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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Interaction and multiscale mechanics
Journal Basic Information
Journal DOI :
Editor in Chief :
J. S. Chen / Y.B. Yang / C. S. David Chen
Volume & Issues
Volume 2, Issue 4 - Dec 2009
Volume 2, Issue 3 - Sep 2009
Volume 2, Issue 2 - Jun 2009
Volume 2, Issue 1 - Mar 2009
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The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams
Lim, C.W. ; Li, C. ; Yu, J.L. ;
Interaction and multiscale mechanics, volume 2, issue 3, 2009, Pages 223~233
DOI : 10.12989/imm.2009.2.3.223
This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.
Strain localization and failure load predictions of geosynthetic reinforced soil structures
Alsaleh, Mustafa ; Kitsabunnarat, Akadet ; Helwany, Sam ;
Interaction and multiscale mechanics, volume 2, issue 3, 2009, Pages 235~261
DOI : 10.12989/imm.2009.2.3.235
This study illustrates the differences between the elasto-plastic cap model and Lade`s model with Cosserat rotation through the analyses of two large-scale geosynthetic-reinforced soil (GRS) retaining wall tests that were brought to failure using a monotonically increasing surcharge pressure. The finite element analyses with Lade`s model were able to reasonably simulate the large-scale plane strain laboratory tests. On average, the finite element analyses gave reasonably good agreement with the experimental results in terms of global performances and shear band occurrences. In contrast, the cap model was not able to simulate the development of shear banding in the tests. In both test simulations the cap model predicted failure loads that were substantially less than the measured ones.
Vehicle/bridge interactions of a rail suspension bridge considering support movements
Yau, J.D. ;
Interaction and multiscale mechanics, volume 2, issue 3, 2009, Pages 263~276
DOI : 10.12989/imm.2009.2.3.263
This paper is intended to investigate interaction response of a train running over a suspension bridge undergoing support settlements. The suspension bridge is modeled as a single-span suspended beam with hinged ends and the train as successive moving oscillators with identical properties. To conduct this dynamic problem with non-homogeneous boundary conditions, this study first divides the total response of the suspended beam into two parts: the static and dynamic responses. Then, the coupled equations of motion for the suspended beam carrying multiple moving oscillators are transformed into a set of nonlinearly coupled generalized equations by Galerkin`s method, and solved using the Newmark method with an incremental-iterative procedure including the three phases: predictor, corrector, and equilibrium-checking. Numerical investigations demonstrate that the present iterative technique is available in dealing with the dynamic interaction problem of vehicle/bridge coupling system and that the differential movements of bridge supports will significantly affect the dynamic response of the running vehicles but insignificant influence on the bridge response.
Convergence studies for Enriched Free Mesh Method and its application to fracture mechanics
Matsubara, Hitoshi ; Yagawa, Genki ;
Interaction and multiscale mechanics, volume 2, issue 3, 2009, Pages 277~293
DOI : 10.12989/imm.2009.2.3.277
The Enriched Free Mesh Method (EFMM) is a patch-wise procedure in which both a displacement field on an element and a stress/strain field on a cluster of elements connected to a node can be defined. On the other hand, the Superconvergent Patch Recovery (SPR) is known to be an efficient post-processing procedure of the finite element method to estimate the error norm at a node. In this paper, we discuss the relationship between solutions of the EFMM and those of the SPR through several convergence studies. In addition, in order to solve the demerit of the smoothing effect on the fracture mechanics fields, we implement a singular stress field to a local patch in the EFMM, and its effectiveness is investigated.
A study on convergence and complexity of reproducing kernel collocation method
Hu, Hsin-Yun ; Lai, Chiu-Kai ; Chen, Jiun-Shyan ;
Interaction and multiscale mechanics, volume 2, issue 3, 2009, Pages 295~319
DOI : 10.12989/imm.2009.2.3.295
In this work, we discuss a reproducing kernel collocation method (RKCM) for solving
order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.
Stress analysis of a two-phase composite having a negative-stiffness inclusion in two dimensions
Wang, Yun-Che ; Ko, Chi-Ching ;
Interaction and multiscale mechanics, volume 2, issue 3, 2009, Pages 321~332
DOI : 10.12989/imm.2009.2.3.321
Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young`s modulus of the inclusion is negative. Assumption of negative stiffness is a priori in the present analysis. For stress analysis, a closed form solution for the HS model and finite element solutions for the 2D composite are presented. A static loading condition is adopted to estimate the effective modulus of the composites by the ratio of stress to average strain on the loading edges. It is found that the interfacial stresses between the circular inclusion and matrix increase dramatically when the negative stiffness is so tuned that overall stiffness is unbounded. Furthermore, it is found that stress distributions in the inclusion are not uniform, contrary to Eshelby`s theorem, which states, for two-phase, infinite composites, the inclusion`s stress distribution is uniform when the shape of the inclusion has higher symmetry than an ellipse. The stability of the composites is discussed from the viewpoint of deterioration of perfect interface conditions due to excessive interfacial stresses.