A new discrete analysis method of solid mechanical problems is proposed in this paper. In this method, we use isolated elements which are completely cut off a solid to be analyzed. A set of displacement functions is provided for each isolated element so that be able to express the translation and the rotation of a rigid body. The principle of minimum potential energy that is expanded in order to satisfy the continuity of the displacement of isolated elements adjoining to each other is applied. Therefore, node or spring, Lagrange’s multiplier and penalty functions don’t exist in this method. The displacement functions of power series are used to describe the mechanical state of an isolated element and finally, the coefficients of series are determined by the variational principle. When analysis is executed, the apart isolated elements are returned to one deformed continuum by the action of natural boundary conditions of the variational principle. Two numerical examples of the plane stress problem are shown at the end of this paper.

This paper presents a damage model for simulating fracture behavior involving frictional contact on material interfaces or crack faces. The model consists of a scalar-valued damage variable based on fracture mechanics for evaluating the crack growth and modeling of frictional contact on crack faces based on the Coulomb friction law for simulating mode II crack behavior in a compressive field. A new formulation of the damage model for 3-dimensional (3D) problems is presented on the basis of 1-dimensional composite bar problems. Several numerical examples on 3D cohesive mode II fracture problems are solved to demonstrate the validity of the proposed model. The results reveal that the proposed model allows simulation of mode II crack behavior involving frictional contact with little mesh-dependency. Good agreement is also found between the numerical and experimental results.

This study presents a new framework of simulation-based tsunami risk assessment with the help of a mode decomposition technique. In the proposed framework, a series of numerical simulations is performed in consideration of uncertainties to investigate tendency of a risk index. Spatial modes are then extracted from the simulated results using the theory of the proper orthogonal decomposition (POD), and a surrogate model is defined as a linear combination of the spatial modes. After the surrogate model is obtained, the Monte Carlo simulation is performed using the surrogate model to discuss tsunami risk based on probabilistic risk analysis. In this study, the proposed method is applied to risk evaluation of the tsunami force acting on the buildings in a simple condition. According to the obtained results, the proposed framework can provide an efficient approach of the probabilistic tsunami risk analysis, and it has high potential for disaster risk evaluation.

This paper addresses an advance issue in the computational fluid-structure interaction (FSI) method that applies an extended finite element method (XFEM) to interface of fluid and structure to reproduce requisite flow discontinuities at the interface. We especially focus on how the inertial term of the incompressible Navier-Stokes equations is discretized by the XFEM in the FSI method where the velocity function is enriched. We show the inertial term includes a spatial time derivative of the enrichment function and show the importance of computing the derivative to obtain a stable computation result in time. To verify the result, we also introduce an interface-tracking FSI computation method that is based on an arbitrary Lagrangian-Eulerian (ALE) formulation.

In the last decade, one of the gradient damage models called “phase-field fracture model” has been receiving attention. The model for brittle fractures has acquired great success, but that for ductile fractures is still under development. In this context, we propose a novel phase-field model with a variable regularization length parameter that is defined as an increasing function of the measure of the plastic strain. Since the regularization length parameter l representing the width of a diffuse crack is known to determine the damaged region around the crack, it has been modified so as to increase depending on the amount of plastic deformation. Thanks to this variable regularization length parameter l ^∗, the phase-field parameter d is calculated in consideration of the damage due to plastic deformation. The conventional elasto-plastic model with J₂ theory in plasticity is employed and couple to our proposed phase-field model. Several numerical examples are conducted to demonstrate the capability of our proposed model and validate the introduction of l ^∗ in comparison with the experimental result.

The present study proposes a simplified topology optimization method to improve structural strength. Topology optimization considering structurally nonlinear behavior is one of the important topics. However, most of those methodologies request the complicated analytical derivation of sensitivity analysis and also high computational costs to obtain the optimal solution. This is the reason why the optimal design method based on linear structural analysis is still common approach in practice. However, optimal layouts based on linear structural analysis may lose the structural stability under larger or uncertain load.

