For honeycomb subjected to in-plane loading, there exist deformations in the height direction for cell walls due to effect of Poisson's ratio. Because these deformations are different for adjacent walls, the elastic modulus of honeycomb should be analyzed as a 3-dimensional problem. In this paper, the method of analysis for the equivalent elastic modulus proposed by authors in the previous report, in which the effect of height h of the honeycomb core on the elastic modulus is taken into account, is applied to theoretical formula for calculating Young's modulus E₁ and shear modulus G₁₂. Then, the validity of the proposed theoretical formula for elastic moduli E₁ andG₁₂ is verified comparing with the numerical results by FEM.

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It is recognized strongly that the reliance of the material properties is extremely important. The material properties that we use in the numerical analysis, controls the quality of the analysis result directly. The best choice to use the correct properties is that we measure them by ourselves. However, it is sometimes difficult to get them by ourselves because of the problem such as expense, equipment and/or time.
The reliance of the material properties used in the numerical analysis for the reliability assessment of high density packaging is studied, in this paper, especially focusing on the encapsulant.
The result of a numerical analysis with the material properties, that the material supplier announced, did not support the result of the actual hardware testing. On the research process, the material properties were focused, and then I actually measured the material properties with the piece of the actual hardware parts which were constructing this product. As the result, we found the order difference between the material suppliers announced data and our measured data.
With this established numerical model, the optimized parameter of the encapsulant has been studied.

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The stiffness of an engineering structure with joints depends not only on the materials and dimensions of the structure but also on the stiffness of the fasteners that connect its components. To evaluate the mechanical behaviour of a complex structure with bolted joints, it is important to develop a simple finite element (FE) modelling technique that accounts for the effect of the joints on stiffness. In this study, we developed a modelling technique that simplifies bolted joint structures by using shell and beam elements. It was found that the stiffness of the beam element was related to the stiffness of the jointed plates and the bolt. We set the equivalent pressure area on the bearing surface region and the nodes in the equivalent pressure area were connected to the beam element as a rigid region by using constraint equations. We measured the eigenvalues of test pieces and calculated them by FE analysis. The analytical eigenvalues were found to agree well with the experimental results. Using this modelling method of bolted joints makes it possible to evaluate the supporting force of each bolt in any structure with a large number of bolted joints.

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The stiffness of an engineering structure with joints depends not only on the materials and dimensions of the structure but also on the stiffness of the fasteners that connect its components. To evaluate the mechanical behaviour of a complex structure with bolted joints, we first developed a simple finite element (FE) modelling technique that was simplified by using shell and beam elements and accounts for the effect of the stiffness of jointed plates and bolts. In evaluating the mechanical behaviour, we also need a method for evaluating the strength of bolt joints from the results of FE analysis. In this study, we have developed a strength evaluation method for the beam forces of FE analysis by considering the mechanics of bolt joints. This method can be used to evaluate static failure and fatigue failure of bolts and slip on clamped plates and bearing surfaces. We can easily evaluate the strength of bolt joints of industrial products with many bolted joints by using this method.

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A two-stage general optimization approach is presented for generating link mechanisms from a highly connected ground structure. The structure is modeled as a pinjointed truss, which is to be optimized so that a large displacement is generated in the specified direction at the output node. The design variables are the cross-sectional areas of the members and the nodal locations. The equilibrium path of an unstable mechanism is traced by the displacement control method. In the first step, the unnecessary members are removed by solving the optimization problem for minimizing the total structural volume under constraints on the maximum load, the displacement at the specified node, and the stiffnesses at the initial and final states. In the second step, the deviation of the displacement of the output node from the specified direction is minimized. It is shown in the numerical examples that several mechanisms can be naturally found as a result of the two-stage optimization starting from randomly selected initial solutions.

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In this paper, a simple solution scheme for frictionless contact problems of linear elastic bodies is proposed. The proposed method is a variant of the semismooth Newton method. The frictionless contact problem, which is discretized using the finite element method with lower-order elements and a node-to-node contact model, is considered, although the proposed method can be extended to a node-to-segment or segment-to-segment contact model. The present method can be implemented by slightly modifying a computer program for the semismooth Newton method. In the iterative loop of the proposed method, a symmetric linear structural problem with multi-point constraints is solved. Therefore, the proposed method can be applied to large-scale contact problems. Good convergence of the proposed method compared to the semismooth Newton method is demonstrated in some examples.

