimensional finite element analysis with realistic assumptions. The members of the superstructure and substructure are descretized using 20 node isoparametric continuum elements while the interface between the soil and pile is modeled using 16 node isoparametric interface elements. Owing to viability in terms of computational resources and memory requirement, the approach of uncoupled analysis is generally preferred to coupled analysis of the system. However, an interactive analysis of the system is presented in this paper where the building frame and pile foundation are considered as a single compatible unit. This study is focused on the interaction between the pile cap and underlying soil. In the parametric study conducted using the coupled analysis, the effect of pile spacing in a pile group and configuration of the pile group is evaluated on the response of superstructure. The responses of the superstructure considered include the displacement at top of the frame and moments in the superstructure columns. The effect of soil-structure interaction is found to be quite significant for the type of foundation used in the study. The percentage variation in the values of displacement obtained using the coupled and uncoupled analysis is found in the range of 4-17 and that for the moment in the range of 3-10. A reasonable agreement is observed in the results obtained using either approach.

Key Words
soil-structure interaction; coupled analysis; uncoupled analysis; pile group; pile spacing; series arrangement; parallel arrangement; top displacement of frame and bending moment in columns.

Address
H. S. Chore: Department of Civil Engineering, Datta Meghe College of Engineering, Sector-3, Airoli, Navi Mumbai- 400 708, India
R. K. Ingle: Department of Applied Mechanics, Visvesvaraya National Institute of Technology (VNIT), Nagpur- 440 010, India
V. A. Sawant: Department of Civil Engineering, Indian Institute of Technology (IIT), Roorkee - 247 667, India

Abstract
The stator tooth is a key component of the electromechanical integrated toroidal drive system. The stator tooth is spiral in shape and the calculation of its displacements is difficult. In this paper, using the coordinate transformation method, the displacements of the stator tooth in the local coordinate system are expressed as the function of the variable in the drive coordinate system. Using the minimum potential energy principle, the equations of the displacements of the stator tooth under the loads are deduced. The displacement distributions within the stator tooth are investigated and the changes of the displacement distributions along with the main parameters are analyzed. This research can offer the basis for the strength and stiffness design of the drive system.

Key Words
toroidal drive; electromechanical integrated; displacement; strain energy.

Address
Lizhong Xu: Mechanical engineering institute, Yanshan University, Qinhuangdao 066004, China
Dazhou Zheng: Mechanical engineering institute, Yanshan University, Qinhuangdao 066004, China

Abstract
This paper presents a simple model for studying the dynamic response of multi-span bridges resting on piers with different heights and subjected to earthquake forces acting transversely to the bridge, but varying spatially along its length. The analysis is carried out using the modal superposition technique, while the solution of the resulting integral-differential equations is obtained via the Laplace transformation. It has been found that the piers height and the quality of the foundation soil can affect significantly the dynamic behavior of such bridges. Typical examples showing the effectiveness of the method are presented with useful results listed.

Key Words
bridge dynamics; piers; earthquake actions; transverse motion.

Address
George T. Michaltsos: Laboratory of Steel Structures, Department of Civil Engineering, National Technical University of Athens, 9 Iroon Polytechneiou St., Zografou Campus, Athens 15780, Greece
Ioannis G. Raftoyiannis: Laboratory of Steel Structures, Department of Civil Engineering, National Technical University of Athens, 9 Iroon Polytechneiou St., Zografou Campus, Athens 15780, Greece


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