From this background, we propose a method of practical and simplified topology optimization to improve structural buckling behavior with much lower computational costs than that of optimal design based on complicated nonlinear structural analysis. Finally, we discuss the setting of the optimization problem improving the structural strength and demonstrate the accuracy and performance of the proposed method by a series of numerical examples.

In the field of coastal engineering, it is important to evaluate the wave pressure due to Tsunami bore for the maintenance of coastal structures. The purpose of this study is to improve the quasi-compressibility source term for Moving Particle Semi-implicit (MPS) method to calculate the pressure value stability. As a verification of accuracy, the hydrostatic pressure of a stationary fluid was simulated. The simulation results showed the high accuracy compared with the theoretical value. Furthermore, as an application to the coastal engineering field, Tsunami bore was simulated. The relationship between impact pressure and standing wave pressure, standing wave pressure and water elevation in front of seawall, and standing wave pressure and offshore wave height showed satisfactory results compared with the experiment.

This paper proposes a method for modeling three-dimensional (3D) concrete’’s meso-structure composed of mortar and coarse aggregates. The method consists of an automatic generation of coarse aggregates and their random arrangement in concrete’’s domain. The phase-field method is applied to generate large number of coarse aggregates, each of which has arbitrary 3D shape. The aggregates are arranged randomly in concrete’’s domain by repeating trial-and-error calculation with random numbers. After explaining the modeling procedure, several numerical examples are presented to demonstrate the validity and availability of the proposed method. First, the comparison of meso-scale model with an actual concrete verifies the validity of the method. The availability is then demonstrated by generating concrete’’s meso-scale models with various grain size distributions. Finally, the application to a numerical experiment reveals that the proposed method allows the simulation of 3D crack propagation behavior in concrete’’s meso-scale.

QSI test analyses of CFRP laminate were performed by FEM using interface elements considering cohesive zone model (CZM), which models delamination and matrix cracks. Damage propagation analyses for four different kinds of laminates were conducted by both implicit and explicit methods considering materially, geometrically and boundary nonlinear. QSI test analyses can be performed by the implicit method using Zig-zag CZM, and the results are almost the same as the explicit method using bi-linear CZM. Moreover, the numerical models were validated through comparison with experimental results including the relation between the load point displacement and applied load, and delamination area.

This paper presents a strong coupling method of impulse-based rigid body simulations and incompressible fluid simulations using particle method, by adopting velocity-based formulation of fluid incompressibility constraint. Conventional coupling simulation of rigid bodies and fluids using particle method are commonly weakly coupled, or using approximations to rigid bodies that are not faithful to rigid body dynamics. Our proposed method however, achieves strong coupling of rigid bodies and incompressible fluids by solving contact constraints and incompressibility constraints simultaneously, without any non-faithful approximation to both rigid body dynamics and fluid dynamics. Computational examples show that the proposed method accurately simulates rigid bodies, fluids, and interactions between rigid bodies and fluids.

In the thermodynamically consistent formulation of the material behavior of thermosetting resins subjected to curing, a dual dissipation potential (DDP) for the cure state is originally derived in conjunction with that for viscoelasticity, and the free energy combined with these DDPs is applied to the incremental variational framework (IVF) to construct an algorithm to efficiently solve the equilibrium problem. By the introduction of the ‘cure’ multiplier as an internal variable to the cure’s DDP, a flow rule for the degree of cure (DOC), which is equivalent to the stationary condition of the Legendre-Fenchel transformation, is defined as a constraint condition for the rate of change of the total energy in the IVF. The flow condition of the DOC for the prescribed flow rule that is analogous with that of viscoplasticity is transformed along the lines of Perzyna’s viscoplastic over-stress theory and is therefore fully consistent with the vairational structure of mathematical theory for plasticity. As a result, the governing equation for the global equilibrium and the constitutive equations for local material behavior, which correspond to the stationary conditions of the rate of change of the total energy within the IVF, are also variationally consistent so that all the state variables can be implicitly solved in the numerical scheme. The verification analysis is carried out to confirm that the proposed method provides the same numerical result with that obtained by the conventional framework.