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This paper is concerned with the application of the boundary element method (BEM) with the analog equation method (AEM), proposed by Katsikadelis and Nerantzaki, and Green's theorem to analyze steady-state heat conduction in anisotropic solids. In this study, the linear differential operator (the Laplacian) of steady-state heat conduction in isotropic solids is extracted from the governing differential equation. The integral equation formulated employs the fundamental solution of the Laplace equation for isotropic solids, and therefore, from the anisotropic part of the governing differential equation, a domain integral appears in the boundary integral equation. This domain integral is transformed into boundary integrals using Green's theorem with a polynomial function. The mathematical formulation of this approach for two-dimensional problems is presented in detail. The proposed solution is applied to two typical examples, and the validity and other numerical properties of the proposed BEM are demonstrated in the discussion of the results obtained.

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With the rapid growth of WAN infrastructure and development of Grid middleware, it's become a realistic and attractive methodology to connect cluster machines on wide-area network for the execution of computation-demanding applications. Many existing parallel finite element (FE) applications have been, however, designed and developed with a single computing resource in mind, since such applications require frequent synchronization and communication among processes. There have been few FE applications that can exploit the distributed environment so far. In this study, we explore the feasibility of FE applications on the cluster-of-clusters. First, we classify FE applications into two types, tightly coupled applications (TCA) and loosely coupled applications (LCA) based on their communication pattern. A prototype of each application is implemented on the cluster-of-clusters. We perform numerical experiments executing TCA and LCA on both the cluster-of-clusters and a single cluster. Thorough these experiments, by comparing the performances and communication cost in each case, we evaluate the feasibility of FEA on the cluster-of-clusters.

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It is well known that the compressibility or incompressibility of biological tissue stems from its microscopic structure, which is generally composed of material with varied compressibility, including incompressibility. This paper proposes a framework for a homogenization method in which the compressibility/incompressibility of the macrostructure properly reflects that of the microstructure. The formulation is based on the mixed variational principle with a perturbed Lagrange-multiplier. It is shown that the rate of volumetric change of the macrostructure can be controlled through the homogenization procedure by introducing the constraint on the microstructure only. A couple of numerical examples are given to demonstrate the validity of the proposed method. By comparing the numerical results with theoretical solutions, the method is also confirmed to be free from locking.

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An efficient homogenization method for nonlinear problems is introduced. We have already developed a homogenization technique using characteristic deformation mode superposition that avoids prohibitive computational cost. However, in the mode superposition technique, the approximation error created depends on the analysis case. In this paper a new method is proposed, in which the same accuracy as the exact method is preserved by solving the microscopic equilibrium equation, while approximating the tangential matrix of the multi-scale equilibrium equation using the mode superposition method. The performance of the proposed method is examined together with the block LU factorization algorithm, and satisfactory results are obtained.

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This paper proposes an analytical method to determine the stress distribution in an elastic body using the stress measured on the surface. The basic equation is derived from the boundary integral equation approach introducing a point source which produces displacement and stress fields in an elastic body. The point source is called as a body force dipole and composed of two body forces with identical magnitude acting in the opposite directions at the same location. The fundamental solutions on the displacement and stress fields by a body force dipole are derived theoretically and confirmed numerically that it produces the same fields generated by a pair of body forces. The input condition are then discussed how the location, the number and the components of known surface stress effect on the accuracy of the body force distribution. The results show that the tangential component of normal stress measured on the surface should be used alone in the inverse analysis.

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In this paper, we first point out that the finite element interpolation functions sometime lose their linear independencies when the elements are superposed each other in s-Version finite element (s-FEM) analyses. This problem has been known among engineers/researchers who have studied and used the s-FEM for solid mechanics analyses. Once the interpolation functions lose their linear independencies, resulting global stiffness matrix becomes singular and, therefore, the solutions lose their uniqueness. Although it is rare for an analyst to come across such a problem, it degrades the robustness of s-FEM. This paper describes a way to judge the occurrence of such a problem and propose a method to circumvent it.

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The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for solving fracture mechanics problems efficiently. In the present study, the principle of superposition is used to solve crack problems in conjunction with the X-FEM. In the proposed method, the surface load distributed on the crack surface, which is modeled implicitly by the interpolation functions with enrichment terms, is introduced to X-FEM analysis. Moreover, the energy release rate at the crack front is evaluated by the domain integral method with boundary integral terms for the surface load. The proposed method is verified through numerical analyses of two- and three-dimensional crack problems in linear fracture mechanics.

