X-FEM (eXtended Finite Element Method) is a powerful method to handle arbitrary shaped domain with fixed mesh by introducing embedded functions in element-wise approximation, as an alternative of conventional FEM, which is very effective for moving boundary problems such as crack propagations, two-phase flow problems and optimal design. However there exist two sources of numerical error in X-FEM, caused from the poor geometrical representation in partitioned numerical integration and the discretized error in fixed mesh as in usual FEM. Since the quality of optimal design greatly depends on the quality of CAE solution, this is a big issue if you apply X-FEM to optimal design seriously. In this paper, we'll newly propose a two-step algorithm with geometrical error control by partitioned numerical integration and h-adaptation with posteriori error estimation for X-FEM.

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In the present paper, we discuss the accuracy improvement for the free mesh method: a node based finite element technique. We propose here a scheme where the strain field is defined over clustered local elements in addition to the standard finite element method field. In order to determine the unknown parameter, the Hellinger-Reissner Principle is employed. Through some bench mark examples, the proposed technique has shown excellent performances.

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This paper describes the parallel enriched Free Mesh Method, intending the large scale analysis by saving of memories. Saving of memories is attained by using the node by node technique.

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In recent years computer performance has been improving by laps and bounds. Simultaneously, numerical computation technology is also developing greatly. On the other hand, objects for analysis are becoming increasingly large-scale and complicated. Large-scale analysis needs much computational complexity including unnecessary calculation. Re-meshing function prevents the unnecessary increase in computational cost. In this paper, we discribe the remeshing technique by using the Free Mesh Method.

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J-integral is the major fracture parameter and many evaluation methods have been proposed for three-dimensional problems. But there are usually some limitations with mesh patterns in neighbor of the crack front for each evaluation method. These limitations are not fundamental but may be fatal for comparison the results to other calculations with different crack shape, different mesh pattern or different evaluation method by other researchers. The authors proposed a simple evaluation method of J-integral independent from mesh pattern. The solution is obtained by usual FEM, but J-integral is evaluated with a simple path independently defined from the mesh pattern. The required values are interpolated by Moving Least Square (MLS) method. MLS method is often used to interpolate approximated solutions in meshless method with locally distributed nodes data. Some numerical examples will be presented to show validity and effectiveness of the proposed method.

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Ab initio analyses on ideal tensile strength of Cu nano-films with 1, 3 and 6 atomic layers are conducted, and the results are compared with that of the bulk. 1-layer film has the highest Young's modulus and the ideal strength, and as the thickness of the film increases, the strength decreases and approaches to the bulk value. This is because electrons shift to inter-layer regions from atomic layers to combine the layers in the film, which causes weak binding of atoms against in-plane tension.

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Atomic structure of PbTiO_3 with the polarization parallel to the surface and its response to in-plane isotropic strain are investigated using ab initio calculations. Termination-dependence of ferroelectricity (FE) is found: suppression at TiO_2-termination and enhancement at PbO-termination. Tensile strain enhances FE, while the opposite behavior is found under compression in both TiO_2- and PbO-terminations. On the other hand, antiferrodistortive (AFD) rotation is suppressed by tensile strain. At c (2×2) PbO-terminated surface, where FE and AFD coexists, FE and AFD compete against each other.

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Plastic bending deformation of single-wall carbon nanotubes (SWNTs) is analyzed using minimum energy path calculation with a bond-order potential. The calculation demonstrates that plastic deformation is thermodynamically favorable above a threshold "yield curvature" ρ_<yield>, and is also kinetically feasible above 1500K, which agree with our experimental observations. A deformation mechanism map as function of temperature and bending curvature is constructed, and the dependence of ρ_<yield> on the nanotube diameter is analyzed.

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The transition among C_<84> fullerene isomers is investigated by using molecular simulations, where the sequence of the typical long time-scale intermittent isomerization reaction called Stone-Wales transformation is realized by using temperature-accelerated dynamics (TAD) method. A transition path-map obtained through the TAD simulations indicates that some specific isomers should be preferred as a stable point. The equilibrium state is calculated assuming the transition to be in Markov chain, and shows that the isomer production ratio depends rather on the transition path than on the symmetricity of the structure.

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By using molecular dynamics method, helium, neon, and argon ion impacts on an amorphous carbon are simulated for the acceleration energy E_a ranging from 10 to 800eV in order to investigate the sputtering properties. The sputtering yield and probability increase linearly to the acceleration energy for around E_a&le;200eV and saturate for E_a>200eV while the penetration depth is simply proportional to the acceleration energy. The sputtering yield and probability take the maximum for the incident angle around 25 to 40 degrees where the energetic ion may stir the target around the surface.

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We have developed the periodic FMM in Helmholtz' equation in 2D. Indeed periodic boundary problems are deemed to be more and more important in engineering. In particular, photonic cristals, which have periodic structures, attract a great deal of interest as new types of optic devices in the field of electronics. As the first step of development of the solver of models of such periodic devices, we focus on scattering problems with cracks in 2D in this reserch. Through numerical analyses, the stop-band phenomenon is observed, which is the typical of photonic cristals.

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