A new mixed and hybrid variational principle is proposed for the elasticity in this paper. This principle is composed from the potential energy functional and the complemental energy functional that the pair of these energy are constrained by a formula. Using this principle for the analysis of the solid mechanics, that is discretized or not, stress and displacement be able to analyze at the same time. Upper and lower bounds of numerical stress be able to analyze by the isolated element method that is based on the proposed principle.

To quickly and accurately predict the dispersion of hazardous materials released over urban areas, we propose a combined method in which dispersion fields are simulated using a Reynoldsaveraged Navier-Stokes model with pre-calculated flow fields from a large-eddy simulation (LES) model. First, the combined model is conducted for dispersion in a simple street canyon. The results of the combined model are compared with those of a wind-tunnel experiment to adjust empirical parameters in the turbulent scalar flux. The horizontal dispersion fields predicted in the combined model with the best parameters are well consistent with those calculated from our LES model. We then apply the combined model to predict the scalar dispersion over a real urban area. The combined model well predicts the results obtained from the LES model with less calculation time. Therefore, we find that the combined model is potentially effective for emergency response to hazardous-material release over urban areas.

In this paper, we proposed an interpolation/distribution function based on the discretized Dirac delta function and a reduction parameter to distribute less force outside the interface in interface-capturing methods. Compared to conventional methods such as half distribution (HD) forcing strategy which distributes force only inside the interface, our proposed interpolation/distribution function can adjust the force distributed outside the interface by the reduction parameter. We coupled the proposed interpolation/distribution function with the Direct-Forcing/Fictitious Domain Method (DF/FDM) to solve fluid-rigid body interactions. The numerical results show that the proposed interpolation/distribution function is effective to improve accuracy of the solution for fluid-rigid interaction problems.

Piezoelectric bimorphs in actuator and sensor applications are usually connected to an external circuit. The mechanical behavior of the piezoelectric bimorph is affected by charge from the circuit, and it behaves as a kind of capacitor in the circuit. Therefore, the interaction between the electrical circuit and piezoelectric bimorph forms the multiphysics inverse piezoelectric – direct piezoelectric – circuit interaction problem. This multiphysics coupling should be taken into account in the design process of the actuators and sensors using the piezoelectric bimorph. Here, the novel finite element analysis method is proposed for this inverse piezoelectric - piezoelectric - circuit coupled problem. The inverse piezoelectric and direct piezoelectric analyses are performed using the finite element method with the shell and solid elements, respectively, in order to consider the thin composite structure. Therefore, the transformation method between the solid and shell variables are used. The description of the circuit is a single degree of freedom. The coupled equations for the direct piezoelectric – circuit interaction are proposed from the continuous conditions for the electric potential and the charge. The coupled algorithm is based on the block Gauss-Seidel method. In the inverse piezoelectric analysis, the homogenization method about the bending rigidity and the mass is used. In the direct piezoelectric analysis, the pseudo-piezoelectric evaluation method for the conductor is used. Finally, it is demonstrated that the proposed method can analyze the coupling phenomena in the RC circuit and the shunt damping application accurately.

The purpose of this study is to establish a method to obtain face-to-face multi-point constraint (MPC) conditions that connect two nonconforming meshes in 3D problems. In this study, the formulation of the MPC conditions proposed by El-Abbasi and Bathe is employed, which considers the compatibility of deformation and the distribution of constraint traction on the connecting surface. The MPC conditions are expressed as a coefficient matrix by an integration of the product of shape functions over a connecting surface. The integration domain is divided using the Delaunay triangulation so that each integration domain contains just a polynomial. Then, the integration is numerically and precisely evaluated. Two examples are presented to verify the computational accuracy and validate the triangulation for numerical integration. In the first example, it has been confirmed that the numerical integration values calculated via the Delaunay triangulation coincide with the corresponding theoretical values. In the second example, a simple elastic problem in which two rectangular parallelepiped domains are connected by the face-to-face MPC has been solved. It has been confirmed that the displacement, the constraint traction and the first principal stress on the connecting surface are more accurate than those obtained with a node-to-face MPC. Additionally, we have found that Gaussian integration using a small number of integration points gave rise to unexpectedly inaccurate numerical results.

