Regions Of High Stress Gradients Research Articles

Error Approximation in Mesoscale Material Property Field Representations

AbstractLocally averaged random fields can be used to represent composite material properties at an intermediate scale. These types of fields provide the basis for stochastic simulation to generate nominally identical realizations of random composite microstructures to be used in reliability analysis. One challenge in choosing an appropriate local averaging technique and mesoscale length parameter is the difficulty of quantifying the accuracy of the locally averaged model. Although mesoscale models may offer advantages over the use of a representative volume element (RVE), particularly in regions of high stress gradients, mesoscale approximations do not converge to an effective medium, so the accuracy of the mesoscale representation cannot be quantified. In this paper, a matrix norm error is developed to test locally averaged material property approximations where loading is not specified a priori. This norm-based approach illustrates the advantage of local averaging over global averaging when small-scale...

Failure analysis of a hybrid composite structural beam

The purpose of this study was to identify the failure mode of a particular composite structural beam developed for the civil infrastructure market and to develop a strength prediction that could be utilized in fatigue life predictions. First, a global–local finite element stress analysis is utilized to examine the possibility of compression failure. We then investigate the possibility of a delamination failure using a successive sub-modeling approach that allows detailed analysis of the inter-laminar stresses in regions of high stress gradients, including free edges and tapered laminates. The results of the analyses are compared with experimental test data from full-scale bending tests. The results indicate a compression dominated failure in the top flange in the vicinity of the load patch. This study highlights the difficulty in applying a stress-based approach to predicting delamination failure, particularly in complex laminated structures.

Recovery based error estimation and adaptivity applied to a modified element-free Galerkin method

In this work, we propose an error estimator of the recovery type, which considers the equilibrium and boundary traction conditions, and an h-refinement procedure that is applied to the modified element-free Galerkin (MEFG) method. The approximate solution obtained by the MEFG method satisfies accurately the essential boundary condition. However, the approximate MEFG stress field presents some discontinuities on a neighborhood of the essential boundary condition and may present some spurious oscillations at regions of high stress gradients or discontinuities. Thus, the h-adaptive scheme is responsible for the reduction not only of the global error but also of the local errors associated with the discontinuities and oscillations of the approximate stress field. In order to validate the proposed procedures, we present some numerical solution for some simple problems and consider the analysis of a complex component.

Anisotropic elasticity of cortical and cancellous bone in the posterior mandible increases peri-implant stress and strain under oblique loading.

The aim of this study was to compare implant-bone interface stresses and peri-implant principal strains in anisotropic versus isotropic three-dimensional finite element models of an osseointegrated implant in the posterior mandible. We obtained anisotropic (transversely isotropic) elastic constants for mandibular bone and derived equivalent isotropic constants by averaging over all possible spatial orientations. A finite element model was constructed using ten-node tetrahedral p-elements, providing curved edges where necessary and increasing the accuracy of the results in regions of high stress gradients. Perfect bonding was assumed at the implant-bone interface. An oblique load was applied at the coronal aspect of the crown with 100 N vertical and 20 N bucco-to-lingual components. Implant-bone interface stresses exceeded reported bond strengths and principal strains reached yield strain levels in the cortical crest. Anisotropy increased what were already high levels of stress and strain in the isotropic case by 20 to 30% in the cortical crest. In cancellous bone, anisotropy increased what were relatively low levels of interface stress in the isotropic case by three- to four-fold to exceed bond strength levels. Anisotropy has subtle, yet significant effects on interface stresses and peri-implant strains and careful consideration should be given to its use in finite element studies of dental implants.

Mesh optimization: some results in 3D elasticity

Though the mathematical theory of classical linear elasticity is well established, there still lack some ingredients toward the numerical solution of real technological problems. In this paper we address one of these critical ingredients, namely the automatic construction of three-dimensional meshes in arbitrary geometries. Several methods exist for this purpose, but further improvements are still required to achieve the needed robustness and generality. We present and discuss the idea of mesh optimization, namely the manipulation of the mesh geometry and topology so as to maximize some suitable quality measure. The effects of mesh optimization in the finite element solution of a linear thermoelastic problem are evaluated. Finally, we report on a recent method that couples mesh optimization with a posteriori error estimation ideas, so that mesh refinement in regions of high stress gradients is achieved through optimization using a suitable space-varying metric. Numerical results for this last techniques are restricted to two dimensions, as a 3D implementation is under way.

