Segmentation is a critical and necessary procedure of reverse engineering with the aim of partitioning scanner data or polygonal meshes into meaningful parts. In this paper, an automatic segmentation technique is proposed for triangular meshes with the identification of surface types of the mesh segments according to the following surface's classification: the planar, cylindrical, conical, spherical, and toroidal surfaces, extrusion surfaces, ruled surfaces, and filleted surfaces. Sharp edges are detected and identified as boundaries of segments. An assumption-verification method is developed for extracting the mesh segments which identified according to surface's classification. The sequence of the extraction of the mesh segments is determined according to the dimensions and shapes of the Gauss maps of the segments. The algorithm starts from calculating normal vectors and principle curvatures of the neighborhoods of nearby mesh vertices of the triangle meshes to identify sharp edges and areas with high curvature. Triangles of the segments are assembled based on region growing method where the sharp edges are defined as boundaries of the segments. A fundamental partitioning the surface mesh based on sharp edges allows the accurate identification of the surfaces of the segments based on delicately proposed fitting technique and statistical error distribution.

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An explicit MPS algorithm is much faster to analyze free surface flow than the traditional semi-implicit algorithm. However, validation of the algorithm has not been studied enough. This paper shows comparisons about numerical stability and accuracy of pressure the between explicit and semi-implicit MPS in a hydrostatic pressure problem and a dam break problem. Pressure oscillations by the explicit MPS is as the same lebel as those of the semi-implicit MPS. In the hydrostatic pressure problem, the time average of pressure is equal to its theoretical value. With Mach number 0.2, compressibility is about 1.0 percent from the initial state. It is shown by both of the calculation and theory. The explicit MPS is as accurate as the semi-implicit MPS with less calculation costs.

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This paper proposes a simulation-based design (SBD) framework for fluid and fluid-structure interactions that allows to use it without generation of boundary-fitted meshes for fluid domains. Simulation techniques featuring this framework are developed in advanced computational technologies of the eXtended finite element method (X-FEM). A shape measuring instrument for obtaining three-dimensional CAD data of simulation objects is connected to this framework for showing potential usability of the proposed framework. This paper also shows a set of CFD applications that demonstrates future vision of the proposed SBD framework.

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The XFEM is a numerical method which employs the local enrichment considering a priori knowledge of the solution in the framework of the FEM. The XFEM has an essential problem in the approximation of the partially enriched ‘blending elements’, which causes a lack of accuracy. Using the weighted XFEM, the numerical accuracy was effectively improved for the problem. It was however found that the influence of the blending elements still remains by the detailed examination in the numerical results. In the present paper, the incompleteness of the weighted XFEM is proved through a theoretical error analysis. Then, a ‘PU-XFEM’ is proposed in order to correct the incompleteness in the existing XFEM approximations. The PU-XFEM is formulated as the exact development of the PUFEM with local enrichment. As a result of the error analysis, it is found that the PU-XFEM is a proper XFEM without problem of the blending elements.

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This paper describes vibration analysis using FEM for frame structures supported by multiple nonlinear concentrated springs with hysteresis damping. The restoring forces of the springs have cubic nonlinearity, and the springs have complex spring constants. Finite elements for the nonlinear springs with hysteresis are expressed and are connected to the frame structures modeled by linear solid finite elements. The frame structures have complex modulus of elasticity. The discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. By using Modal Strain Energy Method, modal loss factors are approximately computed from complex eigenvalue problem and are introduced into the nonlinear coupled equations. Harmonic balance method is applied to the equations to obtain nonlinear resonance responses. The calculated responses by the proposed method are verified. As numerical examples, influences of rigidity of the frames on nonlinear resonance responses are investigated.

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This paper examines performance of MRTR method using GS (Gauss-Seidel) preconditioning combined with Eisenstat trick (hereafter, we refer to Eis. GS-MRTR method). A crucial point of our preconditioned MRTR method is the appropriate choice of its components, which allows for an efficient implementation. The principle idea of GS preconditioning with Eisenstat trick is to use lower and upper triangular matrices L and U of the original coefficient matrix A. New efficient Eis. GS-MRTR method and Eis. GS(m)-MRT method with parameter of m are derived from combining appropriately the choice of preconditionings.