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Kinetic Monte Carlo (KMC) method realizes the millisecond or second order atomistic thin film growth. Twenty five kinds of events which may occur on Al(111) surface were classified. An attempt frequency and an activation energy of each event were defined using vibration analyses and nudged elastic band (NEB) method by which the minimum energy path (MEP) can be reasonably predicted. Temperature and deposition rate dependences of Al(111) film growth were intensively investigated in the present paper. The higher temperature and the lower rate drive the layer-by-layer film structural change. Two types of islands (fcc and hcp) were seen by modeling without considering the events of diffusion of dimer and trimer, while only fcc islands remain with considering such events. Thus, we find that the primitive events of diffusion of dimer and trimer take important roles in determination of surface morphology.

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A gold (Au) micro-interconnection, which connects through-hole electrodes in a three-dimensional chip-stacking LSI, is composed of several tens of grains. If the size of the interconnection becomes small in comparison with the grain, the anisotropic property of grains influences mechanical reliability. In this study, the stress distribution in the Au micro-interconnection is investigated by finite element method (FEM) analysis. The crystallographic structure of the Au micro-interconnection is obtained by a three-dimensional simulation based on a nucleation and growth model. The FEM analysis shows that the stress is concentrated on the region near the micro- interconnection/substrate interface edge and that a stress singularity exists there. The stress distribution of the micro-interconnection varies because of microscopic factors, which are due to the shape and crystallographic orientation of grains. Statistical evaluations of plural analytical models show that the stress variation approximates a normal distribution.

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In present paper a new approach for hexahedral mesh generation is suggested. The process of hexahedral mesh generation for an arbitrary volume is an open subject. Two main stages exist: determining topological connectivity of the mesh and its geometrical embedding. There are many interesting solutions proposed in various methods, which mostly rely on topological validity of the mesh. Nevertheless, the final quality of the mesh strongly depends on the step of mesh embedding, which has direct connection with geometry of the mesh and shapes of the elements. In order to generate hexahedral meshes topologically valid and geometrically qualitative, we propose a new guide for hexahedral meshing that combines both geometrical and topological aspects of hexahedral complex, which is to be generated. This guide includes topological construction of the spine of three-manifold and encoding with a matrix of incidence based on curvature information.

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Mesh simplification (decimation) refers to reducing the number of vertices and elements in an initial mesh while preserving the appearance of the dataset. In either case, some degree of simplification may be required for various reasons, for example, reducing visualization and calculation times or reducing storage requirements. The goal of the algorithm discussed in the paper is to reduce the total number of tetrahedral elements in the volume meshes for acceleration of calculation processes and to test the feasibility of proposed solution. One of the decimation criterions proposed in this approach is a bending energy as a decimation metrics to select tetrahedral elements as the candidates for collapsing. The final step of our algorithm is improving a quality of the simplified mesh. For improving we apply interpolation approach based on radial basis functions. To interpolate the overall displacement, we use a volume spline and employ an approach that uses displacement of N control points as a difference between the original and deformed geometric forms of tetrahedral mesh elements

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We propose a new method of design called MORDE (multi-objective robust design exploration) that combines a multi-objective robust optimization approach and data-mining techniques for analyzing trade-offs. The probabilistic representation of design parameters, which is compatible with the Taguchi method, is incorporated into the optimization system we previously developed that uses a multi-objective genetic algorithm. The means and standard deviations of responses of evaluation functions against uncertainties in design variables are evaluated by descriptive Latin hypercube sampling using Kriging surrogate models. Design space is visualized by Self-organizing map (SOM). To extract design rules further, a new approach that adopts the association rule with an "aspiration vector" is proposed. MORDE is then applied to an industrial design problem with a centrifugal fan for a washer-dryer. Taking dimensional uncertainty into account, we optimize the means and standard deviations of the resulting distributions of the fan efficiency and turbulent noise level. Steady Reynolds-averaged Navier Stokes simulations are carried out to collect the necessary dataset for Kriging models. We demonstrate the advantages of the proposed method of multi-objective robust optimization over traditional non-robust ones in that the solutions are diverse. We clarify that the association rule can extract both sufficient and necessary conditions as design rules to achieve trade-off balances. The association rule is also more beneficial than SOM in finding quantitative relations, particularly those that are concerned with more than three design parameters.