Defects in optical fibres in regions of high stress gradients

Germanosilicate optical fibres produced by the modified chemical vapour deposition process are characterised by point defects which disrupt the tetrahedral network structure. It is shown that the GeE' defect profiles in germanosilicate preforms and fibres, as measured by cathodoluminescence, do not follow the Ge composition profile, but are most intense in regions of high stress gradients, at the core-cladding interface and the Ge depletion region. The results suggest that the GeE' centres arise from Si–Ge bond rupture during the draw of the fibre to reduce the thermoelastic stress.

Numerical integration of differential viscoelastic models

Various numerical techniques are compared in the integration of the upper-convected Maxwell constitutive model on the basis of given kinematics in the planar stick-slip problem. The techniques include three different finite element methods (Galerkin, streamline-upwind, and streamline-upwind Petrov-Galerkin), and a streamline integration scheme. The results illustrate the failure of Galerkin's method in flows possessing steep solution gradients or singularities. The two upwinding techniques are shown to be superior to Galerkin's method but they remain inaccurate near singularities and in flow regions where the solution gradients are transverse to the streamlines. The streamline integration scheme, which in essence is a method of characteristics applied to the purely hyperbolic constitutive model, leads to stable and accurate stress predictions even close to singularities. In view of these results, we have developed a Picard iterative method based on streamline integration to produce solutions to the full set of governing equations for an Oldroyd-B fluid. Results for the stick-slip flow problem could only be obtained for modestly low values of the Weissenberg number with a rather coarse discretization of the flow domain. The reason for the poor convergence properties of the iterative scheme is the large sensitivity of the computed extra-stress to minute changes in kinematics in flow regions of high stress gradients. Our stress integrator based on streamline integration increases the (iterative) convergence difficulties since it captures those stress gradients with great accuracy. The successful use of streamline integration in viscoelastic calculations requires further work towards decoupled iterative schemes capable of handling large stress sensitivity.

Micro- and macromechanical stress and failure analyses of laminated composites

The micro- and macromechannical responses of laminated composites in regions of high stress gradients are examined within the framework of linear plane elasticity. The micromechanical model is based on a system of alternating layers of heterogeneous reinforcement and matrix, whereas the macromechanical counterpart is characterized by the effective homogeneous, orthotropic properties of the constituents. The Fourier transform and the stiffness matrix formulation are employed. As a numerical illustration, a semi-infinite medium made of aluminum and boron layers subjected to a concentrated load is considered. The micro- and macromechanical stress fields as well as the corresponding failure stresses are presented to measure the degree of correspondence between the two models.

Adaptive space-time elements in the dynamic elastic-viscoplastic problem

An adaptive technique for the solution of the dynamic elastic-viscoplastic problem has been developed. The mesh modification is performed by the use of the space-time element method according to error estimation. The number of joints is preserved and the mesh is refined in regions of high stress gradients. This enables the size of the problem to be reduced and increases the speed of computations. The incremental procedure in the case of a small time step allows the nonlinear path iteration to be associated with the time marching scheme. The remesh and remap problems related to stresses are described. Numerical examples of a plane strain rolling contact problem and collision of the plane strain object prove the efficiency of the approach.

Stability analysis of soil–steel structures

A finite element analysis to predict the instability of soil–steel structures is presented. For the steel segment, beam–column elements that accommodate geometric nonlinearity as well as plastic hinge formation are used. Constant and linear strain triangular and quadrilateral elements simulate the soil media in conjunction with spring-type interface elements. A hyperbolic stress–strain relationship models the soil remote from the conduit; an elastoplastic soil model is chosen for regions of high stress gradients above and around the conduit. The formulation is capable of following the initiation and propagation of failure in the soil and its effect on the conduit stability. Analytical failure loads are compared with experimental results and those predicted by the Ontario Highway Bridge Design Code (OHBDC) and the American Association of State Highway and Transportation Officials (AASHTO) specifications.

