Search

The boundary element method has been applied with success to linear elastic fracture mechanic problems, involving static and dynamic cases. In order to solve body force problems (e.g., gravitational forces and transient problems with velocities and accelerations), Nardini and Brebbia presented, in 1982, the dual reciprocity formulation. Originally with the intention of solving transient problems using fundamental solutions of the static formulation, the procedure was found to be very efficient in the solution of body force problems as well. Also, a Green's function corresponding to an embedded crack within the infinite medium can be introduced into the boundary element formulation as the fundamental solution. This yields accurate means of calculating only the external boundary unknown displacements and tractions and, in a post-processing scheme, determining the crack opening displacements. This paper introduces an approach that involves the numerical Green's function procedure, of Telles and coworkers, and the dual reciprocity formulation. It compares beam solutions with the simulated effect of the total weight applied as a concentrated boundary force, the actual self-weight as a body force and a frequency- and time-dependent transient Heaviside load applied to a plate with a central crack. [ABSTRACT FROM AUTHOR]

This paper develops a semi-analytic solution for multiple cracks in an isotropic half-space under contact loading. The solution takes into account interactions among all the cracks as well as the interactions between the cracks and the loading body. In formulating the governing equations for the subsurface crack problem, each crack of mixed modes I and II is modeled as a continuous distribution of climb and glide dislocations with unknown densities. Such a treatment converts the original contact problem concerning an inhomogeneous half-space into a homogeneous half-space contact problem, for which governing equations with unknown surface contact areas and normal pressure and tangential tractions within the areas can be conveniently formulated. All the unknowns in the governing equations are determined by means of iteration. The iterative process is performed until the convergence of the half-space surface displacements, which are the sum of the displacements due to the surface contact load and subsurface cracks. The solution is validated by the finite element method. Numerical examples are calculated to demonstrate the generality of the solution. [ABSTRACT FROM AUTHOR]

As asphalt pavements age and deteriorate, recurring pothole repair failures and propagating alligator cracks in the asphalt pavements have become a serious issue to our daily life and result in high repair costs for pavement and vehicles. To solve this urgent issue, pothole repair materials with superior durability and long service life are warranted. In the present work, revolutionary pothole patching materials reinforced with nano-molecular resin with high toughness and high fatigue resistance have been developed to enhance their resistance to traffic loads and the service life of repaired potholes. In particular, DCPD resin (dicyclopentadiene, CH) with a ruthenium-based catalyst is employed to develop controlled properties that are compatible with aggregates and asphalt binders. A micromechanics-based model is developed in this paper to predict the mechanical behavior of these innovative nano-molecular resin reinforced pothole patching materials by indirect tensile test (ASTM D6931). Irregular coarse aggregates in the finite element analysis are modeled as three sizes of randomly dispersed multilayer-coated particles. The overall properties of asphalt mastic, which consists of fine aggregates, asphalt binder (PG64-10), cured DCPD (p-DCPD) and air voids, are theoretically estimated by the homogenization technique of micromechanics. An elastic damage model, based on a continuum thermodynamic framework, is incorporated within an initial elastic strain energy-based formulation. Numerical predictions are compared with suitably designed experimental laboratory results. [ABSTRACT FROM AUTHOR]

In this paper, a new type of hybrid fundamental solution-based finite element method (HFS-FEM) is developed for analyzing plane piezoelectric problems with defects by employing fundamental solutions (or Green's functions) as internal interpolation functions. The hybrid method is formulated based on two independent assumptions: an intra-element field covering the element domain and an inter-element frame field along the element boundary. Both general elements and a special element with a central elliptical hole or crack are developed in this work. The fundamental solutions of piezoelectricity derived from the elegant Stroh formalism are employed to approximate the intra-element displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. By using Stroh formalism, the computation and implementation of the method are considerably simplified in comparison with methods using Lekhnitskii's formalism. The special-purpose hole element developed in this work can be used efficiently to model defects such as voids or cracks embedded in piezoelectric materials. Numerical examples are presented to assess the performance of the new method by comparing it with analytical or numerical results from the literature. [ABSTRACT FROM AUTHOR]

In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs' parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs' parameters, α and β, while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α, and the value is symmetric about the axis on which β = 0. [ABSTRACT FROM AUTHOR]

In traditional reliability analysis, the uncertain parameters are generally treated by some ideal probability distributions with infinite tails, which, however, seems inconsistent with the practical situations as nearly all the uncertain parameters in engineering structures will get their values within a limited interval. To eliminate such an inconsistence and thereby improve the precision of the reliability analysis, the truncated probability distributions are then employed to quantify the uncertainty in this paper, and a corresponding reliability analysis method is developed. Two cases of positional relations are summarized for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty. The probability and non-probability convex model methods are employed to deal with these two cases, respectively, and based on it, a hybrid reliability model is then constructed for truncated distribution problems. An efficient approach is also provided to distinguish these two positional relations and thereby determine which one of the probability and non-probability methods should be used when computing a real hybrid reliability. Five numerical examples are investigated to demonstrate the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

In this paper, the mixed-mode fracture problem of a functionally graded piezoelectric material strip with two penny-shaped or annular cracks is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under electric loading. The problem is formulated in terms of a system of singular integral equations, which are solved numerically. Numerical calculations are carried out, and the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity. [ABSTRACT FROM AUTHOR]