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In this paper, stress intensity factors for a three dimensional planar interfacial crack are considered on the idea of the body force method. The formulation leads to a system of singular integral equation, whose unknowns are three types of crack opening displacements. The unknown body force densities are approximated by the products of the fundamental density functions and power series; here, the fundamental density functions are chosen to express singular stress fields due to a two-dimensional interface crack exactly. The calculation shows that the present method gives rapidly converging numerical solutions. It is found that the stress intensity factors K_I and K_II are determined by bimaterials constant ε alone, independent of elastic modulus ratio and Poisson's ratio.

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In this paper, stress intensity factors for a three dimensional rectangular interfacial crack are considered on the idea of the body force method. In the numerical calculations, unknown body force densities are approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack exactly. The calculation shows that the present method gives rapidly converging numerical solutions and highly satisfied boundary conditions. The stress intensity factors for a rectangular interface crack are indicated accurately with varying the aspect ratio, and biomaterial parameter.

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In this paper, a mixed-mode interfacial crack in three dimensional bimaterials is analyzed by singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express a two-dimensional interface crack exactly. The results show that the present method yields smooth variations of mixed mode stress intensity factor along the crack front accurately. The effect of crack shape on the stress intensity factor for 3D interface cracks is also discussed on the basis of present solution. Then, it is found that the stress intensity factors K_II and K_III are always insensitive to the varying ratio of shear modulus, and determined by Poisson's ratio alone. Distributions of stress intensity factor are indicated in tables and figures with varying the rectangular shape and Poisson's ratio.

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The large-scale cast steel has been used in broad fields of industries, such as power generation, construction, vessels, and automobiles. In the solidification process of a hummer used for press machine, for example, sometimes defects such as shrinkage cavity, segregation and cracks appear at hummer's surface. Shrinkage cavity and segregation can be predicted by performing non-steady state heat transfer analysis; and therefore such two types of defects can be eliminated by using chills which control solidification process. However, uneven cooling rates at different regions of the large-scale cast steel generate thermal stresses, which cause solidification cracks, between the chills. For causing those cracks, thermal stress may be important; however, there have been few studies for this thermal stress analysis. In this study, a three dimensional thermal elastic-plastic stress analysis has been performed by using finite element method in connection with three dimensional non-steady state heat transfer analysis, including interaction between the temperature and stress field. The results provide further understanding of the observed solidification crack failure for large-scale cast steel.

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In this paper, a three-dimensional digital human-head model was developed and several dynamic analyses on the head trauma were conducted. This model was built up by the VOXEL approach using 433 slice CT images (512×512 pixels) and made of 1.22 million parallelepiped finite elements with 10 anatomical tissue properties such as scalp, CSF, skull, brain, dura mater and so on. The numerical analyses were conducted using a finite element code the authors have developed. The main features of the code are 1) it is based on the explicit time integration method and 2) it uses the one point integration method to evaluate the equivalent nodal forces with the hourglass control proposed by Flanagan and Belytschko⁽¹⁾ and 3) it utilizes the parallel computation system based on MPI. In order to verify the developed model, the head impact experiment for a cadaver by Nahum et al.⁽²⁾ was simulated. The calculated results showed good agreement with the experimental ones. A front and rear impact analyses were also performed to discuss on the characteristic measure of the brain injury, in which the von-Mises stress was high in the frontal lobe in both of the analyses because of the large deformations of a frontal cranial base. This result suggests that the von-Mises stress can be a good measure of the brain injury since it is empirically well known that the frontal lobe tends to get injured regardless of the impact positions.

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A numerical prediction scheme of crystal growth on various substrates by using the first-principles calculation was proposed to analyze the epitaxial processes of the piezoelectric thin films, such as the sputtering, the chemical vapor deposition and the molecular beam epitaxy processes. At first, we analyze the epitaxial strain of crystal cluster in piezoelectric thin film, which is caused by the lattice mismatch with the substrate. When the epitaxial strain is introduced in the unit cell of the crystal cluster, the total energy can be calculated by employing the pseudo-potential method based on the density functional theory. Then, a preferred orientation of crystal cluster is selected from the crystal conformations on the substrate which satisfy the structural stability condition. This numerical scheme was applied to BaTiO₃ thin films processes fabricated on various substrates, such as SrTiO₃(110), SrTiO₃(001), MgO(100) and LaTiO₃(001). Numerical results show that our process crystallographic design scheme, which employs the total energy increment of cluster, is efficient tool to evaluate the possibility of thin film crystal growth. Finally, it was confirmed that numerical results of preferred orientations have good correspondence with experimental ones.

