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Showing papers in "Journal of Computational Science and Technology in 2009"


Journal ArticleDOI
TL;DR: In this article, the authors presented a new method for simulating flows driven by a body traveling with neither restriction on motion nor a limit of a region size, where the whole computational domain including bodies inside moves in the physical space without the limit of region size.
Abstract: This paper presents a new method for simulating flows driven by a body traveling with neither restriction on motion nor a limit of a region size. In the present method named 'Moving Computational Domain Method', the whole of the computational domain including bodies inside moves in the physical space without the limit of region size. Since the whole of the grid of the computational domain moves according to the movement of the body, a flow solver of the method has to be constructed on the moving grid system and it is important for the flow solver to satisfy physical and geometric conservation laws simultaneously on moving grid. For this issue, the Moving-Grid Finite-Volume Method is employed as the flow solver. The present Moving Computational Domain Method makes it possible to simulate flow driven by any kind of motion of the body in any size of the region with satisfying physical and geometric conservation laws simultaneously. In this paper, the method is applied to the flow around a high-speed car passing through a hairpin curve. The distinctive flow field driven by the car at the hairpin curve has been demonstrated in detail. The results show the promising feature of the method.

30 citations


Journal ArticleDOI
TL;DR: In this paper, a two-stage general optimization approach is presented for generating link mechanisms from a highly connected ground structure, where 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.
Abstract: 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.

16 citations


Journal ArticleDOI
TL;DR: It is clarified that the association rule can extract both sufficient and necessary conditions as design rules to achieve trade-off balances and is also more beneficial than SOM in finding quantitative relations, particularly those that are concerned with more than three design parameters.
Abstract: 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.

14 citations



Journal ArticleDOI
TL;DR: 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 to improve multiple objective functions simultaneously.
Abstract: 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.

9 citations


Journal ArticleDOI
TL;DR: In this paper, the authors point out that the finite element interpolation functions sometimes lose their linear independencies when the elements are superposed each other in s-Version finite element (s-FEM) analyses.
Abstract: 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.

8 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed a finite element (FE) modeling technique that accounts for the effect of the joints on stiffness of a complex structure with bolted joints and measured the eigenvalues of test pieces and calculated them by FE analysis.
Abstract: 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.

8 citations



Journal ArticleDOI
TL;DR: In this paper, the authors used the principle of superposition to solve crack problems in conjunction with the extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface.
Abstract: 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.

6 citations


Journal ArticleDOI
TL;DR: In this paper, a 3D digital human head model was developed and several dynamic analyses on the head trauma were conducted using 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.
Abstract: 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.

6 citations


Journal ArticleDOI
TL;DR: In this paper, the adjoint variable method was used to reduce the number of sensitivity calculations for structural sizing and shape optimization problems, which can be used to solve multi-objective structural sizing problems efficiently.
Abstract: 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.


Journal ArticleDOI
TL;DR: In this paper, elastic stiffness coefficients are calculated using the interatomic potential function, which does not need to prepare reference node (atomic) positions, and found that the criterion values estimated using deformation gradients and elastic stiffness coefficient show a positive correlation.
Abstract: Adaptivemesh refinement and local/non-local transition in our quasicontinuum method (Phys. Rev. B, Vol. 69, No. 21(2004), pp.214104(1-10)) are studied in this paper. Although deformation gradients have been used to determine the mechanical state of an element in the original quasicontinuum method, we adopt elastic stiffness coefficients, which govern stress-strain relationships at finite deformation. Because elastic stiffness coefficients are calculated using the interatomic potential function, we do not need to prepare reference node (atomic) positions. To confirm its applicability, we performed nano-indentation simulations in two dimensions, and found that the criterion values estimated using deformation gradients and elastic stiffness coefficients show a positive correlation.

