Numerical Boundary Element Method Research Articles

Analysis of Axial Cracks in Hollow Cylinders Subjected to Thermal Shock by Using the Thermal Weight Function Method

In this study, stress intensity factors for axial cracks in hollow cylinders subjected to thermal shock are determined by using the thermal weight function method. The thermal weight function is a universal function for a given cracked body and can be obtained from any arbitrary mechanical loading system. The thermal weight function may be thought of as Green’s function for the stress intensity factor of cracked bodies subject to thermal loadings. Once the thermal weight function for a cracked body is determined, the stress intensity factor for any arbitrary distributed thermal loading can be simply and efficiently evaluated through the integration of the product of the temperature and the correspondent thermal weight function. A numerical boundary element method for the determination of thermal weight functions for axial cracks in hollow cylinders is used in this study to evaluate the transient stress intensity factor. As a demonstration, some examples of axial cracks in hollow cylinders subjected to thermal shock are solved by using the thermal weight function method, and the results are compared with available results in the published literature.

Body force weight functions of cracked bodies

Most of the investigation which calculate the stress intensity factor by using the weight function concept all focus on the problem with traction boundary conditions. In this study, the expression of body force weight functions in a two-dimensional cracked body is formulated. Stress intensity factors can be calculated easily for any arbitrary distribution of body force from the predetermined weight functions. Body force weight functions for rectangular cracked plates with finite dimensions are calculated by the numerical boundary element method. Some practical examples of various crack configurations and boundary conditions are given and a very satisfactory accuracy is obtained. It should be noted that the ordinary traction type of weight function is a special case of the body force weight function discussed in this study.

DETERMINATIONS OF MIXED-MODE STRESS INTENSITY FACTORS FOR CRACKED BODIES SUBJECTED TO THERMAL LOADINGS BY USING THE THERMAL WEIGHT FUNCTION METHOD

In this study, mixed-mode stress intensity factors for cracked bodies subjected to thermal loadings are determined by using the thermal weight function method. The thermal weight function is a universal junction for a given cracked body and can be obtained from any arbitrary mechanical loading system. The thermal weight function may be thought of as the Green's junction for the stress intensity factor of cracked bodies subject to thermal loadings. Once the thermal weight function for a cracked body is determined, the stress intensity factor for any arbitrary distributed temperature can be simply and efficiently evaluated through the integration of the product of the temperature and the correspondent thermal weight function. A numerical boundary element method for the determination of thermal weight functions is used in this study to evaluate mixed-mode stress intensity factors. As a demonstration, some examples of cracked bodies subjected to thermal loadings are solved by using the thermal weight function method, and the results are compared with solutions obtained from other methods.

Separation of principal stresses in dynamic photoelasticity

A new and effective method used to separate the transient principal stresses for dynamic photoelasticity is proposed. This is a hybrid method combining the optical method of dynamic caustics and the boundary element numerical method. Firstly, a modified Cranz-Schardin spark camera is used to record simultaneously the isochromatic fringe patterns of photoelasticity and the shadow spot patterns in the dynamic process. By means of the isochromatic fringe patterns, the difference between transient principal stresses in the whole domain and the principal stresses along the free boundary can be solved. In addition, the method of caustics is a very powerful technique for measuring the concentrative load. Then, the sum of the principal stresses is calculated by the boundary integral equation obtained from the Laplace integral transform of the wave equation. So, the transient principal stresses can be determined from the experimental and numerical results. As an example, the transient principal stresses in a polycarbonate disk under an impact load are resolved.

The geometry of echelon fractures in rock: implications from laboratory and numerical experiments

The traces of echelon joints, veins and dikes in rock range from curving to straight. Theoretical analyses using boundary element numerical methods have concluded that straight, open fractures imply a significant remote differential stress whereas curving traces imply a more nearly isotropic stress. We present a series of laboratory experiments which investigate the two-dimensional propagation paths of echelon fractures in PMMA plates as a function of the applied biaxial loading and the initial geometry of a simple fracture array. The experimental results support the theoretical conclusions and verify the accuracy of the numerical method. At the grain scale, rock does not rigorously conform to the assumptions of isotropy, homogeneity and linear elasticity demanded by the numerical method. Nevertheless, results from crack path stability theory suggest that small-scale deviations of a fracture from the ideal path generally do not affect its large-scale behavior. Fracture paths which become kinked or curved by local heterogeneities are found to self-correct to a path governed by competition between the fracture tip and remote stress fields, provided the remote differential stress is non-zero. This enhances our confidence that the numerical method can be used to produce and explain realistic fracture geometries in rock. An unexpected experimental result is the non-perpendicular intersection of fractures grown in the laboratory. Free surface boundary conditions require that the walls of an open fracture be free of shear stress. The principal stresses are therefore aligned with the crack wall, and we might consequently expect an approaching opening mode fracture either to intersect the free surface at a right angle or to turn away and follow an asymptotic, nonintersecting path. Experimental and numerical modeling, however, shows how the near-tip stresses generated by an approaching fracture dominate the local stress field and allow it to propagate along an oblique path very close to intersection with the adjacent free surface.

Reflection of ultrasonic waves from imperfect interfaces: A combined boundary element method and independent scattering model approach

A numerical technique for obtaining interface reflection coefficients for imperfect bonds between similar materials for a wide range of distributed defects is developed. A numerical boundary element method is utilized to find the far-field scattering amplitudes of a single defect for a normally incident plane wave. Then, the normal incidence reflection coefficient for a planar distribution of such defects is obtained from the independent scattering model. As a validation, the reflection coefficients are compared to the quasi-static model results where the latter are available. This establishes the basis for one application of the new model, the determination of spring constants which are not available. Other applications of the model, including studies of the response at frequencies beyond the quasi-static limit, the ratio of longitudinal to transverse wave reflectivities, and the effects of selected multiple scattering are discussed.

Conformal mapping method for calculation of rectangular winding parameters

A novel method to determine the values of equivalent parameters of a high-power shell-form transformer in high-frequency state is developed. In order to obtain a circular form for the rectangular winding, two conformal mappings are used. The inductances and capacitances are then computed by using a classical 2D finite elements code. Thus, the third dimension is easily taken into account. The authors present a satisfactory comparison between the capacitances computed using a 3D numerical boundary element method and those computed using a 2D finite element method combined with the transformation of the windings. Other comparisons between computation results and measurements for the inductances are in good agreement. The proposed method avoids using 3D electromagnetic fields computations, with an equivalent accuracy.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The boundary element numerical method for two-dimensional linear quadratic elliptic problems. I. Neumann control

For two-dimensional distributed control systems governed by the Laplace equation, the boundary element method is an efficient numerical method to solve problems whose quadratic cost involves boundary integrals only. In this paper we formulate a duality-boundary integral equation scheme and use piecewise constant boundary elements to approximate the problem. This method involves discretization of the boundary curve only and it can conveniently handle the compatibility constraint due to the Neumann data. Convergence and optimal error estimates O ( h ) \mathcal {O}(h) have been proved. Numerical data for the case of a disk are computed to illustrate the theory.

Calculation of the fields and power in a short magnetic cylinder in a transverse time-harmonic magnetic field

This paper applies the boundary integral equations for the rotating field problem to the case of a short non-magnetic or magnetic conducting cylinder in a uniform, transverse time-varying magnetic field to calculate the fields and losses in the cylinder, Both an exact formulation, in terms of four coupled, one-dimensional Fredholm integral equations of the second kind, and an approximate formulation, using the impedance boundary condition and two-coupled, one-dimensional integral equations, are presented and compared. Using the two approaches and a boundary element numerical method, accurate results are obtained over the entire frequency range.