Showing papers on "von Mises yield criterion published in 1998"

Adaptive topology optimization of elastoplastic structures

Abstract: Material topology optimization is applied to determine the basic layout of a structure. The nonlinear structural response, e.g. buckling or plasticity, must be considered in order to generate a reliable design by structural optimization. In the present paper adaptive material topology optimization is extended to elastoplasticity. The objective of the design problem is to maximize the structural ductility which is defined by the integral of the strain energy over a given range of a prescribed displacement. The mass in the design space is prescribed. The design variables are the densities of the finite elements. The optimization problem is solved by a gradient based OC algorithm. An elastoplastic von Mises material with linear, isotropic work-hardening/softening for small strains is used. A geometrically adaptive optimization procedure is applied in order to avoid artificial stress singularities and to increase the numerical efficiency of the optimization process. The geometric parametrization of the design model is adapted during the optimization process. Elastoplastic structural analysis is outlined. An efficient algorithm is introduced to determine the gradient of the ductility with respect to the densities of the finite elements. The overall optimization procedure is presented and verified with design problems for plane stress conditions.

The influence of rounded edges on indentation by a flat punch

Abstract: The contact problem and stress state for indentation by a flat punch with rounded edges is studied. For the contact problem itself analytical solutions are obtained for both surface pressure and interior stress fields. Cases of normal indentation and frictional contact, the latter in both sliding or partial slip conditions, are all treated. The transition from the Hertzian configuration to the contact between a nominally flat pad and contacting flat surface is discussed, and it is found that the strength of the contact decays surprisingly slowly. Regarding the von Mises yield parameter, there is a range of configurations for which the strength is actually higher than the Hertzian one, and the strength decays only when the corner radii are very small. The present solution is therefore a realistic alternative to the classical rigid-flat punch idealization, and has particular application to fretting fatigue tests.

Computation of collapse states with von Mises type yield condition

Abstract: A new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested. The problem is solved with the exact convex yield condition and the general case of unbounded yield set, corresponding to unrestricted hydrostatic pressure, is treated. The solution method simultaneously approximates the collapse fields for stresses and flow. The approach consists of two separate steps: first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form; then this problem is solved by a suitable optimization method. This way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program. The efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model: approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node. In two space dimensions this may be overkill, but it shows that we are able to solve problems in three space dimensions.

A review of the biaxial strength of fibre-reinforced plastics

Abstract: Several strength criteria for laminae and laminates are presented and compared numerically. It is concluded that the von Mises hypothesis is not suitable for composites, instead strength criteria should be derived from Mohr's hypothesis. In industry mostly laminates are used. It would be desirable if the strength properties could be determined for any arbitrary laminate from those of the laminae included. Since this is spoiled by interaction between the layers, some of these interaction effects are described. In order to become established, a strength criterion has to be verified experimentally. Thus, different techniques for biaxial testing with their characteristic problems are shown.

Boundary element analysis of two-dimensional elastoplastic contact problems

Abstract: A general boundary element formulation for contact problems, capable of dealing with local elastoplastic effects and friction, is presented. Both conforming and non-conforming problems may be analysed. The contact problem is solved by means of a direct constraint technique, in which compatibility and equilibrium conditions are directly enforced in the general system of equations. The contact areas are modelled with linear interpolation functions, and quadratic interpolation functions are used everywhere else. Elastoplasticity is solved by a BEM initial strain approach The Von Mises yield criterion with its associated flow rule is adopted. Both perfectly plastic and work hardening materials are studied in the proposed formulation. An incremental loading technique is proposed, which allows accurate development of the loading history of the problem. The non-linear nature of these problems demands the use of an iterative procedure, to determine the correct frictional conditions at every node of the contact area and the value of the plastic strains at selected points where local yielding may have occurred. Several numerical examples are presented to demonstrate the efficiency of the proposed formulation.

Estimating the probability distribution of von Mises stress for structures undergoing random excitation. Part 1: Derivation

Abstract: The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. For deterministic loads, both static and dynamic, the calculation of von Mises stress is straightforward, as is the resulting calculation of reliability. For loads modeled as random processes, the task is different; the response to such loads is itself a random process and its properties must be determined in terms of those of both the loads and the system. This has been done in the past by Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the problem. Here, the authors present a method that provides analytic expressions for the probability distributions of von Mises stress which can be evaluated efficiently and with good precision numerically. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution.

