Kalmanフィルタと境界要素法による構造要素に内在する未知空洞欠陥の形状同定解析

Solidification problems by the boundary element method

A plasticity model with yield limit degradation is implemented in a boundary element program to study the fracture behavior of quasi-brittle materials. A special integration method is applied to deal with the singular integrations encountered in the volume integrals over internal cells. Strain-softening damage localizations are investigated. It is found that the damage tends to localize into a zone of one cell wide which leads to an incorrect result when different cell meshes are used in the analysis. Some sort of localization limiter has to be incorporated into the analysis in order to achieve meaningful results. INTRODUCTION In the simulation of fracture behavior of quasi-brittle materials such as concrete or ceramics, it is essential to take into account the evolution of a relative large fracture process zone forms in front of the crack tip. The process zone consists of hundreds of microcracks and its overall behavior can generally be simulated either by discrete-cracking models such as the fictitious crack model [4, 5] or smeared-cracking models such as strain-softening damage models [2, 3]. In this paper the fracture process zone is simulated by a plasticity model with yield limit degradation. When the stresses near the crack tip reach the yield surface, the yield surface will contract rather than expand. This results in a decrease in stresses during an increase in strains, i.e., a strain softening. The decrease in stresses simulates a material damage caused by mainly the formation of microcracks. Difficulty has been encountered in the finite element analysis involving strain-softening behavior. As different meshes are used in an analysis, Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X 304 Boundary Elements different results are obtained. The results are not objective with respect to finite element meshes. Also, the energy dissipation of a structure at failure decreases with the refinement of the finite element mesh. It implies that the structure will fail at near zero energy dissipation when a very fine mesh is used. This is in contradiction with the reality. All these problems are considered due to damage localization [1,2,3]. In this paper, the plasticity model with yield limit degradation is incorporated into a boundary element program to study the damage localization problems. Many publications on the boundary element analysis of elastoplastic problems [7-14] have been seen since the first paper on the problem published in 1971 by Swedlow and Cruse [6]. However, the literature on the study of damage localization problems using boundary element approach is rarely seen. The initial stress boundary element method is applied to deal with the nonlinear damage problems, For localization problems, damage tends to localize into a small region of the body, and thus the internal cells required for integration purposes are needed only in a small region rather than the entire body. A special semi-analytical integration method for triangular cell is used to carry out the volume integration over the cell that contains a singular node. A rectangular panel with three different cell meshes are analyzed. It is shown that the results are not objective to the cell meshes even though all other conditions are kept the same. BOUNDARY ELEMENT FORMULATION FOR ELASTOPLASTIC ANALYSIS For elastoplastic problems based on small strain theory, the basic equations in incremental form are as follows: The governing equations are da^ + db* = 0 (1) with boundary conditions du;(x) = (x) x e I (2) cR (x) x e I I + T^T and total strain increment de^ = de^ 4de^= (du + dUjJ/2 (3) where de^ and de^ are elastic and plastic strain increments. T is the boundary of body 0 under consideration, da^ ,db; ,du;, dr; are the stress, body force (per unit volume), displacement, and traction increment respectively. du ± and df j are prescribed displacements and tractions on boundary I and r%. Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X Boundary Elements 305 The yield criterion is F(a%,k)= f(a$ <Kk) = 0 (4) where F and f are yield functions, $ is a work hardening function, and k is the work hardening parameter. The constitutive equations are de'u) = d<^ do, = DV^U (5) where D^= &pvl(l-2v)] 6fo + M<Wji + W

Unknown defect identification in elastic field by boundary element method with filtering procedure

This paper presents the transient dynamic analysis of micro-cracks of arbitrary shape in two-dimensional, linear piezoelectric fiber reinforced composite materials. Interface cracks between fiber and matrix as well as cracks inside the matrix and fibers are investigated. For this purpose, a symmetric Galerkin time-domain boundary element method in conjunction with a multi-domain technique is developed. The time-domain fundamental solutions for linear piezoelectric materials are applied. The time discretization is performed by a collocation method. An explicit time-stepping scheme is obtained to compute the discrete boundary data including the generalized crack-opening-displacements (CODs). Iterative solution algorithms are implemented to solve the nonlinear semi-permeable electrical crack-face boundary conditions and for a crack-face contact analysis at time-steps when a physically unacceptable crack-face intersection occurs. Several numerical examples are presented to reveal the influences of the micro-cracks, the material combinations and the transient dynamic loading on the intensity factors and the scattered wave fields.

