Stress Singularities (stress + singularity)

Distribution by Scientific Domains

Selected Abstracts

Lower bound limit analysis with adaptive remeshing

Andrei V. Lyamin
Abstract The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field. Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707,1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented. The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Vibrations of skewed cantilevered triangular, trapezoidal and parallelogram Mindlin plates with considering corner stress singularities

C. S. Huang
Abstract Based on the Mindlin shear deformation plate theory, a method is presented for determining natural frequencies of skewed cantilevered triangular, trapezoidal and parallelogram plates using the Ritz method, considering the effects of stress singularities at the clamped re-entrant corner. The admissible displacement functions include polynomials and corner functions. The admissible polynomials form a mathematically complete set and guarantee the solution convergent to the exact frequencies when sufficient terms are used. The corner functions properly account for the singularities of moments and shear forces at the re-entrant corner and accelerate the convergence of the solution. Detailed convergence studies are carried out for plates of various shapes to elucidate the positive effects of corner functions on the accuracy of the solution. The results obtained herein are compared with those obtained by other investigators to demonstrate the validity and accuracy of the solution. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Why would cement porosity reduction be clinically irrelevant, while experimental data show the contrary

D. Janssen
Abstract Laboratory bench tests have shown that porosity reduction increases the fatigue life of bone cement specimens. Clinically, however, the effect porosity reduction is subject to debate. We hypothesized that the discrepancy between clinical and experimental findings is related to differences in the stress distribution, which is typically uniform in experimental test specimens, while stress concentrations exist in cement around hip implants. We simulated fatigue failure of cement in a finite element model of an experimental test specimen and of a transverse slice of a total hip arthroplasty with a sharp-cornered stem. Four levels of porosity were introduced. In the fatigue test specimen model, the fatigue life clearly was dependent on the level of porosity, while in the transverse slice model, the level of porosity had virtually no effect on failure of the cement mantle. The results of the simulations confirmed our hypothesis. In simulations of laboratory tests, pores clearly acted as crack initiators, while in the simulation of a real total hip reconstruction, crack formation was governed by local stress singularities. This explains why the beneficial effect of cement porosity reduction on the lifetime of total hip reconstructions may be hard to detect clinically. © 2005 Orthopaedic Research Society. Published by Elsevier Ltd. All rights reserved. [source]

Asymptotic Analysis of Free-Edge and Free-Corner Effects in Laminate Structures

Christian Mittelstedt
Stress fields in the vicinity of free edges and corners of composite laminates exhibit singular characteristics and may lead to premature interlaminar failure modes like delamination fracture. It is of practical interest to investigate the nature of the arising free-edge and free-corner stress singularities - i.e. the singularity orders and modes - closely. The present investigations are performed using the Boundary Finite Element Method (BFEM) which in essence is a fundamental-solution-less boundary element method employing standard finite element formulations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A closed-form analysis of material and geometry effects on stress singularities at unsymmetric bimaterial notches

A.; Hohe, J.; Becker, Müller, W. Nachname
An important issue in the mechanics of adhesive bonds is the knowledge of local mechanical fields. In the present study, an asymptotic analysis of the stress fields near an unsymmetric bimaterial notch with arbitrary opening angle is performed. Using the complex potential method, the order of the singularity of the stress fields at a notch tip can be determined in closed-form analytical manner, so that the dependency of the occurring singularity exponents on geometry and material properties can be studied systematically. [source]

A conservative integral for bimaterial notches subjected to thermal stresses

Leslie Banks-Sills
Abstract In this investigation, a conservative integral based on the Betti reciprocal principle is developed to obtain stress intensity factors for a bimaterial notch in which the body is subjected to a thermal load. The bonded materials are linear elastic, isotropic and homogeneous. According to the linear theory of elasticity, stresses in the neighbourhood of the notch tip are generally singular as a result of the mismatch of the elastic constants. Eigenvalues and eigenfunctions depend upon the mechanical properties and wedge angles. They may be real, complex or power-logarithmic. Real and complex eigenvalues are considered in this study. The stress intensity factor represents the amplitude of the stress singularity and depends upon material properties, geometry and load or temperature. Because of the highly singular behaviour of one of the integrals that is part of the conservative integral, the former is carried out by a hybrid analytical/numerical scheme. The finite element method is employed to obtain displacements caused by the temperature distribution in the body. The conservative integral is applied to several problems appearing in the literature. Both good agreement between those results and the ones obtained here, as well as path stability for all problems is attained. A wide range of material parameters is also studied. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Application of two-state M -integral for analysis of adhesive lap joints

Yongwoo Lee
Abstract With the aid of the two-state M -integral and finite element analysis, the asymptotic solution in terms of the complete eigenfunction expansion is obtained for adhesive lap joints. The notch stress intensity is introduced to characterize the singular stress field near the notch vertex of adhesive lap joints. The proposed scheme enables us to extract the intensity of each eigenfunction term from the far field data without resort to special singular elements at the vertex. It turns out that a weak stress singularity is not negligible around the vertex when it exists in addition to the major singularity. For a thin adhesive layer, there exist two asymptotic solutions: one is the inner solution approaching the eigenfunction solution for the vertex at which the adherend meets with the adhesive and the other is intermediate solution represented by the eigenfunction series that would be obtained in the absence of the adhesive layer. An appropriate guideline for choosing the geometric parameters in designing the adhesive lap joints, particularly the overlap length or the size of the adhesive zone, is suggested from the viewpoint of minimizing the notch stress intensity. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Modeling the Ultimate Tensile Strength of Unidirectional Glass-Matrix Composites

R. E. Dutton
The ultimate tensile strengths of a unidirectional glass-matrix composite were measured as a function of fiber volume fraction. The results were compared with predictions, using a refined solution of the stress field generated by an axisymmetric damage model, which incorporated the effect of stress concentration in the fiber caused by the presence of a matrix crack both before and after deflection at the fiber/matrix interface. Two possible locations for the fiber failure were considered: (1) at a transverse matrix crack, near a bonded fiber/coating interface and (2) at the tip of a debond, at the fiber/coating interface. At low fiber volume fractions, the measured ultimate tensile strength matched the prediction calculated, assuming no crack deflection. For higher volume fractions, the predictions calculated for a debonded crack matched the observed values. The model results were relatively insensitive to debond length and interfacial shear stress for the range of values in this study. In comparison, the global load-sharing model, which does not account for the stress singularity at the fiber/matrix interface, was found to overpredict the values of the ultimate tensile strength for all fiber volume fractions. An important contribution of the present work was to introduce the use of fiber volume fraction as a parameter for testing theoretical predictions of the mode of fiber failure. [source]