Method of identifying critical elements in fatigue analysis with von mises stress bounding and filtering modal displacement history using dynamic windowing

Abstract: A method of dynamic durability analysis and fatigue area identification using modal techniques for a structure includes the steps of simulating a finite element model of the structure to determine modal stresses and modal displacements for an element of the structure and performing a modal transient analysis using the modal displacements. The method also includes the steps of determining a stress bound for the element from the modal stresses and modal transient analysis, determining if a stress bound for the element is greater than a predetermined value and identifying the element as a critical element if the stress bound for the element is greater than the predetermined value. The method further includes the steps of determining a stress time history for the critical element and using the stress time history to perform a fatigue analysis to identify an area of fatigue within the structure.

An efficient method for calculating RMS von Mises stress in a random vibration environment

Abstract: An efficient method is presented for calculation of RMS von Mises stresses from stress component transfer functions and the Fourier representation of random input forces. An efficient implementation of the method calculates the RMS stresses directly from the linear stress and displacement modes. The key relation presented is one suggested in past literature, but does not appear to have been previously exploited in this manner.

Deformation and fracture of metal matrix particulate composites under combined loadings

Abstract: Flow and fracture behaviour of 17% and 25% SiC particulate reinforced 2124 aluminium is examined from combining torsion with either tension or compression. Incremental loadings were applied along both radial and stepped paths. The results of all tests show that the yield locus for the material obeys a von Mises description. The observed flow behaviour is compared with that predicted from the Prandtl-Reuss incremental plasticity theory. Regions of elasticity are apparent for both paths. Flow beyond the yield point under each path revealed a limited amount of parabolic hardening consistent with the normality rule. Pure torsion, tension and compression tests were also conducted to establish the yield and hardening behaviour for the mmc in its low and higher strain ranges. Void damage renders these materials brittle under all loadings except compression. This points to a more appropriate flow theory modified with a suitable damage parameter sensitive to the sense of the applied stress.

Modified Fracture Mechanics Approach in Structural Analysis of Solid-Rocket Motors

Abstract: A deŽ ciency in current failure initiation criteria used in the structural design and service-life prediction of solid-rocket motors, where the critical failure mode is structural failure, is the uncertainties associated with the criteria used in predicting crack initiation and propagation. Also, the constitutive models that describe the propellants’ nonlinear behavior require an extensive experimental testing program to characterize the softening functions. A modiŽ ed fracture mechanics method that accounts for bulk inelastic behavior in the calculation of a critical strain energy release rate and a relatively simple method for nonlinear viscoelastic analysis, where a three-dimensional interpolation scheme is used to solve the Prony series equations that represent Young’s and shear relaxation moduli as functions of time, temperature, and strain level, have been developed and implemented into a Ž nite element code. Predictions for a thermal shock loading on an end-burning research and development motor were made using the fracture mechanics and nonlinear viscoelastic analysis capabilities developed in this study. Reasonable agreement between the measured stresses from instrumented rocket motors and the predicted von Mises stresses was obtained. The regions of high propensity for crack propagation corresponded to the critical regions of maximum tensile principal stress in the motor.

Finite element solutions comparing the normal contact of an elastic—plastic layered medium under loading by (a) a rigid and (b) a deformable indenter

Abstract: The main purpose of this paper is to assess the influence of a deformable indenter by comparing the finite element results for a deformable indenter with those of a rigid indenter. Elastic-plastic solutions for the case of a stiff hard layer rigidly bonded to a softer substrate are given and the effect of the indenters (i.e. rigid; deformable, E = 600 GPa; deformable, E = 1000 GPa) on the contact pressures and stresses and strains are critically examined. The results showed that, when the indenter is assumed to be rigid, the contact pressures in the elastic regime are higher than those given by the deformable indenters. However, as deformation proceeds and plasticity becomes dominant, the differences between the three sets of results reduce. The rigid indenter results were also shown to give the lowest peak radial tensile stress which is responsible for cracking of the film normal to the surface. Finally, comparison of the von Mises stress contours revealed that varying the indenter properties affects the point at which yielding commences. Results showed that the rigid indenter caused the coating and substrate to yield prematurely, i.e. at a lower load than the deformable indenters.

Brine transport in porous media : on the use of Von Mises and similarity transformations

Abstract: In this paper we use a Von Mises transformation to study brine transport in porous media. The model involves mass balance equations for fluid and salt, Darcy's law and an equation of state, relating the salt mass fraction to the fluid density. Application of the Von Mises transformation recasts the model equations into a single nonlinear diffusion equation. A further reduction is possible if the problem admits similarity. This yields a formulation in terms of a boundary value problem for an ordinary differential equation which can be treated by semi‐analytical means. Three specific similarity problems are considered in detail: (i) one‐dimensional, stable displacement of fresh water and brine in a porous column, (ii) flow of fresh water along the surface of a salt rock, (iii) mixing of parallel layers of brine and fresh water.