Rail squats are surface initiated rolling contact fatigue cracks due to the repeated passage of the train wheels. In this study, numerical simulations were performed of propagating horizontal fissures in squats. The growth was based on boundary element analyses of stress intensity factor (K-value) for a two-dimensional (2D) inclined surface crack under a Hertzian contact patch. By arranging several such 2D cracks in parallel and connecting their tips, K-values for a three-dimensional (3D) semi-elliptical horizontal crack can be obtained approximately. This approach can give the great speed advantages over fully 3D methods. A Paris-type crack growth law with an equivalent K-value range proposed by Richard was obtained using data from mode I/II and mode I/III non-proportional mixed-mode experiments. The direction of branching was predicted according to the Hourlier-Pineau criterion.

A sequential data assimilation for elemental stiffness ratio in plane stress model and its application to damage detection are presented. In this research, stiffness parameters in each finite element are estimated as a state vector in the extended Kalman filter. The stiffness parameter distributions estimated over finite element model are utilized to detect regions damaged. A numerical example, where stiffness parameters in a rectangular plate with damage is estimated, is given to verify the effectiveness of the presented approach. The experimental results indicate that the damage can be detected based on the stiffness parameter distributions estimated, where the parameters are reduced in damaged regions and are almost unchanged in other regions.

In the field of coastal engineering, it is important to use irregular waves to solve problems such an overtopping in coastal areas. The purpose of this study is to verify the accuracy of irregular waves simulated by the Moving Particle Semi-implicit (MPS) method. The analysis of irregular waves is performed by the zero-up cross method and the spectrum analysis. The simulated results were shown that the wave height of waves with high frequency, or short period attenuated. In addition, the problem of increase in calculation time and data capacity were suggested because the simulation of irregular waves requires many waves.

Many incidents are occurred frequently, educations for digital forensics are necessary. In order to drive training for digital forensics effectively, we propose a problem solving environment to provide a guide for digital forensics works. To accelerate the users understanding of the works, this system provides user flowchart images are generated from log data of maintenance works in the forensics. We also adopt the recognition whether the works are correct or not by using a convolution neural network. As the result, users obtained accuracy is 98.1% as the recognition of correctness in particular conditions.

It is essential to deal with contact problems in assembly analyses of mechanical components. However, the usual voxel-based FEM with consideration of contact conditions often exhibits numerical difficulties. In this paper, a practical procedure for 3D frictionless contact in the voxel-based FEM using the EBE-PCG method based on the finite cover method (FCM) is proposed. To assure accuracy in the penalty method for contact conditions, a large penalty parameter, which causes numerical instability and convergence deterioration in iterative linear solvers, is required. In this paper, the Nitsche’’s method is applied to contact constraint in the FCM to circumvent such difficulties. Moreover, the ghost penalty is employed to alleviate instability caused by elements with minuscule volume fraction in the FCM. A multi-phased analysis using different voxel size is also proposed to accelerate calculation. To show the effectiveness of the present approach, we calculate basic and practical 3D contact problems.

The present study proposes a level set-based topology optimization method to maximize heat exchange performance. The topology optimization allows not only the boundary advection but also a new boundary to be created during the optimization process. The location and the shape of the heat transfer boundary has a significant influence on the temperature distribution, because heat exchange occurs at the boundary of the structure. In this study, sensitivity analysis considering heat transfer boundary, which is a design-dependent boundary condition, is performed. In particular, considering that the topological derivative and shape sensitivity are defined by different equations in this problem, we propose a new sensitivity that combines these two sensitivities. In addition, we introduce a method to automatically set the heat transfer boundary condition that occurs during the optimization process. It is verified by a series of numerical examples that the proposed method provides reliable optimization results.