Journal ArticleDOI
TL;DR: In this paper, the linear differential operator (the Laplacian) of steady-state heat conduction in isotropic solids is extracted from the governing differential equation, and a domain integral appears in the boundary integral equation.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, a virtual crack closure integral method (VCCM) for the generalized finite element with drilling and strain degrees of freedoms (DOFs) is presented for fracture mechanics analysis.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, the feasibility of finite element (FE) applications on the Grid is explored and a prototype of each application is implemented on the cluster-of-clusters and a single cluster.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this paper, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption, and it was shown that conservation laws are still valid in the 2-layer model.
Abstract: 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.

Journal ArticleDOI
TL;DR: This paper focuses on an iterative solver which is often used in FEA: the conjugate gradient (CG) method and proposes methods for a priori finding the optimal number of processes.
Abstract: With the rapid growth of WAN infrastructures and development of Grid middleware, the cluster-of-clusters has become a realistic methodology for executing computationdemanding applications. While distributed computing or loosely connected applications have been successfully ported to the Grid environment, few tightly connected applications such as parallel finite element analysis (FEA) have been attempted. In this paper we focus on an iterative solver which is often used in FEA: the conjugate gradient (CG) method. By using both predictions and numerical experiments we evaluate the performance of the CG method parallelized via domain decomposition. From numerical experiments we measure the inter-cluster execution time and find it to be close to that obtained by the slowest cluster. At the level of performance currently found in most WAN systems, as long as the number of processes is kept adequately small, the increase in communication cost due to WAN is small relative to the computation cost. For a very large test model which realistically requires the utilization of remote resources, the work ratio stays above 86% even for 64 processes. Especially for very large models, using the distributed environment is expected to be a practical methodology even for parallel computations with communication as frequent as the one found in FEA. To evaluate the feasibility of parallel FEA on the C-of-C, we have proposed methods for a priori finding the optimal number of processes.


Journal ArticleDOI
TL;DR: In this article, a mixed-mode interfacial crack in 3D bimaterials is analyzed by singular integral equations on the basis of the body force method, where unknown body force densities are approximated by the products of the fundamental density functions and power series.
Abstract: 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 KII and KIII 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.

Journal ArticleDOI
TL;DR: In this paper, the authors considered a three dimensional planar interfacial crack and derived the stress intensity factors for a two-dimensional interface crack using the idea of the body force method, which leads to a system of singular integral equation, whose unknowns are three types of crack opening displacements.
Abstract: 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 KI and KII are determined by bimaterials constant e alone, independent of elastic modulus ratio and Poisson's ratio.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the stress distribution in the Au micro-interconnection by finite element method (FEM) analysis and showed that the stress is concentrated on the region near the micro- interconnection/substrate interface edge and a stress singularity exists there.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, the effects of changing the structure and the control of a fuel cell can be made clear through numerical analysis, and a two-phase two-dimensional analysis effects of pressure and temperature for liquid water distribution in fuel cells are described.
Abstract: In this paper, numerical modeling methods for a fuel cell are explained. The aim of this study is to make an analysis system to perform investigation on the whole behavior of a fuel cell with higher precision. Through numerical analysis, the effects of changing the structure and the control can be made clear. Liquid water distribution and temperature distribution inside the fuel cell are analyzed and evaluated in general under various situations. This paper describes through a two-phase two-dimensional analysis effects of pressure and temperature for liquid water distribution in fuel cells.

Journal Article
TL;DR: In this article, 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 is presented.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a framework for a homogenization method in which the compressibility/incompressibility of the macrostructure properly reflects that of the microstructure.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this paper, an efficient homogenization method for nonlinear problems is introduced, 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.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, the axial compression with finite element method was used to predict the deformation of a two-and three-stepped cylindrical tubes, from which the compression load for a three-stacked cylinder can be predicted in approximation from the loads for the two-stpped cylinders.
Abstract: 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.

Journal ArticleDOI
TL;DR: A new guide is proposed that combines both geometrical and topological aspects of hexahedral complex, which is to be generated, which includes topological construction of the spine of three-manifold and encoding with a matrix of incidence based on curvature information.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, a simple solution scheme for frictionless contact problems of linear elastic bodies is proposed, which is a variant of the semismooth Newton method and can be applied to large-scale contact problems.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this paper, 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 forces and the energy required to deform the tube.
Abstract: 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.