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With smooth objective functions and constraint conditions, gradient-based methods can be used to solve multi-objective optimization problems efficiently. However, when applied to structural sizing optimization problems, using the Finite Element Method (FEM) and a finite difference scheme to calculate sensitivities can be computationally expensive. The adjoint variable method can be used to reduce computational cost. In order to solve multi-objective structural sizing and shape optimization problems efficiently, this paper proposes using the adjoint variable method. The adjoint variable method efficiently calculates multiple sensitivities for objectives that involve structural responses and cuts down computational cost by reducing the number of sensitivity calculations required per design variable.

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We propose a new multi-objective parameter design method that uses the combination of the following data mining techniques: analysis of variance, self-organizing map, decision tree analysis, rough set theory, and association rule. This method first aims to improve multiple objective functions simultaneously using as much predominant main effects of different design variables as possible. Then it resolves the remaining conflictions between the objective functions using predominant interaction effects of design variables. The key to realizing this method is the obtaining of various design rules that quantitatively relate levels of design variables to levels of objective functions. Based on comparative studies of data mining techniques, the systematic processes for obtaining these design rules have been clarified, and the points of combining data mining techniques have also been summarized. This method has been applied to a multi-objective robust optimization problem of an industrial fan, and the results show its superior capabilities for controlling parameters to traditional single-objective parameter design methods like the Taguchi method.

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A virtual crack closure-integral method (VCCM) for the generalized finite element with drilling and strain degrees of freedoms (DOFs) is presented in this paper. Free mesh method (FMM) is one of useful methods for fracture mechanics analysis. However, in FMM, quadratic elements with mid-side nodes cannot be employed due to restrictions arising from its local mesh generation rule around each node. Generalized elements with drilling and strain DOFs which have no mid-side nodes may improve the accuracy in fracture mechanics analysis over the conventional constant strain elements. Present authors have proposed a VCCM for two-dimensional generalized elements with drilling DOFs, in their previous papers. In this paper, in order to improve the accuracy in fracture mechanics analysis further, we present a VCCM for generalized finite element with drilling and strain DOFs. Finally, some numerical examples are presented and it is demonstrated that the generalized element with drilling and strain DOFs has superior accuracy over that with drilling DOFs only.

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We verified the generalization ability of the response surfaces of artificial neural networks (NNs), and that the surfaces could be applied to an engineering-design problem. A Bayesian framework to regularize NNs, which was proposed by Gull and Skilling, can be used to generate NN response surfaces with excellent generalization ability, i.e., to determine the regularizing constants in an objective function minimized during NN learning. This well-generalized NN might be useful to find an optimal solution in the process of response surface methodology (RSM). We, therefore, describe three rules based on the Bayesian framework to update the regularizing constants, utilizing these rules to generate NN response surfaces with noisy teacher data drawn from a typical unimodal or multimodal function. Good generalization ability was achieved with regularized NN response surfaces, even though an update rule including trace evaluation failed to determine the regularizing constants regardless of the response function. We, next, selected the most appropriate update rule, which included eigenvalue evaluation, and then the NN response surface regularized using the update rule was applied to finding the optimal solution to an illustrative engineering-design problem. The NN response surface did not fit the noise in the teacher data, and consequently, it could effectively be used to achieve a satisfactory solution. This may increase the opportunities for using NN in the process of RSM.

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A new theoretical model of axial crushing of cylindrical tubes with corrugated surfaces has been developed in which the crushing force is analyzed by considering the equilibrium of work done by the crushing force and the energy required to deform the tube. The energy absorbed by the cylindrical tube being crushed is taken to be the sum of the bending energy term and the membrane energy term, which results from compression or extension of a tube wall in the radial direction. The analysis results of the model predict two different modes, termed P- and S-modes, may occur in the collapse of cylindrical tubes with corrugated surfaces. In the P-mode, the compressive force oscillates with folding one after another, whereas in the S-mode the compressive force increases monotonically. Both the mode classification charts and the average crushing force predicted by the developed model are found to be in good agreement with FEM numerical calculation results. In addition, it is found that the increase in the compressive force load for the S-mode is principally due to an increase in the bending energy with deformation.