Direct dynamic analysis of shells of revolution using high-precision finite elements

For the transient dynamic analysis of structural systems, the direct numerical integration of the equations of motion may be regarded as an alternative to the mode superposition method for linear problems and a necessity for nonlinear problems. When compared to a modal superposition solution, the direct integration approach is attractive in that the eigenvalue problem is avoided. Depending on the amount of information required from the dynamic analysis, e.g. frequencies, frequencies and mode shapes, and/or a complete time history, a direct integration scheme may prove to be more efficient than a modal superposition solution for some linear problems as well. The purpose of this study is to develop and demonstrate a direct integration algorithm which is compatible with an existing high-precision rotational shell finite element. Excellent comparative efficiency for static problems was achieved with this element by the incorporation of the exact geometry, the utilization of high-order interpolation polynomials and, yet, the retention of only a minimum number of nodal variables in the global formulation. Likewise, accurate and efficient results for the free vibration analysis of rotational shells were facilitated by the inclusion of a consistent mass matrix and the utilization of a rationally justified kinematic condensation procedure. The approach to the direct integration stage is strongly tempered by the established characteristics of this element which enable a given shell to be modeled accurately in the spatial domain with a comparatively coarse discretization. The equations of motion for a shell of revolution under conservative loading are derived from Hamilton's variational principle and specialized for the discretization of a rotational shell into curved shell elements. Degrees of freedom in excess of those required to establish minimum (C°) continuity at the nodal circles are eliminated through kinematic condensation. Some guidance as to the proper order of the polynominal approximations for a dynamic analysis is provided by earlier free vibration studies. Whereas the condensation is exact for static problems, it is only approximate for dynamic response and it was found that the accuracy of the eigenvalues obtained for the reduced problem decreases with increasing order of the condensed functions. This tendency is counted by the desirability of using sufficiently high-order interpolations so as to permit accurate stress computations, both at the nodal circles and between nodes since a coarse discretization is necessary to realize maximum efficiency. It was found that cubic polynomials were generally satisfactory from both standpoints, except in localized regions of high stress gradients where quintic polynomials were employed. The finite element discretizations for the direct integration studies were selected on this basis. For the high-precision finite element at hand, the efficiencies achieved in the space domain are demonstrated by the ability to achieve precise solutions with relatively coarse discretization patterns. The resulting comparatively large elements are not subject to accurate representation by diagonal mass matrices so that an implicit, consistent mass approach is followed. Efficiency in the time domain as well rests on the successful modeling of rotational shells subject to dynamic loading using coarse discretitations in space and large increments in time. Computational efficiency and accuracy are demonstrated for various problems documented in the literature, including a shallow spherical cap subject to a step pulse and a hyperboloidal shell under a simulated dynamic wind pressure.

Influence of transverse shear on the small displacement theory of circular plates.

The six governing, coupled, linear partial-differential equations of plates can be derived using a method suggested by J. N. Goodier. These equations, which are only slightly different from those derived by E. Reissner using the calculus of variations, are solved for a wide class of problems. Any loading that satisfies the Dirichlet conditions of Fourier analysis and virtually any boundary conditions may be handled. Most problems that can be solved using classical theory are also solvable by the methods presented with only a slightly greater amount of effort. The solution obtained for the Reissner-Goodier theory is comparable in method to the solution of the biharmonic equation in polar coordinates of classical plate theory given by A. Clebsch in his Theorie der Elasticitat fester Korper, 1862, Leipzig. Two examples are considered in detail. Both solutions are obtained by specialization of the more general solution with the first example solved in closed form. Numerical results are displayed in a series of nondimensiona l curves. These curves show that the effects of transverse shear are most significant on the plate boundaries and in regions of high stress gradients.