The paper deals with robust parameter estimation (rotor and stator resistances), shaft speed estimation, and flux observation of induction motors using the extended Kalman filter (EKF) technique. The novelty of the paper is that it develops the EKF in a frame rotating synchronously with the stator current vector with the use of a reduced dynamic motor model in order to economise the computational requirements of the EKF. Different problems have been studied. First, the EKF technique is applied to the estimation of the rotor and stator resistances. This is used for the indirect field-oriented control of the induction machine. Next, the EKF technique is applied to the estimation of the induction machine rotor fluxes and rotor resistance, and is used to perform the direct field oriented control of the induction machine. Finally, speed sensorless control is carried out. In this case, the rotor flux and the motor shaft speed are estimated. Computer simulations and experimental tests have been carried out to show the effectiveness of the proposed methods.

In order to investigate the effects of elliptical defects on rock failure under ultrasonic vibrations, ultrasonic vibration tests and PFC2D numerical simulations were conducted on rocks with single elliptical defects. The research results indicated that the fracture fractal dimension, axial strain, and crack depth of specimens with elliptical defects at 45° and 90° were the smallest and largest, respectively. The corresponding strain and fractal dimension showed a positive linear and logarithmic function relationship with time. The maximum crack depth of 46.50 mm was observed on the specimens with an elliptical defect angle of 90°. Specimens with elliptical defects at 0°, 30°, 75°, and 90° exhibited more dense and frequent acoustic emission events than those with elliptical defects at 15°, 45°, and 60°. During the ultrasonic vibration process, the maximum total energy (87.86 kJ) and energy consumption coefficient (0.963) were observed on specimens with elliptical defect angles of 30° and 45°, respectively. The difference in the stress field led to varying degrees of plastic strain energy in the specimens, resulting in different forms of crack propagation and triggering differential acoustic emission events, ultimately leading to specimen failure with different crack shapes and depths. The fractal dimensions of elliptical defect specimens under ultrasonic vibration have a high degree of consistency with the changes in axial strain and failure depth, and the fractal dimension of defect specimens is positively correlated with the degree of failure of defect specimens.

We propose a GaAs 2D photonic crystal tunable filter that takes advantage of rotation of a shape defect, which has a different cross-section from that of rods surrounding defect. Recent optical MEMS technology is used. Numerical simulation with boundary element method is carried out and shows the feasibility of tuning peak frequency with rotation of shape defect.

A direct traction BIE approach for three-dimensional crack problems

Application of boundary element method for elastodynamics to defect shape identification

The influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach. The problem is formulated by using the generalized displacements and generalized tractions. The boundary integral equation formulation is obtained by extending the reciprocity theorem to magneto-electro-elastic problems; it is numerically implemented by using the boundary element method multidomain technique to address problems involving nonhomogeneous configurations. Results under different magnetic configurations are compared highlighting the characteristic features of magnetopiezoelectric behavior particularly focusing on the link between interlaminar stress and magnetic induction.

Numerical analysis of acoustic radiation responses of shear deformable laminated composite shell panel in hygrothermal environment

Solution of some 2D transport problems by a high order A N–SP 2 N−1 method

A numerical solution of general frictional contact problems by the direct boundary element and mathematical programming approach

Linearly arrayed ultrasonic transducer has the advantage of receiving flaw echoes simultaneously at various points on a flat surface of the specimen. We develop here a new imaging technique to reconstruct flaw shapes from waveforms measured by the arrayed transducer. The imaging technique is based on the linearized inverse scattering method and here an algorithm of the synthetic aperture focusing technique in the frequency domain is incorporated into the inverse method. Since we adopt 2D-FFT to the shape reconstruction process, the high-speed imaging of flaw shapes is possible at small computational cost. The performances of the inverse scattering imaging technique are demonstrated by numerical simulations using the boundary element method.

The performance, reliability, and safety of 400 kV bus post insulators remain dependent on the design of high-potential electrodes, such as bus conductors, grading rings, and corona rings. Reduced localised stress and insulation failure are two benefits of proper dimensioning, which also helps regulate electric field stress along the insulator string. To mitigate these effects, corona ring dimensions must be assessed, but practical testing is expensive and challenging. Comprehensive knowledge of dielectric field stress analysis for these insulators is complex and costly to obtain. As a result, design engineers often rely on computer models that have been validated through experimental testing. While they are used to study field stress, traditional 2D approaches such as the Finite Element aprroache (FEM) and Boundary Element approach (BEM) have accuracy limits. In this study, a 400 kV porcelain bus post insulator was constructed using 3D simulation software using industry-standard design dimensions. The standard dimension configuration was compared with a various dimension configurations. The electrical simulations were carriedout using the COULOMB 3D tool, which employs BEM for accuracy and efficiency. Various case study dimensions are carried out and presented for deep field stress analysis of proposed insulator performance, which is major lacuna in experimental testing facility.