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In the application of the XFEM to the fracture mechanics, the complex remeshing procedures can be avoided. It was however reported that the lack of accuracy is caused by the incompleteness of the XFEM approximation called as ‘the problem of blending elements’. In order to solve the problem, the general form of the PU-XFEM was presented in our previous study by the redefinition of the XFEM approximation as the exact development of the PUFEM approximation. In the present paper, the PU-XFEM is applied to the two-dimensional linear fracture mechanics. The numerical accuracies are evaluated by using the models assuming the finite domains near the crack tip in the infinite plates. As the results of the evaluation, it is found that the incompleteness of the XFEM approximation in the application to the crack analyses is solved by the PU-XFEM.

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The conventional Galerkin FEM sometimes can not converge on, for example, the original Poisson's equation locally when unstructured linear meshes are used. This problem arises from the inconsistency from the viewpoint of conservation law between the discretization of the source team and one of other terms. This research tries to solve this problem by distributing the source term to nodal algebraic equations in proportion to the areas of nodal domains. The nodal domains are introduced using second-order fluxes. Only the source distribution within an element is counted even for an obtuse triangle, which reduces numerical error effectively where the source term changes spatially. Numerical simulation of heat conduction with both Dirichlet and Neumann boundary conditions shows that the numerical accuracy has been improved obviously comparing with the conventional Galerkin FEM for unstructured triangular meshes, especially for bad quality elements.

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Numerical approximation techniques of stress and consistent tangent moduli using complex-step derivative approximation (CSDA) are presented, and its applications to nonlinear hyperelastic models are demonstrated. The stress calculated by this technique does not suffer from inherent subtractive cancellations that limit the accuracy of finite difference approximations, such as the forward Euler method and so on. Therefore, the accuracy of output has as same as analytical one. In addition, once the proposed approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and the accuracy of this approach are first demonstrated with a simple Mooney-Rivlin model. Subsequently, an anisotropic hyperelastic material model is applied to analyze the simple tensile test.

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The propagation of the stress waves in thick circular cylindrical shells subjected to radially symmetric loads is investigated. Exact analysis is developed using the method of eigenfunction expansion based on the three dimensional theory of elastodynamics. The impact load applied is a uniformly distributed load over the outer surface of the shell. Numerical calculations are made for the steel shells, and stresses variations at transient states of the shells are shown graphically. The present results can be served as a reference to approximate solutions using numerical approaches such as the finite element method.

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Accurate numerical integration technique for a discontinuous integrand by the Delaunay decomposition has been proposed to calculate the interactive terms in the 2-D finite element mesh superposition method (FEMS). In this paper, the preprocessing for appropriate triangulation or tetrahedralization as an alternative to swapping algorithm is proposed for 2-D and 3-D FEMS. All vertices are categorized into the groups which are defined for every global element. All decomposed integral domains have no discontinuous integrand because the groups are composed along the boundaries of global elements. In the first two 2-D examples, we indicate that the proposed technique can apply the superimposed models which have not been able to decompose the integral domains adequately. In the third example, we apply the proposed technique to 3-D practical superimposed model.

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Electromagnetic metamaterials are artificial materials with extraordinary physical properties not available in nature, such as a negative refractive index, that is, negative permittivity and permeability. This paper proposes a level set-based topology optimization method for the structural design of negative permeability dielectric metamaterials. The purpose of the optimization problem is to find the optimal layout of dielectric metamaterials that achieves negative permeability. The presence of grayscale areas in the optimal configurations significantly affects the performance of metamaterials. However these grayscale areas are impractical to manufacture, so an optimization method in which the boundaries of optimal configurations are clearly expressed is desirable, such as those provided by topology optimization methods utilizing level set-based boundary expressions. In this paper, first, the level set-based topology optimization method is explained, and the optimization problem that addresses the design of negative permeability dielectric metamaterials is then formulated. Finally, several numerical examples are provided to confirm the utility and validity of the proposed method.

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