Structural strength analysis of the bogie frame in Taipei rapid transit systems

Abstract: The importance of bogie fatigue in railway rolling stock has been recognized as a contributing factor in structural failure. A bogie frame designed for Taipei rapid transit systems is analysed in order to confirm the technical strength requirements for static and dynamic loadings. A numerical finite element analysis is utilized in view of the complex geometry, and detailed plots are also presented in this report to give a complete understanding of the behaviour of the bogie frame. The von Mises stresses are adopted as equivalent stresses in the static strength calculation while the principal stresses are adopted in fatigue strength evaluation. Material yield stress and modified Goodman diagrams showing the permissible stress ranges are used as failure criteria respectively for static and dynamic loadings. It is demonstrated that the static strength and fatigue strength of the bogie frame satisfy the strength requirements specified by Taipei rapid transit systems.

The effect of stress triaxiality on the local cleavage fracture stress in a granular bainitic weld metal

Abstract: The local cleavage fracture stress σF measured at the cleavage initiation sites of a granular bainitic weld metal is only an apparent fracture parameter dependent on stress triaxialities at the local sites in the propagation controlled cleavage regime. This dependence can be explained by the stress triaxiality modified Smith equation in which the intrinsic cleavage fracture stress σF0 is introduced, considered to be an invariant characterizing a material's fracture property. In the nucleation controlled cleavage regime σF is temperature dependent and coincident with the local yield stresses defined by Von Mises criterion at the local sites. It is suggested that the modified Smith model would provide a unified physical basis for the intrinsic correlation among various macroscopic fracture properties as well as their temperature transition behaviors from the temperature dependence of material's yield strength.

Self‐designing structures: a practical approach

Abstract: Demonstrates the simple but effective application of a standard finite element program (PAFEC), and the associated geometric modelling code (PIGS), to the improvement of the design of an engineering component. The technique adopted involves augmenting material around zones of high stress and removing material in zones of low stress. This evolutionary procedure is related to the behaviour of bones in animals. The essentially two‐step procedure involves; finite element analysis of the preliminary component design using PAFEC; and, definition of a new geometry using PIGS, with selected stress contours giving an indication of the new shape. The technique, which proceeds iteratively, was first tested successfully on some classical academic optimisation problems. Its subsequent application to the industrial problem of a twin chamber pressurised extruded aluminium section, the primary component of an air drying system, resulted in material savings of up to 50 per cent and an associated drop in the maximum von Mises stress of 45 per cent. While this method does not determine the optimal structural form, it does generate substantial improvements in terms of material usage and reduced maximum stresses. It has the advantage that it can be used by any competent engineer with a working knowledge of the strength of materials, finite elements and structural form.

Similarity solutions for granular flows in hoppers

Abstract: Similarity solutions for the steady state equations governing flow of granular materials under gravity in a conical or wedge-shaped hopper are constructed. Such solutions can be considered for various plasticity models. Results obtained under the classical Mohr-Coulomb yield condition are com- pared with those obtained when a von Mises yield condition is imposed. A thorough stability study in the case of Mohr-Coulomb materials, for which several simplications take place, is proposed.

Statistics of the von Mises stress response for structures subjected to random excitations

Abstract: Finite element-based random vibration analysis is increasingly used in computer aided engineering software for computing statistics (e.g., root-mean-square value) of structural responses such as displacements, stresses and strains. However, these statistics can often be computed only for Cartesian responses. For the design of metal structures, a failure criterion based on an equivalent stress response, commonly known as the von Mises stress, is more appropriate and often used. This paper presents an approach for computing the statistics of the von Mises stress response for structures subjected to random excitations. Random vibration analysis is first performed to compute covariance matrices of Cartesian stress responses. Monte Carlo simulation is then used to perform scatter and failure analyses using the von Mises stress response.

On plastic buckling of cylindrical shells struck axially with a mass

Abstract: Buckling of elastic-plastic cylindrical shells axially struck with a mass is discussed. The effect of stress wave fronts travelling along the shell is taken into account. This allows us to cast some more light on the mechanism of progressive buckling. Only axisymmetric buckling modes are considered. The analysis is based on the Kirchhoff-Love hypotheses. As a constitutive law, the rate independent elasto-plastic relations with linear strain hardening and von Mises yield condition are adopted. A method for calculating bifurcation times and buckling modes is presented. Numerical examples are given.