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In this paper, the elastoplastic deformation behaviors of cylindrical tubes subjected to statically axial compression are studied by using finite element method (FEM). Specifically, the effects of tube geometries and strain hardening are investigated. Although it is generally recognized that the deformation in the circumferential direction is dependent on the ratio of the radius to thickness (R/t), the deformation is also greatly dependent on the edge constraint. In this study, we used flanges as an edge constraint. The deformation mode in the circumferential direction also affects the deformation in the axial direction. A method to control the deformation mode, such as adding a disk in the tube center, is proposed to maintain the deformation in the axisymmetric mode.

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In this paper, telescopic deformations of stepped circular tubes are studied by axial compression with finite element method. It is found that three-stepped circular tubes can be considered as a combination of two two-stepped circular tubes, from which the compression load for a three-stepped cylinder can be predicted in approximation from the loads for the two-stepped cylinders. However, the predicted values by this technique are higher than those of the three-step cylinder, because the restraint of the vertical wall in the two-stepped cylinders is larger than that in the three-stepped cylinder. The mechanism of the telescopic deformation of stepped circular tube is mainly composed of bending, rotating, and stretching of the tube wall. However, another mechanism has appeared when the radius difference of the small and the big cylinders is small enough. As far as geometric parameters concerned, the average load of a two-step cylinder goes up as the radius difference ΔR decreases and as the cylinder height H or the thickness t increase. And, the initial load grows with the increase of fillet radius. Further, the average of compressive load is also investigated.

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In this paper, a cylindrical particle method to simulate a squeezing flow in a high aspect ratio domain is proposed. In a high aspect ratio domain, the scale of the vertical direction is incomparably smaller than that of the plane direction. It is practically impossible to simulate such a domain in three dimensions because a large number of calculation points are needed and it takes too much time. A high aspect ratio domain is represented by a two dimensional model and particles are regarded as cylinders. The size of particles is changed according to the height and the pressure term is computed so as to make the fluid incompressible. As a result, a fluid flow in the two dimensional plane is calculated. Three dimensional viscosity resistance is evaluated so that viscosity in simulation accords with that in an experiment. Simulation results agree with the experiments qualitatively.

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In our previous papers, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. Also, it was noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. Then, the two-layer equations were approximated by a finite element method which followed our numerical scheme established for the one-layer model in 1978. Also, it was numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference. In this paper, we newly show that conservation laws are still valid in the two-layer model. Also, we show results of a new physical experiment for the interfacial instability.

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This paper proposes a systematic scheme of removing void elements to achieve fast and efficient level set based topology optimization. When performing optimization, unless special treatment is applied to the stiffness matrix, the density of these void elements are usually represented numerically by a small positive value. In level set based topology optimization, since the amount of computational resources required for FEM dwarfs those required for level set evolution, the removal of these elements from the global stiffness matrix can drastically reduce total computation time. The proposed scheme removes the void elements, determined by their nodes' level set values, from the optimization process by use of mapping procedures. The results presented here show time reductions of at least 70%. An additional advantage of the presented scheme is that it can be easily used with any black box FEM routine.

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Recently, tightly coupled partitioned iterative methods have drawn a great deal of attentions due to easy implementation and encapsulation features, and several nonlinear algorithms have been proposed so far. However, their practical performances have not been well understood yet. This paper describes the intensive parametric study on convergence and stability performances of four nonlinear algorithms and their relaxed variations for partitioned iterative methods of steady / unsteady fluid-structure interaction (FSI) problems. Here we choose three typical FSI problems as test problems, i.e. (1) Collapsible channel as a steady problem, (2) Cavity with flexible bottom membrane and (3) Channel with flexible wall as unsteady problems. Efficiency and robustness dependency of those nonlinear algorithms on physical parameters such as degree of nonlinearity, added mass effect, time step, and on control parameters peculiar to each algorithm are clarified. Through those tests, we demonstrate that Broyden method is the fastest algorithm for easy FSI problems such as weakly coupling and Line Search method has robustness even for difficult FSI problems such as strongly coupling.

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